Cubit Adaptive Meshing Algorithm Library
Energy Science and Technology Software Center (ESTSC)
2004-09-01
CAMAL (Cubit adaptive meshing algorithm library) is a software component library for mesh generation. CAMAL 2.0 includes components for triangle, quad and tetrahedral meshing. A simple Application Programmers Interface (API) takes a discrete boundary definition and CAMAL computes a quality interior unstructured grid. The triangle and quad algorithms may also import a geometric definition of a surface on which to define the grid. CAMALs triangle meshing uses a 3D space advancing front method, the quadmore » meshing algorithm is based upon Sandias patented paving algorithm and the tetrahedral meshing algorithm employs the GHS3D-Tetmesh component developed by INRIA, France.« less
Fully implicit adaptive mesh refinement MHD algorithm
NASA Astrophysics Data System (ADS)
Philip, Bobby
2005-10-01
In the macroscopic simulation of plasmas, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former results in stiffness due to the presence of very fast waves. The latter requires one to resolve the localized features that the system develops. Traditional approaches based on explicit time integration techniques and fixed meshes are not suitable for this challenge, as such approaches prevent the modeler from using realistic plasma parameters to keep the computation feasible. We propose here a novel approach, based on implicit methods and structured adaptive mesh refinement (SAMR). Our emphasis is on both accuracy and scalability with the number of degrees of freedom. To our knowledge, a scalable, fully implicit AMR algorithm has not been accomplished before for MHD. As a proof-of-principle, we focus on the reduced resistive MHD model as a basic MHD model paradigm, which is truly multiscale. The approach taken here is to adapt mature physics-based technologyootnotetextL. Chac'on et al., J. Comput. Phys. 178 (1), 15- 36 (2002) to AMR grids, and employ AMR-aware multilevel techniques (such as fast adaptive composite --FAC-- algorithms) for scalability. We will demonstrate that the concept is indeed feasible, featuring optimal scalability under grid refinement. Results of fully-implicit, dynamically-adaptive AMR simulations will be presented on a variety of problems.
A parallel adaptive mesh refinement algorithm
NASA Technical Reports Server (NTRS)
Quirk, James J.; Hanebutte, Ulf R.
1993-01-01
Over recent years, Adaptive Mesh Refinement (AMR) algorithms which dynamically match the local resolution of the computational grid to the numerical solution being sought have emerged as powerful tools for solving problems that contain disparate length and time scales. In particular, several workers have demonstrated the effectiveness of employing an adaptive, block-structured hierarchical grid system for simulations of complex shock wave phenomena. Unfortunately, from the parallel algorithm developer's viewpoint, this class of scheme is quite involved; these schemes cannot be distilled down to a small kernel upon which various parallelizing strategies may be tested. However, because of their block-structured nature such schemes are inherently parallel, so all is not lost. In this paper we describe the method by which Quirk's AMR algorithm has been parallelized. This method is built upon just a few simple message passing routines and so it may be implemented across a broad class of MIMD machines. Moreover, the method of parallelization is such that the original serial code is left virtually intact, and so we are left with just a single product to support. The importance of this fact should not be underestimated given the size and complexity of the original algorithm.
Adaptive mesh and algorithm refinement using direct simulation Monte Carlo
Garcia, A.L.; Bell, J.B.; Crutchfield, W.Y.; Alder, B.J.
1999-09-01
Adaptive mesh and algorithm refinement (AMAR) embeds a particle method within a continuum method at the finest level of an adaptive mesh refinement (AMR) hierarchy. The coupling between the particle region and the overlaying continuum grid is algorithmically equivalent to that between the fine and coarse levels of AMR. Direct simulation Monte Carlo (DSMC) is used as the particle algorithm embedded within a Godunov-type compressible Navier-Stokes solver. Several examples are presented and compared with purely continuum calculations.
Adaptive-mesh algorithms for computational fluid dynamics
NASA Technical Reports Server (NTRS)
Powell, Kenneth G.; Roe, Philip L.; Quirk, James
1993-01-01
The basic goal of adaptive-mesh algorithms is to distribute computational resources wisely by increasing the resolution of 'important' regions of the flow and decreasing the resolution of regions that are less important. While this goal is one that is worthwhile, implementing schemes that have this degree of sophistication remains more of an art than a science. In this paper, the basic pieces of adaptive-mesh algorithms are described and some of the possible ways to implement them are discussed and compared. These basic pieces are the data structure to be used, the generation of an initial mesh, the criterion to be used to adapt the mesh to the solution, and the flow-solver algorithm on the resulting mesh. Each of these is discussed, with particular emphasis on methods suitable for the computation of compressible flows.
Fully implicit adaptive mesh refinement algorithm for reduced MHD
NASA Astrophysics Data System (ADS)
Philip, Bobby; Pernice, Michael; Chacon, Luis
2006-10-01
In the macroscopic simulation of plasmas, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. Traditional approaches based on explicit time integration techniques and fixed meshes are not suitable for this challenge, as such approaches prevent the modeler from using realistic plasma parameters to keep the computation feasible. We propose here a novel approach, based on implicit methods and structured adaptive mesh refinement (SAMR). Our emphasis is on both accuracy and scalability with the number of degrees of freedom. As a proof-of-principle, we focus on the reduced resistive MHD model as a basic MHD model paradigm, which is truly multiscale. The approach taken here is to adapt mature physics-based technology to AMR grids, and employ AMR-aware multilevel techniques (such as fast adaptive composite grid --FAC-- algorithms) for scalability. We demonstrate that the concept is indeed feasible, featuring near-optimal scalability under grid refinement. Results of fully-implicit, dynamically-adaptive AMR simulations in challenging dissipation regimes will be presented on a variety of problems that benefit from this capability, including tearing modes, the island coalescence instability, and the tilt mode instability. L. Chac'on et al., J. Comput. Phys. 178 (1), 15- 36 (2002) B. Philip, M. Pernice, and L. Chac'on, Lecture Notes in Computational Science and Engineering, accepted (2006)
A structured multi-block solution-adaptive mesh algorithm with mesh quality assessment
NASA Technical Reports Server (NTRS)
Ingram, Clint L.; Laflin, Kelly R.; Mcrae, D. Scott
1995-01-01
The dynamic solution adaptive grid algorithm, DSAGA3D, is extended to automatically adapt 2-D structured multi-block grids, including adaption of the block boundaries. The extension is general, requiring only input data concerning block structure, connectivity, and boundary conditions. Imbedded grid singular points are permitted, but must be prevented from moving in space. Solutions for workshop cases 1 and 2 are obtained on multi-block grids and illustrate both increased resolution of and alignment with the solution. A mesh quality assessment criteria is proposed to determine how well a given mesh resolves and aligns with the solution obtained upon it. The criteria is used to evaluate the grid quality for solutions of workshop case 6 obtained on both static and dynamically adapted grids. The results indicate that this criteria shows promise as a means of evaluating resolution.
An adaptive mesh refinement algorithm for the discrete ordinates method
Jessee, J.P.; Fiveland, W.A.; Howell, L.H.; Colella, P.; Pember, R.B.
1996-03-01
The discrete ordinates form of the radiative transport equation (RTE) is spatially discretized and solved using an adaptive mesh refinement (AMR) algorithm. This technique permits the local grid refinement to minimize spatial discretization error of the RTE. An error estimator is applied to define regions for local grid refinement; overlapping refined grids are recursively placed in these regions; and the RTE is then solved over the entire domain. The procedure continues until the spatial discretization error has been reduced to a sufficient level. The following aspects of the algorithm are discussed: error estimation, grid generation, communication between refined levels, and solution sequencing. This initial formulation employs the step scheme, and is valid for absorbing and isotopically scattering media in two-dimensional enclosures. The utility of the algorithm is tested by comparing the convergence characteristics and accuracy to those of the standard single-grid algorithm for several benchmark cases. The AMR algorithm provides a reduction in memory requirements and maintains the convergence characteristics of the standard single-grid algorithm; however, the cases illustrate that efficiency gains of the AMR algorithm will not be fully realized until three-dimensional geometries are considered.
Lober, R.R.; Tautges, T.J.; Vaughan, C.T.
1997-03-01
Paving is an automated mesh generation algorithm which produces all-quadrilateral elements. It can additionally generate these elements in varying sizes such that the resulting mesh adapts to a function distribution, such as an error function. While powerful, conventional paving is a very serial algorithm in its operation. Parallel paving is the extension of serial paving into parallel environments to perform the same meshing functions as conventional paving only on distributed, discretized models. This extension allows large, adaptive, parallel finite element simulations to take advantage of paving`s meshing capabilities for h-remap remeshing. A significantly modified version of the CUBIT mesh generation code has been developed to host the parallel paving algorithm and demonstrate its capabilities on both two dimensional and three dimensional surface geometries and compare the resulting parallel produced meshes to conventionally paved meshes for mesh quality and algorithm performance. Sandia`s {open_quotes}tiling{close_quotes} dynamic load balancing code has also been extended to work with the paving algorithm to retain parallel efficiency as subdomains undergo iterative mesh refinement.
The parallelization of an advancing-front, all-quadrilateral meshing algorithm for adaptive analysis
Lober, R.R.; Tautges, T.J.; Cairncross, R.A.
1995-11-01
The ability to perform effective adaptive analysis has become a critical issue in the area of physical simulation. Of the multiple technologies required to realize a parallel adaptive analysis capability, automatic mesh generation is an enabling technology, filling a critical need in the appropriate discretization of a problem domain. The paving algorithm`s unique ability to generate a function-following quadrilateral grid is a substantial advantage in Sandia`s pursuit of a modified h-method adaptive capability. This characteristic combined with a strong transitioning ability allow the paving algorithm to place elements where an error function indicates more mesh resolution is needed. Although the original paving algorithm is highly serial, a two stage approach has been designed to parallelize the algorithm but also retain the nice qualities of the serial algorithm. The authors approach also allows the subdomain decomposition used by the meshing code to be shared with the finite element physics code, eliminating the need for data transfer across the processors between the analysis and remeshing steps. In addition, the meshed subdomains are adjusted with a dynamic load balancer to improve the original decomposition and maintain load efficiency each time the mesh has been regenerated. This initial parallel implementation assumes an approach of restarting the physics problem from time zero at each interaction, with a refined mesh adapting to the previous iterations objective function. The remeshing tools are being developed to enable real time remeshing and geometry regeneration. Progress on the redesign of the paving algorithm for parallel operation is discussed including extensions allowing adaptive control and geometry regeneration.
Unstructured mesh generation and adaptivity
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.
1995-01-01
An overview of current unstructured mesh generation and adaptivity techniques is given. Basic building blocks taken from the field of computational geometry are first described. Various practical mesh generation techniques based on these algorithms are then constructed and illustrated with examples. Issues of adaptive meshing and stretched mesh generation for anisotropic problems are treated in subsequent sections. The presentation is organized in an education manner, for readers familiar with computational fluid dynamics, wishing to learn more about current unstructured mesh techniques.
The design of a parallel adaptive paving all-quadrilateral meshing algorithm
Tautges, T.J.; Lober, R.R.; Vaughan, C.
1995-08-01
Adaptive finite element analysis demands a great deal of computational resources, and as such is most appropriately solved in a massively parallel computer environment. This analysis will require other parallel algorithms before it can fully utilize MP computers, one of which is parallel adaptive meshing. A version of the paving algorithm is being designed which operates in parallel but which also retains the robustness and other desirable features present in the serial algorithm. Adaptive paving in a production mode is demonstrated using a Babuska-Rheinboldt error estimator on a classic linearly elastic plate problem. The design of the parallel paving algorithm is described, and is based on the decomposition of a surface into {open_quotes}virtual{close_quotes} surfaces. The topology of the virtual surface boundaries is defined using mesh entities (mesh nodes and edges) so as to allow movement of these boundaries with smoothing and other operations. This arrangement allows the use of the standard paving algorithm on subdomain interiors, after the negotiation of the boundary mesh.
Parallel Implementation and Scaling of an Adaptive Mesh Discrete Ordinates Algorithm for Transport
Howell, L H
2004-11-29
Block-structured adaptive mesh refinement (AMR) uses a mesh structure built up out of locally-uniform rectangular grids. In the BoxLib parallel framework used by the Raptor code, each processor operates on one or more of these grids at each refinement level. The decomposition of the mesh into grids and the distribution of these grids among processors may change every few timesteps as a calculation proceeds. Finer grids use smaller timesteps than coarser grids, requiring additional work to keep the system synchronized and ensure conservation between different refinement levels. In a paper for NECDC 2002 I presented preliminary results on implementation of parallel transport sweeps on the AMR mesh, conjugate gradient acceleration, accuracy of the AMR solution, and scalar speedup of the AMR algorithm compared to a uniform fully-refined mesh. This paper continues with a more in-depth examination of the parallel scaling properties of the scheme, both in single-level and multi-level calculations. Both sweeping and setup costs are considered. The algorithm scales with acceptable performance to several hundred processors. Trends suggest, however, that this is the limit for efficient calculations with traditional transport sweeps, and that modifications to the sweep algorithm will be increasingly needed as job sizes in the thousands of processors become common.
NASA Astrophysics Data System (ADS)
Northrup, Scott A.
A new parallel implicit adaptive mesh refinement (AMR) algorithm is developed for the prediction of unsteady behaviour of laminar flames. The scheme is applied to the solution of the system of partial-differential equations governing time-dependent, two- and three-dimensional, compressible laminar flows for reactive thermally perfect gaseous mixtures. A high-resolution finite-volume spatial discretization procedure is used to solve the conservation form of these equations on body-fitted multi-block hexahedral meshes. A local preconditioning technique is used to remove numerical stiffness and maintain solution accuracy for low-Mach-number, nearly incompressible flows. A flexible block-based octree data structure has been developed and is used to facilitate automatic solution-directed mesh adaptation according to physics-based refinement criteria. The data structure also enables an efficient and scalable parallel implementation via domain decomposition. The parallel implicit formulation makes use of a dual-time-stepping like approach with an implicit second-order backward discretization of the physical time, in which a Jacobian-free inexact Newton method with a preconditioned generalized minimal residual (GMRES) algorithm is used to solve the system of nonlinear algebraic equations arising from the temporal and spatial discretization procedures. An additive Schwarz global preconditioner is used in conjunction with block incomplete LU type local preconditioners for each sub-domain. The Schwarz preconditioning and block-based data structure readily allow efficient and scalable parallel implementations of the implicit AMR approach on distributed-memory multi-processor architectures. The scheme was applied to solutions of steady and unsteady laminar diffusion and premixed methane-air combustion and was found to accurately predict key flame characteristics. For a premixed flame under terrestrial gravity, the scheme accurately predicted the frequency of the natural
Adaptive Skin Meshes Coarsening for Biomolecular Simulation.
Shi, Xinwei; Koehl, Patrice
2011-06-01
In this paper, we present efficient algorithms for generating hierarchical molecular skin meshes with decreasing size and guaranteed quality. Our algorithms generate a sequence of coarse meshes for both the surfaces and the bounded volumes. Each coarser surface mesh is adaptive to the surface curvature and maintains the topology of the skin surface with guaranteed mesh quality. The corresponding tetrahedral mesh is conforming to the interface surface mesh and contains high quality tetrahedral that decompose both the interior of the molecule and the surrounding region (enclosed in a sphere). Our hierarchical tetrahedral meshes have a number of advantages that will facilitate fast and accurate multigrid PDE solvers. Firstly, the quality of both the surface triangulations and tetrahedral meshes is guaranteed. Secondly, the interface in the tetrahedral mesh is an accurate approximation of the molecular boundary. In particular, all the boundary points lie on the skin surface. Thirdly, our meshes are Delaunay meshes. Finally, the meshes are adaptive to the geometry. PMID:21779137
Adaptive Skin Meshes Coarsening for Biomolecular Simulation
Shi, Xinwei; Koehl, Patrice
2011-01-01
In this paper, we present efficient algorithms for generating hierarchical molecular skin meshes with decreasing size and guaranteed quality. Our algorithms generate a sequence of coarse meshes for both the surfaces and the bounded volumes. Each coarser surface mesh is adaptive to the surface curvature and maintains the topology of the skin surface with guaranteed mesh quality. The corresponding tetrahedral mesh is conforming to the interface surface mesh and contains high quality tetrahedral that decompose both the interior of the molecule and the surrounding region (enclosed in a sphere). Our hierarchical tetrahedral meshes have a number of advantages that will facilitate fast and accurate multigrid PDE solvers. Firstly, the quality of both the surface triangulations and tetrahedral meshes is guaranteed. Secondly, the interface in the tetrahedral mesh is an accurate approximation of the molecular boundary. In particular, all the boundary points lie on the skin surface. Thirdly, our meshes are Delaunay meshes. Finally, the meshes are adaptive to the geometry. PMID:21779137
Parallel Adaptive Mesh Refinement
Diachin, L; Hornung, R; Plassmann, P; WIssink, A
2005-03-04
As large-scale, parallel computers have become more widely available and numerical models and algorithms have advanced, the range of physical phenomena that can be simulated has expanded dramatically. Many important science and engineering problems exhibit solutions with localized behavior where highly-detailed salient features or large gradients appear in certain regions which are separated by much larger regions where the solution is smooth. Examples include chemically-reacting flows with radiative heat transfer, high Reynolds number flows interacting with solid objects, and combustion problems where the flame front is essentially a two-dimensional sheet occupying a small part of a three-dimensional domain. Modeling such problems numerically requires approximating the governing partial differential equations on a discrete domain, or grid. Grid spacing is an important factor in determining the accuracy and cost of a computation. A fine grid may be needed to resolve key local features while a much coarser grid may suffice elsewhere. Employing a fine grid everywhere may be inefficient at best and, at worst, may make an adequately resolved simulation impractical. Moreover, the location and resolution of fine grid required for an accurate solution is a dynamic property of a problem's transient features and may not be known a priori. Adaptive mesh refinement (AMR) is a technique that can be used with both structured and unstructured meshes to adjust local grid spacing dynamically to capture solution features with an appropriate degree of resolution. Thus, computational resources can be focused where and when they are needed most to efficiently achieve an accurate solution without incurring the cost of a globally-fine grid. Figure 1.1 shows two example computations using AMR; on the left is a structured mesh calculation of a impulsively-sheared contact surface and on the right is the fuselage and volume discretization of an RAH-66 Comanche helicopter [35]. Note the
Adaptive and Unstructured Mesh Cleaving
Bronson, Jonathan R.; Sastry, Shankar P.; Levine, Joshua A.; Whitaker, Ross T.
2015-01-01
We propose a new strategy for boundary conforming meshing that decouples the problem of building tetrahedra of proper size and shape from the problem of conforming to complex, non-manifold boundaries. This approach is motivated by the observation that while several methods exist for adaptive tetrahedral meshing, they typically have difficulty at geometric boundaries. The proposed strategy avoids this conflict by extracting the boundary conforming constraint into a secondary step. We first build a background mesh having a desired set of tetrahedral properties, and then use a generalized stenciling method to divide, or “cleave”, these elements to get a set of conforming tetrahedra, while limiting the impacts cleaving has on element quality. In developing this new framework, we make several technical contributions including a new method for building graded tetrahedral meshes as well as a generalization of the isosurface stuffing and lattice cleaving algorithms to unstructured background meshes. PMID:26137171
NASA Technical Reports Server (NTRS)
Kleb, William L.; Williams, Marc H.; Batina, John T.
1990-01-01
A temporal adaptive algorithm for the time-integration of the two-dimensional Euler or Navier-Stokes equations is presented. The flow solver involves an upwind flux-split spatial discretization for the convective terms and central differencing for the shear-stress and heat flux terms on an unstructured mesh of triangles. The temporal adaptive algorithm is a time-accurate integration procedure which allows flows with high spatial and temporal gradients to be computed efficiently by advancing each grid cell near its maximum allowable time step. Results indicate that an appreciable computational savings can be achieved for both inviscid and viscous unsteady airfoil problems using unstructured meshes without degrading spatial or temporal accuracy.
TRIM: A finite-volume MHD algorithm for an unstructured adaptive mesh
Schnack, D.D.; Lottati, I.; Mikic, Z.
1995-07-01
The authors describe TRIM, a MHD code which uses finite volume discretization of the MHD equations on an unstructured adaptive grid of triangles in the poloidal plane. They apply it to problems related to modeling tokamak toroidal plasmas. The toroidal direction is treated by a pseudospectral method. Care was taken to center variables appropriately on the mesh and to construct a self adjoint diffusion operator for cell centered variables.
A 3-D adaptive mesh refinement algorithm for multimaterial gas dynamics
Puckett, E.G. ); Saltzman, J.S. )
1991-08-12
Adaptive Mesh Refinement (AMR) in conjunction with high order upwind finite difference methods has been used effectively on a variety of problems. In this paper we discuss an implementation of an AMR finite difference method that solves the equations of gas dynamics with two material species in three dimensions. An equation for the evolution of volume fractions augments the gas dynamics system. The material interface is preserved and tracked from the volume fractions using a piecewise linear reconstruction technique. 14 refs., 4 figs.
Unstructured mesh algorithms for aerodynamic calculations
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.
1992-01-01
The use of unstructured mesh techniques for solving complex aerodynamic flows is discussed. The principle advantages of unstructured mesh strategies, as they relate to complex geometries, adaptive meshing capabilities, and parallel processing are emphasized. The various aspects required for the efficient and accurate solution of aerodynamic flows are addressed. These include mesh generation, mesh adaptivity, solution algorithms, convergence acceleration, and turbulence modeling. Computations of viscous turbulent two-dimensional flows and inviscid three-dimensional flows about complex configurations are demonstrated. Remaining obstacles and directions for future research are also outlined.
Floating shock fitting via Lagrangian adaptive meshes
NASA Technical Reports Server (NTRS)
Vanrosendale, John
1995-01-01
In recent work we have formulated a new approach to compressible flow simulation, combining the advantages of shock-fitting and shock-capturing. Using a cell-centered on Roe scheme discretization on unstructured meshes, we warp the mesh while marching to steady state, so that mesh edges align with shocks and other discontinuities. This new algorithm, the Shock-fitting Lagrangian Adaptive Method (SLAM), is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence.
Auto-adaptive finite element meshes
NASA Technical Reports Server (NTRS)
Richter, Roland; Leyland, Penelope
1995-01-01
Accurate capturing of discontinuities within compressible flow computations is achieved by coupling a suitable solver with an automatic adaptive mesh algorithm for unstructured triangular meshes. The mesh adaptation procedures developed rely on non-hierarchical dynamical local refinement/derefinement techniques, which hence enable structural optimization as well as geometrical optimization. The methods described are applied for a number of the ICASE test cases are particularly interesting for unsteady flow simulations.
Parallel automated adaptive procedures for unstructured meshes
NASA Technical Reports Server (NTRS)
Shephard, M. S.; Flaherty, J. E.; Decougny, H. L.; Ozturan, C.; Bottasso, C. L.; Beall, M. W.
1995-01-01
Consideration is given to the techniques required to support adaptive analysis of automatically generated unstructured meshes on distributed memory MIMD parallel computers. The key areas of new development are focused on the support of effective parallel computations when the structure of the numerical discretization, the mesh, is evolving, and in fact constructed, during the computation. All the procedures presented operate in parallel on already distributed mesh information. Starting from a mesh definition in terms of a topological hierarchy, techniques to support the distribution, redistribution and communication among the mesh entities over the processors is given, and algorithms to dynamically balance processor workload based on the migration of mesh entities are given. A procedure to automatically generate meshes in parallel, starting from CAD geometric models, is given. Parallel procedures to enrich the mesh through local mesh modifications are also given. Finally, the combination of these techniques to produce a parallel automated finite element analysis procedure for rotorcraft aerodynamics calculations is discussed and demonstrated.
NASA Astrophysics Data System (ADS)
Zheng, H. W.; Shu, C.; Chew, Y. T.
2008-07-01
In this paper, an object-oriented and quadrilateral-mesh based solution adaptive algorithm for the simulation of compressible multi-fluid flows is presented. The HLLC scheme (Harten, Lax and van Leer approximate Riemann solver with the Contact wave restored) is extended to adaptively solve the compressible multi-fluid flows under complex geometry on unstructured mesh. It is also extended to the second-order of accuracy by using MUSCL extrapolation. The node, edge and cell are arranged in such an object-oriented manner that each of them inherits from a basic object. A home-made double link list is designed to manage these objects so that the inserting of new objects and removing of the existing objects (nodes, edges and cells) are independent of the number of objects and only of the complexity of O( 1). In addition, the cells with different levels are further stored in different lists. This avoids the recursive calculation of solution of mother (non-leaf) cells. Thus, high efficiency is obtained due to these features. Besides, as compared to other cell-edge adaptive methods, the separation of nodes would reduce the memory requirement of redundant nodes, especially in the cases where the level number is large or the space dimension is three. Five two-dimensional examples are used to examine its performance. These examples include vortex evolution problem, interface only problem under structured mesh and unstructured mesh, bubble explosion under the water, bubble-shock interaction, and shock-interface interaction inside the cylindrical vessel. Numerical results indicate that there is no oscillation of pressure and velocity across the interface and it is feasible to apply it to solve compressible multi-fluid flows with large density ratio (1000) and strong shock wave (the pressure ratio is 10,000) interaction with the interface.
A parallel second-order adaptive mesh algorithm for incompressible flow in porous media.
Pau, George S H; Almgren, Ann S; Bell, John B; Lijewski, Michael J
2009-11-28
In this paper, we present a second-order accurate adaptive algorithm for solving multi-phase, incompressible flow in porous media. We assume a multi-phase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting, the total velocity, defined to be the sum of the phase velocities, is divergence free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single-grid algorithm is described briefly, but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behaviour of the method. PMID:19840985
A Parallel Second-Order Adaptive Mesh Algorithm for Incompressible Flow in Porous Media
Pau, George Shu Heng; Almgren, Ann S.; Bell, John B.; Lijewski, Michael J.
2008-04-01
In this paper we present a second-order accurate adaptive algorithm for solving multiphase, incompressible flows in porous media. We assume a multiphase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting the total velocity, defined to be the sum of the phase velocities, is divergence-free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids areadvanced multiple steps to reach the same time as the coarse grids and the data atdifferent levels are then synchronized. The single grid algorithm is described briefly,but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behavior of the method.
Cunningham, Andrew J.; Frank, Adam; Varniere, Peggy; Mitran, Sorin; Jones, Thomas W.
2009-06-15
A description is given of the algorithms implemented in the AstroBEAR adaptive mesh-refinement code for ideal magnetohydrodynamics. The code provides several high-resolution shock-capturing schemes which are constructed to maintain conserved quantities of the flow in a finite-volume sense. Divergence-free magnetic field topologies are maintained to machine precision by collating the components of the magnetic field on a cell-interface staggered grid and utilizing the constrained transport approach for integrating the induction equations. The maintenance of magnetic field topologies on adaptive grids is achieved using prolongation and restriction operators which preserve the divergence and curl of the magnetic field across collocated grids of different resolutions. The robustness and correctness of the code is demonstrated by comparing the numerical solution of various tests with analytical solutions or previously published numerical solutions obtained by other codes.
Adaptive triangular mesh generation
NASA Technical Reports Server (NTRS)
Erlebacher, G.; Eiseman, P. R.
1984-01-01
A general adaptive grid algorithm is developed on triangular grids. The adaptivity is provided by a combination of node addition, dynamic node connectivity and a simple node movement strategy. While the local restructuring process and the node addition mechanism take place in the physical plane, the nodes are displaced on a monitor surface, constructed from the salient features of the physical problem. An approximation to mean curvature detects changes in the direction of the monitor surface, and provides the pulling force on the nodes. Solutions to the axisymmetric Grad-Shafranov equation demonstrate the capturing, by triangles, of the plasma-vacuum interface in a free-boundary equilibrium configuration.
An efficient parallel algorithm for mesh smoothing
Freitag, L.; Plassmann, P.; Jones, M.
1995-12-31
Automatic mesh generation and adaptive refinement methods have proven to be very successful tools for the efficient solution of complex finite element applications. A problem with these methods is that they can produce poorly shaped elements; such elements are undesirable because they introduce numerical difficulties in the solution process. However, the shape of the elements can be improved through the determination of new geometric locations for mesh vertices by using a mesh smoothing algorithm. In this paper the authors present a new parallel algorithm for mesh smoothing that has a fast parallel runtime both in theory and in practice. The authors present an efficient implementation of the algorithm that uses non-smooth optimization techniques to find the new location of each vertex. Finally, they present experimental results obtained on the IBM SP system demonstrating the efficiency of this approach.
Hybrid Surface Mesh Adaptation for Climate Modeling
Khamayseh, Ahmed K; de Almeida, Valmor F; Hansen, Glen
2008-01-01
Solution-driven mesh adaptation is becoming quite popular for spatial error control in the numerical simulation of complex computational physics applications, such as climate modeling. Typically, spatial adaptation is achieved by element subdivision (h adaptation) with a primary goal of resolving the local length scales of interest. A second, less-popular method of spatial adaptivity is called "mesh motion" (r adaptation); the smooth repositioning of mesh node points aimed at resizing existing elements to capture the local length scales. This paper proposes an adaptation method based on a combination of both element subdivision and node point repositioning (rh adaptation). By combining these two methods using the notion of a mobility function, the proposed approach seeks to increase the flexibility and extensibility of mesh motion algorithms while providing a somewhat smoother transition between refined regions than is produced by element subdivision alone. Further, in an attempt to support the requirements of a very general class of climate simulation applications, the proposed method is designed to accommodate unstructured, polygonal mesh topologies in addition to the most popular mesh types.
Hybrid Surface Mesh Adaptation for Climate Modeling
Ahmed Khamayseh; Valmor de Almeida; Glen Hansen
2008-10-01
Solution-driven mesh adaptation is becoming quite popular for spatial error control in the numerical simulation of complex computational physics applications, such as climate modeling. Typically, spatial adaptation is achieved by element subdivision (h adaptation) with a primary goal of resolving the local length scales of interest. A second, less-popular method of spatial adaptivity is called “mesh motion” (r adaptation); the smooth repositioning of mesh node points aimed at resizing existing elements to capture the local length scales. This paper proposes an adaptation method based on a combination of both element subdivision and node point repositioning (rh adaptation). By combining these two methods using the notion of a mobility function, the proposed approach seeks to increase the flexibility and extensibility of mesh motion algorithms while providing a somewhat smoother transition between refined regions than is produced by element subdivision alone. Further, in an attempt to support the requirements of a very general class of climate simulation applications, the proposed method is designed to accommodate unstructured, polygonal mesh topologies in addition to the most popular mesh types.
Adaption of unstructured meshes using node movement
Carpenter, J.G.; McRae, V.D.S.
1996-12-31
The adaption algorithm of Benson and McRae is modified for application to unstructured grids. The weight function generation was modified for application to unstructured grids and movement was limited to prevent cross over. A NACA 0012 airfoil is used as a test case to evaluate the modified algorithm when applied to unstructured grids and compared to results obtained by Warren. An adaptive mesh solution for the Sudhoo and Hall four element airfoil is included as a demonstration case.
Parallel Adaptive Mesh Refinement Library
NASA Technical Reports Server (NTRS)
Mac-Neice, Peter; Olson, Kevin
2005-01-01
Parallel Adaptive Mesh Refinement Library (PARAMESH) is a package of Fortran 90 subroutines designed to provide a computer programmer with an easy route to extension of (1) a previously written serial code that uses a logically Cartesian structured mesh into (2) a parallel code with adaptive mesh refinement (AMR). Alternatively, in its simplest use, and with minimal effort, PARAMESH can operate as a domain-decomposition tool for users who want to parallelize their serial codes but who do not wish to utilize adaptivity. The package builds a hierarchy of sub-grids to cover the computational domain of a given application program, with spatial resolution varying to satisfy the demands of the application. The sub-grid blocks form the nodes of a tree data structure (a quad-tree in two or an oct-tree in three dimensions). Each grid block has a logically Cartesian mesh. The package supports one-, two- and three-dimensional models.
Parallel adaptive mesh refinement within the PUMAA3D Project
NASA Technical Reports Server (NTRS)
Freitag, Lori; Jones, Mark; Plassmann, Paul
1995-01-01
To enable the solution of large-scale applications on distributed memory architectures, we are designing and implementing parallel algorithms for the fundamental tasks of unstructured mesh computation. In this paper, we discuss efficient algorithms developed for two of these tasks: parallel adaptive mesh refinement and mesh partitioning. The algorithms are discussed in the context of two-dimensional finite element solution on triangular meshes, but are suitable for use with a variety of element types and with h- or p-refinement. Results demonstrating the scalability and efficiency of the refinement algorithm and the quality of the mesh partitioning are presented for several test problems on the Intel DELTA.
Adaptive Mesh Refinement in CTH
Crawford, David
1999-05-04
This paper reports progress on implementing a new capability of adaptive mesh refinement into the Eulerian multimaterial shock- physics code CTH. The adaptivity is block-based with refinement and unrefinement occurring in an isotropic 2:1 manner. The code is designed to run on serial, multiprocessor and massive parallel platforms. An approximate factor of three in memory and performance improvements over comparable resolution non-adaptive calculations has-been demonstrated for a number of problems.
Parallel object-oriented adaptive mesh refinement
Balsara, D.; Quinlan, D.J.
1997-04-01
In this paper we study adaptive mesh refinement (AMR) for elliptic and hyperbolic systems. We use the Asynchronous Fast Adaptive Composite Grid Method (AFACX), a parallel algorithm based upon the of Fast Adaptive Composite Grid Method (FAC) as a test case of an adaptive elliptic solver. For our hyperbolic system example we use TVD and ENO schemes for solving the Euler and MHD equations. We use the structured grid load balancer MLB as a tool for obtaining a load balanced distribution in a parallel environment. Parallel adaptive mesh refinement poses difficulties in expressing both the basic single grid solver, whether elliptic or hyperbolic, in a fashion that parallelizes seamlessly. It also requires that these basic solvers work together within the adaptive mesh refinement algorithm which uses the single grid solvers as one part of its adaptive solution process. We show that use of AMR++, an object-oriented library within the OVERTURE Framework, simplifies the development of AMR applications. Parallel support is provided and abstracted through the use of the P++ parallel array class.
Floating shock fitting via Lagrangian adaptive meshes
NASA Technical Reports Server (NTRS)
Vanrosendale, John
1994-01-01
In recent works we have formulated a new approach to compressible flow simulation, combining the advantages of shock-fitting and shock-capturing. Using a cell-centered Roe scheme discretization on unstructured meshes, we warp the mesh while marching to steady state, so that mesh edges align with shocks and other discontinuities. This new algorithm, the Shock-fitting Lagrangian Adaptive Method (SLAM) is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence. Shock-capturing algorithms like this, which warp the mesh to yield shock-fitted accuracy, are new and relatively untried. However, their potential is clear. In the context of sonic booms, accurate calculation of near-field sonic boom signatures is critical to the design of the High Speed Civil Transport (HSCT). SLAM should allow computation of accurate N-wave pressure signatures on comparatively coarse meshes, significantly enhancing our ability to design low-boom configurations for high-speed aircraft.
Issues in adaptive mesh refinement
Dai, William Wenlong
2009-01-01
In this paper, we present an approach for a patch-based adaptive mesh refinement (AMR) for multi-physics simulations. The approach consists of clustering, symmetry preserving, mesh continuity, flux correction, communications, and management of patches. Among the special features of this patch-based AMR are symmetry preserving, efficiency of refinement, special implementation offlux correction, and patch management in parallel computing environments. Here, higher efficiency of refinement means less unnecessarily refined cells for a given set of cells to be refined. To demonstrate the capability of the AMR framework, hydrodynamics simulations with many levels of refinement are shown in both two- and three-dimensions.
Mesh Algorithms for PDE with Sieve I: Mesh Distribution
Knepley, Matthew G.; Karpeev, Dmitry A.
2009-01-01
We have developed a new programming framework, called Sieve, to support parallel numerical partial differential equation(s) (PDE) algorithms operating over distributed meshes. We have also developed a reference implementation of Sieve in C++ as a library of generic algorithms operating on distributed containers conforming to the Sieve interface. Sieve makes instances of the incidence relation, or arrows, the conceptual first-class objects represented in the containers. Further, generic algorithms acting on this arrow container are systematically used to provide natural geometric operations on the topology and also, through duality, on the data. Finally, coverings and duality are used to encode notmore » only individual meshes, but all types of hierarchies underlying PDE data structures, including multigrid and mesh partitions. In order to demonstrate the usefulness of the framework, we show how the mesh partition data can be represented and manipulated using the same fundamental mechanisms used to represent meshes. We present the complete description of an algorithm to encode a mesh partition and then distribute a mesh, which is independent of the mesh dimension, element shape, or embedding. Moreover, data associated with the mesh can be similarly distributed with exactly the same algorithm. The use of a high level of abstraction within the Sieve leads to several benefits in terms of code reuse, simplicity, and extensibility. We discuss these benefits and compare our approach to other existing mesh libraries.« less
Advanced numerical methods in mesh generation and mesh adaptation
Lipnikov, Konstantine; Danilov, A; Vassilevski, Y; Agonzal, A
2010-01-01
Numerical solution of partial differential equations requires appropriate meshes, efficient solvers and robust and reliable error estimates. Generation of high-quality meshes for complex engineering models is a non-trivial task. This task is made more difficult when the mesh has to be adapted to a problem solution. This article is focused on a synergistic approach to the mesh generation and mesh adaptation, where best properties of various mesh generation methods are combined to build efficiently simplicial meshes. First, the advancing front technique (AFT) is combined with the incremental Delaunay triangulation (DT) to build an initial mesh. Second, the metric-based mesh adaptation (MBA) method is employed to improve quality of the generated mesh and/or to adapt it to a problem solution. We demonstrate with numerical experiments that combination of all three methods is required for robust meshing of complex engineering models. The key to successful mesh generation is the high-quality of the triangles in the initial front. We use a black-box technique to improve surface meshes exported from an unattainable CAD system. The initial surface mesh is refined into a shape-regular triangulation which approximates the boundary with the same accuracy as the CAD mesh. The DT method adds robustness to the AFT. The resulting mesh is topologically correct but may contain a few slivers. The MBA uses seven local operations to modify the mesh topology. It improves significantly the mesh quality. The MBA method is also used to adapt the mesh to a problem solution to minimize computational resources required for solving the problem. The MBA has a solid theoretical background. In the first two experiments, we consider the convection-diffusion and elasticity problems. We demonstrate the optimal reduction rate of the discretization error on a sequence of adaptive strongly anisotropic meshes. The key element of the MBA method is construction of a tensor metric from hierarchical edge
Electrostatic PIC with adaptive Cartesian mesh
NASA Astrophysics Data System (ADS)
Kolobov, Vladimir; Arslanbekov, Robert
2016-05-01
We describe an initial implementation of an electrostatic Particle-in-Cell (ES-PIC) module with adaptive Cartesian mesh in our Unified Flow Solver framework. Challenges of PIC method with cell-based adaptive mesh refinement (AMR) are related to a decrease of the particle-per-cell number in the refined cells with a corresponding increase of the numerical noise. The developed ES-PIC solver is validated for capacitively coupled plasma, its AMR capabilities are demonstrated for simulations of streamer development during high-pressure gas breakdown. It is shown that cell-based AMR provides a convenient particle management algorithm for exponential multiplications of electrons and ions in the ionization events.
Adaptive and Quality Quadrilateral/Hexahedral Meshing from Volumetric Data⋆
Zhang, Yongjie; Bajaj, Chandrajit
2009-01-01
This paper describes an algorithm to extract adaptive and quality quadrilateral/hexahedral meshes directly from volumetric data. First, a bottom-up surface topology preserving octree-based algorithm is applied to select a starting octree level. Then the dual contouring method is used to extract a preliminary uniform quad/hex mesh, which is decomposed into finer quads/hexes adaptively without introducing any hanging nodes. The positions of all boundary vertices are recalculated to approximate the boundary surface more accurately. Mesh adaptivity can be controlled by a feature sensitive error function, the regions that users are interested in, or finite element calculation results. Finally, a relaxation based technique is deployed to improve mesh quality. Several demonstration examples are provided from a wide variety of application domains. Some extracted meshes have been extensively used in finite element simulations. PMID:19750180
Adaptive mesh refinement for stochastic reaction-diffusion processes
Bayati, Basil; Chatelain, Philippe; Koumoutsakos, Petros
2011-01-01
We present an algorithm for adaptive mesh refinement applied to mesoscopic stochastic simulations of spatially evolving reaction-diffusion processes. The transition rates for the diffusion process are derived on adaptive, locally refined structured meshes. Convergence of the diffusion process is presented and the fluctuations of the stochastic process are verified. Furthermore, a refinement criterion is proposed for the evolution of the adaptive mesh. The method is validated in simulations of reaction-diffusion processes as described by the Fisher-Kolmogorov and Gray-Scott equations.
Adaptive mesh refinement in titanium
Colella, Phillip; Wen, Tong
2005-01-21
In this paper, we evaluate Titanium's usability as a high-level parallel programming language through a case study, where we implement a subset of Chombo's functionality in Titanium. Chombo is a software package applying the Adaptive Mesh Refinement methodology to numerical Partial Differential Equations at the production level. In Chombo, the library approach is used to parallel programming (C++ and Fortran, with MPI), whereas Titanium is a Java dialect designed for high-performance scientific computing. The performance of our implementation is studied and compared with that of Chombo in solving Poisson's equation based on two grid configurations from a real application. Also provided are the counts of lines of code from both sides.
Serial and parallel dynamic adaptation of general hybrid meshes
NASA Astrophysics Data System (ADS)
Kavouklis, Christos
The Navier-Stokes equations are a standard mathematical representation of viscous fluid flow. Their numerical solution in three dimensions remains a computationally intensive and challenging task, despite recent advances in computer speed and memory. A strategy to increase accuracy of Navier-Stokes simulations, while maintaining computing resources to a minimum, is local refinement of the associated computational mesh in regions of large solution gradients and coarsening in regions where the solution does not vary appreciably. In this work we consider adaptation of general hybrid meshes for Computational Fluid Dynamics (CFD) applications. Hybrid meshes are composed of four types of elements; hexahedra, prisms, pyramids and tetrahedra, and have been proven a promising technology in accurately resolving fluid flow for complex geometries. The first part of this dissertation is concerned with the design and implementation of a serial scheme for the adaptation of general three dimensional hybrid meshes. We have defined 29 refinement types, for all four kinds of elements. The core of the present adaptation scheme is an iterative algorithm that flags mesh edges for refinement, so that the adapted mesh is conformal. Of primary importance is considered the design of a suitable dynamic data structure that facilitates refinement and coarsening operations and furthermore minimizes memory requirements. A special dynamic list is defined for mesh elements, in contrast with the usual tree structures. It contains only elements of the current adaptation step and minimal information that is utilized to reconstruct parent elements when the mesh is coarsened. In the second part of this work, a new parallel dynamic mesh adaptation and load balancing algorithm for general hybrid meshes is presented. Partitioning of a hybrid mesh reduces to partitioning of the corresponding dual graph. Communication among processors is based on the faces of the interpartition boundary. The distributed
A fast approach for accurate content-adaptive mesh generation.
Yang, Yongyi; Wernick, Miles N; Brankov, Jovan G
2003-01-01
Mesh modeling is an important problem with many applications in image processing. A key issue in mesh modeling is how to generate a mesh structure that well represents an image by adapting to its content. We propose a new approach to mesh generation, which is based on a theoretical result derived on the error bound of a mesh representation. In the proposed method, the classical Floyd-Steinberg error-diffusion algorithm is employed to place mesh nodes in the image domain so that their spatial density varies according to the local image content. Delaunay triangulation is next applied to connect the mesh nodes. The result of this approach is that fine mesh elements are placed automatically in regions of the image containing high-frequency features while coarse mesh elements are used to represent smooth areas. The proposed algorithm is noniterative, fast, and easy to implement. Numerical results demonstrate that, at very low computational cost, the proposed approach can produce mesh representations that are more accurate than those produced by several existing methods. Moreover, it is demonstrated that the proposed algorithm performs well with images of various kinds, even in the presence of noise. PMID:18237961
A parallel algorithm for mesh smoothing
Freitag, L.; Jones, M.; Plassmann, P.
1999-07-01
Maintaining good mesh quality during the generation and refinement of unstructured meshes in finite-element applications is an important aspect in obtaining accurate discretizations and well-conditioned linear systems. In this article, the authors present a mesh-smoothing algorithm based on nonsmooth optimization techniques and a scalable implementation of this algorithm. They prove that the parallel algorithm has a provably fast runtime bound and executes correctly for a parallel random access machine (PRAM) computational model. They extend the PRAM algorithm to distributed memory computers and report results for two-and three-dimensional simplicial meshes that demonstrate the efficiency and scalability of this approach for a number of different test cases. They also examine the effect of different architectures on the parallel algorithm and present results for the IBM SP supercomputer and an ATM-connected network of SPARC Ultras.
Masterlark, Timothy; Lu, Zhiming; Rykhus, Russ
2006-01-01
Interferometric synthetic aperture radar (InSAR) imagery documents the consistent subsidence, during the interval 1992-1999, of a pyroclastic flow deposit (PFD) emplaced during the 1986 eruption of Augustine Volcano, Alaska. We construct finite element models (FEMs) that simulate thermoelastic contraction of the PFD to account for the observed subsidence. Three-dimensional problem domains of the FEMs include a thermoelastic PFD embedded in an elastic substrate. The thickness of the PFD is initially determined from the difference between post- and pre-eruption digital elevation models (DEMs). The initial excess temperature of the PFD at the time of deposition, 640 ??C, is estimated from FEM predictions and an InSAR image via standard least-squares inverse methods. Although the FEM predicts the major features of the observed transient deformation, systematic prediction errors (RMSE=2.2 cm) are most likely associated with errors in the a priori PFD thickness distribution estimated from the DEM differences. We combine an InSAR image, FEMs, and an adaptive mesh algorithm to iteratively optimize the geometry of the PFD with respect to a minimized misfit between the predicted thermoelastic deformation and observed deformation. Prediction errors from an FEM, which includes an optimized PFD geometry and the initial excess PFD temperature estimated from the least-squares analysis, are sub-millimeter (RMSE=0.3 mm). The average thickness (9.3 m), maximum thickness (126 m), and volume (2.1 ?? 107 m3) of the PFD, estimated using the adaptive mesh algorithm, are about twice as large as the respective estimations for the a priori PFD geometry. Sensitivity analyses suggest unrealistic PFD thickness distributions are required for initial excess PFD temperatures outside of the range 500-800 ??C. ?? 2005 Elsevier B.V. All rights reserved.
Numerical modeling of seismic waves using frequency-adaptive meshes
NASA Astrophysics Data System (ADS)
Hu, Jinyin; Jia, Xiaofeng
2016-08-01
An improved modeling algorithm using frequency-adaptive meshes is applied to meet the computational requirements of all seismic frequency components. It automatically adopts coarse meshes for low-frequency computations and fine meshes for high-frequency computations. The grid intervals are adaptively calculated based on a smooth inversely proportional function of grid size with respect to the frequency. In regular grid-based methods, the uniform mesh or non-uniform mesh is used for frequency-domain wave propagators and it is fixed for all frequencies. A too coarse mesh results in inaccurate high-frequency wavefields and unacceptable numerical dispersion; on the other hand, an overly fine mesh may cause storage and computational overburdens as well as invalid propagation angles of low-frequency wavefields. Experiments on the Padé generalized screen propagator indicate that the Adaptive mesh effectively solves these drawbacks of regular fixed-mesh methods, thus accurately computing the wavefield and its propagation angle in a wide frequency band. Several synthetic examples also demonstrate its feasibility for seismic modeling and migration.
Parallel adaptation of general three-dimensional hybrid meshes
NASA Astrophysics Data System (ADS)
Kavouklis, Christos; Kallinderis, Yannis
2010-05-01
A new parallel dynamic mesh adaptation and load balancing algorithm for general hybrid grids has been developed. The meshes considered in this work are composed of four kinds of elements; tetrahedra, prisms, hexahedra and pyramids, which poses a challenge to parallel mesh adaptation. Additional complexity imposed by the presence of multiple types of elements affects especially data migration, updates of local data structures and interpartition data structures. Efficient partition of hybrid meshes has been accomplished by transforming them to suitable graphs and using serial graph partitioning algorithms. Communication among processors is based on the faces of the interpartition boundary and the termination detection algorithm of Dijkstra is employed to ensure proper flagging of edges for refinement. An inexpensive dynamic load balancing strategy is introduced to redistribute work load among processors after adaptation. In particular, only the initial coarse mesh, with proper weighting, is balanced which yields savings in computation time and relatively simple implementation of mesh quality preservation rules, while facilitating coarsening of refined elements. Special algorithms are employed for (i) data migration and dynamic updates of the local data structures, (ii) determination of the resulting interpartition boundary and (iii) identification of the communication pattern of processors. Several representative applications are included to evaluate the method.
Turbulent flow calculations using unstructured and adaptive meshes
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1990-01-01
A method of efficiently computing turbulent compressible flow over complex two dimensional configurations is presented. The method makes use of fully unstructured meshes throughout the entire flow-field, thus enabling the treatment of arbitrarily complex geometries and the use of adaptive meshing techniques throughout both viscous and inviscid regions of flow-field. Mesh generation is based on a locally mapped Delaunay technique in order to generate unstructured meshes with highly-stretched elements in the viscous regions. The flow equations are discretized using a finite element Navier-Stokes solver, and rapid convergence to steady-state is achieved using an unstructured multigrid algorithm. Turbulence modeling is performed using an inexpensive algebraic model, implemented for use on unstructured and adaptive meshes. Compressible turbulent flow solutions about multiple-element airfoil geometries are computed and compared with experimental data.
Adaptive anisotropic meshing for steady convection-dominated problems
Nguyen, Hoa; Gunzburger, Max; Ju, Lili; Burkardt, John
2009-01-01
Obtaining accurate solutions for convection–diffusion equations is challenging due to the presence of layers when convection dominates the diffusion. To solve this problem, we design an adaptive meshing algorithm which optimizes the alignment of anisotropic meshes with the numerical solution. Three main ingredients are used. First, the streamline upwind Petrov–Galerkin method is used to produce a stabilized solution. Second, an adapted metric tensor is computed from the approximate solution. Third, optimized anisotropic meshes are generated from the computed metric tensor by an anisotropic centroidal Voronoi tessellation algorithm. Our algorithm is tested on a variety of two-dimensional examples and the results shows that the algorithm is robust in detecting layers and efficient in avoiding non-physical oscillations in the numerical approximation.
Arbitrary Lagrangian Eulerian Adaptive Mesh Refinement
Koniges, A.; Eder, D.; Masters, N.; Fisher, A.; Anderson, R.; Gunney, B.; Wang, P.; Benson, D.; Dixit, P.
2009-09-29
This is a simulation code involving an ALE (arbitrary Lagrangian-Eulerian) hydrocode with AMR (adaptive mesh refinement) and pluggable physics packages for material strength, heat conduction, radiation diffusion, and laser ray tracing developed a LLNL, UCSD, and Berkeley Lab. The code is an extension of the open source SAMRAI (Structured Adaptive Mesh Refinement Application Interface) code/library. The code can be used in laser facilities such as the National Ignition Facility. The code is alsi being applied to slurry flow (landslides).
A hierarchical structure for automatic meshing and adaptive FEM analysis
NASA Technical Reports Server (NTRS)
Kela, Ajay; Saxena, Mukul; Perucchio, Renato
1987-01-01
A new algorithm for generating automatically, from solid models of mechanical parts, finite element meshes that are organized as spatially addressable quaternary trees (for 2-D work) or octal trees (for 3-D work) is discussed. Because such meshes are inherently hierarchical as well as spatially addressable, they permit efficient substructuring techniques to be used for both global analysis and incremental remeshing and reanalysis. The global and incremental techniques are summarized and some results from an experimental closed loop 2-D system in which meshing, analysis, error evaluation, and remeshing and reanalysis are done automatically and adaptively are presented. The implementation of 3-D work is briefly discussed.
Elliptic Solvers for Adaptive Mesh Refinement Grids
Quinlan, D.J.; Dendy, J.E., Jr.; Shapira, Y.
1999-06-03
We are developing multigrid methods that will efficiently solve elliptic problems with anisotropic and discontinuous coefficients on adaptive grids. The final product will be a library that provides for the simplified solution of such problems. This library will directly benefit the efforts of other Laboratory groups. The focus of this work is research on serial and parallel elliptic algorithms and the inclusion of our black-box multigrid techniques into this new setting. The approach applies the Los Alamos object-oriented class libraries that greatly simplify the development of serial and parallel adaptive mesh refinement applications. In the final year of this LDRD, we focused on putting the software together; in particular we completed the final AMR++ library, we wrote tutorials and manuals, and we built example applications. We implemented the Fast Adaptive Composite Grid method as the principal elliptic solver. We presented results at the Overset Grid Conference and other more AMR specific conferences. We worked on optimization of serial and parallel performance and published several papers on the details of this work. Performance remains an important issue and is the subject of continuing research work.
Performance of a streaming mesh refinement algorithm.
Thompson, David C.; Pebay, Philippe Pierre
2004-08-01
In SAND report 2004-1617, we outline a method for edge-based tetrahedral subdivision that does not rely on saving state or communication to produce compatible tetrahedralizations. This report analyzes the performance of the technique by characterizing (a) mesh quality, (b) execution time, and (c) traits of the algorithm that could affect quality or execution time differently for different meshes. It also details the method used to debug the several hundred subdivision templates that the algorithm relies upon. Mesh quality is on par with other similar refinement schemes and throughput on modern hardware can exceed 600,000 output tetrahedra per second. But if you want to understand the traits of the algorithm, you have to read the report!
Adaptive Mesh Refinement for Microelectronic Device Design
NASA Technical Reports Server (NTRS)
Cwik, Tom; Lou, John; Norton, Charles
1999-01-01
Finite element and finite volume methods are used in a variety of design simulations when it is necessary to compute fields throughout regions that contain varying materials or geometry. Convergence of the simulation can be assessed by uniformly increasing the mesh density until an observable quantity stabilizes. Depending on the electrical size of the problem, uniform refinement of the mesh may be computationally infeasible due to memory limitations. Similarly, depending on the geometric complexity of the object being modeled, uniform refinement can be inefficient since regions that do not need refinement add to the computational expense. In either case, convergence to the correct (measured) solution is not guaranteed. Adaptive mesh refinement methods attempt to selectively refine the region of the mesh that is estimated to contain proportionally higher solution errors. The refinement may be obtained by decreasing the element size (h-refinement), by increasing the order of the element (p-refinement) or by a combination of the two (h-p refinement). A successful adaptive strategy refines the mesh to produce an accurate solution measured against the correct fields without undue computational expense. This is accomplished by the use of a) reliable a posteriori error estimates, b) hierarchal elements, and c) automatic adaptive mesh generation. Adaptive methods are also useful when problems with multi-scale field variations are encountered. These occur in active electronic devices that have thin doped layers and also when mixed physics is used in the calculation. The mesh needs to be fine at and near the thin layer to capture rapid field or charge variations, but can coarsen away from these layers where field variations smoothen and charge densities are uniform. This poster will present an adaptive mesh refinement package that runs on parallel computers and is applied to specific microelectronic device simulations. Passive sensors that operate in the infrared portion of
Gravitational Collapse With Distributed Adaptive Mesh Refinement
NASA Astrophysics Data System (ADS)
Liebling, Steven; Lehner, Luis; Motl, Patrick; Neilsen, David; Rahman, Tanvir; Reula, Oscar
2006-04-01
Gravitational collapse is studied using distributed adaptive mesh refinement (AMR). The AMR infrastructure includes a novel treatment of adaptive boundaries which allows for high orders of accuracy. Results of the collapse of Brill waves to black holes are presented. Combining both vertex centered and cell centered fields in the same evolution is discussed.
Grid adaptation using chimera composite overlapping meshes
NASA Technical Reports Server (NTRS)
Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen
1994-01-01
The objective of this paper is to perform grid adaptation using composite overlapping meshes in regions of large gradient to accurately capture the salient features during computation. The chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using trilinear interpolation. Application to the Euler equations for shock reflections and to shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well-resolved.
Grid adaptation using Chimera composite overlapping meshes
NASA Technical Reports Server (NTRS)
Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen
1993-01-01
The objective of this paper is to perform grid adaptation using composite over-lapping meshes in regions of large gradient to capture the salient features accurately during computation. The Chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using tri-linear interpolation. Applications to the Euler equations for shock reflections and to a shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well resolved.
Grid adaption using Chimera composite overlapping meshes
NASA Technical Reports Server (NTRS)
Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen
1993-01-01
The objective of this paper is to perform grid adaptation using composite over-lapping meshes in regions of large gradient to capture the salient features accurately during computation. The Chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using tri-linear interpolation. Applications to the Euler equations for shock reflections and to a shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well resolved.
PLUM: Parallel Load Balancing for Unstructured Adaptive Meshes
NASA Technical Reports Server (NTRS)
Oliker, Leonid
1998-01-01
Dynamic mesh adaption on unstructured grids is a powerful tool for computing large-scale problems that require grid modifications to efficiently resolve solution features. Unfortunately, an efficient parallel implementation is difficult to achieve, primarily due to the load imbalance created by the dynamically-changing nonuniform grid. To address this problem, we have developed PLUM, an automatic portable framework for performing adaptive large-scale numerical computations in a message-passing environment. First, we present an efficient parallel implementation of a tetrahedral mesh adaption scheme. Extremely promising parallel performance is achieved for various refinement and coarsening strategies on a realistic-sized domain. Next we describe PLUM, a novel method for dynamically balancing the processor workloads in adaptive grid computations. This research includes interfacing the parallel mesh adaption procedure based on actual flow solutions to a data remapping module, and incorporating an efficient parallel mesh repartitioner. A significant runtime improvement is achieved by observing that data movement for a refinement step should be performed after the edge-marking phase but before the actual subdivision. We also present optimal and heuristic remapping cost metrics that can accurately predict the total overhead for data redistribution. Several experiments are performed to verify the effectiveness of PLUM on sequences of dynamically adapted unstructured grids. Portability is demonstrated by presenting results on the two vastly different architectures of the SP2 and the Origin2OOO. Additionally, we evaluate the performance of five state-of-the-art partitioning algorithms that can be used within PLUM. It is shown that for certain classes of unsteady adaption, globally repartitioning the computational mesh produces higher quality results than diffusive repartitioning schemes. We also demonstrate that a coarse starting mesh produces high quality load balancing, at
AN ADAPTIVE PARTICLE-MESH GRAVITY SOLVER FOR ENZO
Passy, Jean-Claude; Bryan, Greg L.
2014-11-01
We describe and implement an adaptive particle-mesh algorithm to solve the Poisson equation for grid-based hydrodynamics codes with nested grids. The algorithm is implemented and extensively tested within the astrophysical code Enzo against the multigrid solver available by default. We find that while both algorithms show similar accuracy for smooth mass distributions, the adaptive particle-mesh algorithm is more accurate for the case of point masses, and is generally less noisy. We also demonstrate that the two-body problem can be solved accurately in a configuration with nested grids. In addition, we discuss the effect of subcycling, and demonstrate that evolving all the levels with the same timestep yields even greater precision.
Parallel tetrahedral mesh adaptation with dynamic load balancing
Oliker, Leonid; Biswas, Rupak; Gabow, Harold N.
2000-06-28
The ability to dynamically adapt an unstructured grid is a powerful tool for efficiently solving computational problems with evolving physical features. In this paper, we report on our experience parallelizing an edge-based adaptation scheme, called 3D-TAG, using message passing. Results show excellent speedup when a realistic helicopter rotor mesh is randomly refined. However, performance deteriorates when the mesh is refined using a solution-based error indicator since mesh adaptation for practical problems occurs in a localized region, creating a severe load imbalance. To address this problem, we have developed PLUM, a global dynamic load balancing framework for adaptive numerical computations. Even though PLUM primarily balances processor workloads for the solution phase, it reduces the load imbalance problem within mesh adaptation by repartitioning the mesh after targeting edges for refinement but before the actual subdivision. This dramatically improves the performance of parallel 3D-TAG since refinement occurs in a more load balanced fashion. We also present optimal and heuristic algorithms that, when applied to the default mapping of a parallel repartitioner, significantly reduce the data redistribution overhead. Finally, portability is examined by comparing performance on three state-of-the-art parallel machines.
Parallel Tetrahedral Mesh Adaptation with Dynamic Load Balancing
NASA Technical Reports Server (NTRS)
Oliker, Leonid; Biswas, Rupak; Gabow, Harold N.
1999-01-01
The ability to dynamically adapt an unstructured grid is a powerful tool for efficiently solving computational problems with evolving physical features. In this paper, we report on our experience parallelizing an edge-based adaptation scheme, called 3D_TAG. using message passing. Results show excellent speedup when a realistic helicopter rotor mesh is randomly refined. However. performance deteriorates when the mesh is refined using a solution-based error indicator since mesh adaptation for practical problems occurs in a localized region., creating a severe load imbalance. To address this problem, we have developed PLUM, a global dynamic load balancing framework for adaptive numerical computations. Even though PLUM primarily balances processor workloads for the solution phase, it reduces the load imbalance problem within mesh adaptation by repartitioning the mesh after targeting edges for refinement but before the actual subdivision. This dramatically improves the performance of parallel 3D_TAG since refinement occurs in a more load balanced fashion. We also present optimal and heuristic algorithms that, when applied to the default mapping of a parallel repartitioner, significantly reduce the data redistribution overhead. Finally, portability is examined by comparing performance on three state-of-the-art parallel machines.
Kinetic solvers with adaptive mesh in phase space.
Arslanbekov, Robert R; Kolobov, Vladimir I; Frolova, Anna A
2013-12-01
An adaptive mesh in phase space (AMPS) methodology has been developed for solving multidimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a "tree of trees" (ToT) data structure. The r mesh is automatically generated around embedded boundaries, and is dynamically adapted to local solution properties. The v mesh is created on-the-fly in each r cell. Mappings between neighboring v-space trees is implemented for the advection operator in r space. We have developed algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive v mesh: the importance sampling, multipoint projection, and variance reduction methods. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions of hot light particles in a Lorentz gas. Our AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light-particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce the computational cost and memory usage for solving challenging kinetic problems. PMID:24483578
Kinetic solvers with adaptive mesh in phase space
NASA Astrophysics Data System (ADS)
Arslanbekov, Robert R.; Kolobov, Vladimir I.; Frolova, Anna A.
2013-12-01
An adaptive mesh in phase space (AMPS) methodology has been developed for solving multidimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a “tree of trees” (ToT) data structure. The r mesh is automatically generated around embedded boundaries, and is dynamically adapted to local solution properties. The v mesh is created on-the-fly in each r cell. Mappings between neighboring v-space trees is implemented for the advection operator in r space. We have developed algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive v mesh: the importance sampling, multipoint projection, and variance reduction methods. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions of hot light particles in a Lorentz gas. Our AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light-particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce the computational cost and memory usage for solving challenging kinetic problems.
Arbitrary Lagrangian Eulerian Adaptive Mesh Refinement
Energy Science and Technology Software Center (ESTSC)
2009-09-29
This is a simulation code involving an ALE (arbitrary Lagrangian-Eulerian) hydrocode with AMR (adaptive mesh refinement) and pluggable physics packages for material strength, heat conduction, radiation diffusion, and laser ray tracing developed a LLNL, UCSD, and Berkeley Lab. The code is an extension of the open source SAMRAI (Structured Adaptive Mesh Refinement Application Interface) code/library. The code can be used in laser facilities such as the National Ignition Facility. The code is alsi being appliedmore » to slurry flow (landslides).« less
A Parallel Ghosting Algorithm for The Flexible Distributed Mesh Database
Mubarak, Misbah; Seol, Seegyoung; Lu, Qiukai; Shephard, Mark S.
2013-01-01
Critical to the scalability of parallel adaptive simulations are parallel control functions including load balancing, reduced inter-process communication and optimal data decomposition. In distributed meshes, many mesh-based applications frequently access neighborhood information for computational purposes which must be transmitted efficiently to avoid parallel performance degradation when the neighbors are on different processors. This article presents a parallel algorithm of creating and deleting data copies, referred to as ghost copies, which localize neighborhood data for computation purposes while minimizing inter-process communication. The key characteristics of the algorithm are: (1) It can create ghost copies of any permissible topological order inmore » a 1D, 2D or 3D mesh based on selected adjacencies. (2) It exploits neighborhood communication patterns during the ghost creation process thus eliminating all-to-all communication. (3) For applications that need neighbors of neighbors, the algorithm can create n number of ghost layers up to a point where the whole partitioned mesh can be ghosted. Strong and weak scaling results are presented for the IBM BG/P and Cray XE6 architectures up to a core count of 32,768 processors. The algorithm also leads to scalable results when used in a parallel super-convergent patch recovery error estimator, an application that frequently accesses neighborhood data to carry out computation.« less
Multigrid solution strategies for adaptive meshing problems
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1995-01-01
This paper discusses the issues which arise when combining multigrid strategies with adaptive meshing techniques for solving steady-state problems on unstructured meshes. A basic strategy is described, and demonstrated by solving several inviscid and viscous flow cases. Potential inefficiencies in this basic strategy are exposed, and various alternate approaches are discussed, some of which are demonstrated with an example. Although each particular approach exhibits certain advantages, all methods have particular drawbacks, and the formulation of a completely optimal strategy is considered to be an open problem.
Unstructured Adaptive Meshes: Bad for Your Memory?
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Feng, Hui-Yu; VanderWijngaart, Rob
2003-01-01
This viewgraph presentation explores the need for a NASA Advanced Supercomputing (NAS) parallel benchmark for problems with irregular dynamical memory access. This benchmark is important and necessary because: 1) Problems with localized error source benefit from adaptive nonuniform meshes; 2) Certain machines perform poorly on such problems; 3) Parallel implementation may provide further performance improvement but is difficult. Some examples of problems which use irregular dynamical memory access include: 1) Heat transfer problem; 2) Heat source term; 3) Spectral element method; 4) Base functions; 5) Elemental discrete equations; 6) Global discrete equations. Nonconforming Mesh and Mortar Element Method are covered in greater detail in this presentation.
GRChombo: Numerical relativity with adaptive mesh refinement
NASA Astrophysics Data System (ADS)
Clough, Katy; Figueras, Pau; Finkel, Hal; Kunesch, Markus; Lim, Eugene A.; Tunyasuvunakool, Saran
2015-12-01
In this work, we introduce {\\mathtt{GRChombo}}: a new numerical relativity code which incorporates full adaptive mesh refinement (AMR) using block structured Berger-Rigoutsos grid generation. The code supports non-trivial 'many-boxes-in-many-boxes' mesh hierarchies and massive parallelism through the message passing interface. {\\mathtt{GRChombo}} evolves the Einstein equation using the standard BSSN formalism, with an option to turn on CCZ4 constraint damping if required. The AMR capability permits the study of a range of new physics which has previously been computationally infeasible in a full 3 + 1 setting, while also significantly simplifying the process of setting up the mesh for these problems. We show that {\\mathtt{GRChombo}} can stably and accurately evolve standard spacetimes such as binary black hole mergers and scalar collapses into black holes, demonstrate the performance characteristics of our code, and discuss various physics problems which stand to benefit from the AMR technique.
Update on Development of Mesh Generation Algorithms in MeshKit
Jain, Rajeev; Vanderzee, Evan; Mahadevan, Vijay
2015-09-30
MeshKit uses a graph-based design for coding all its meshing algorithms, which includes the Reactor Geometry (and mesh) Generation (RGG) algorithms. This report highlights the developmental updates of all the algorithms, results and future work. Parallel versions of algorithms, documentation and performance results are reported. RGG GUI design was updated to incorporate new features requested by the users; boundary layer generation and parallel RGG support were added to the GUI. Key contributions to the release, upgrade and maintenance of other SIGMA1 libraries (CGM and MOAB) were made. Several fundamental meshing algorithms for creating a robust parallel meshing pipeline in MeshKit are under development. Results and current status of automated, open-source and high quality nuclear reactor assembly mesh generation algorithms such as trimesher, quadmesher, interval matching and multi-sweeper are reported.
Details of tetrahedral anisotropic mesh adaptation
NASA Astrophysics Data System (ADS)
Jensen, Kristian Ejlebjerg; Gorman, Gerard
2016-04-01
We have implemented tetrahedral anisotropic mesh adaptation using the local operations of coarsening, swapping, refinement and smoothing in MATLAB without the use of any for- N loops, i.e. the script is fully vectorised. In the process of doing so, we have made three observations related to details of the implementation: 1. restricting refinement to a single edge split per element not only simplifies the code, it also improves mesh quality, 2. face to edge swapping is unnecessary, and 3. optimising for the Vassilevski functional tends to give a little higher value for the mean condition number functional than optimising for the condition number functional directly. These observations have been made for a uniform and a radial shock metric field, both starting from a structured mesh in a cube. Finally, we compare two coarsening techniques and demonstrate the importance of applying smoothing in the mesh adaptation loop. The results pertain to a unit cube geometry, but we also show the effect of corners and edges by applying the implementation in a spherical geometry.
Advances in Patch-Based Adaptive Mesh Refinement Scalability
Gunney, Brian T.N.; Anderson, Robert W.
2015-12-18
Patch-based structured adaptive mesh refinement (SAMR) is widely used for high-resolution simu- lations. Combined with modern supercomputers, it could provide simulations of unprecedented size and resolution. A persistent challenge for this com- bination has been managing dynamically adaptive meshes on more and more MPI tasks. The dis- tributed mesh management scheme in SAMRAI has made some progress SAMR scalability, but early al- gorithms still had trouble scaling past the regime of 105 MPI tasks. This work provides two critical SAMR regridding algorithms, which are integrated into that scheme to ensure efficiency of the whole. The clustering algorithm is an extension of the tile- clustering approach, making it more flexible and efficient in both clustering and parallelism. The partitioner is a new algorithm designed to prevent the network congestion experienced by its prede- cessor. We evaluated performance using weak- and strong-scaling benchmarks designed to be difficult for dynamic adaptivity. Results show good scaling on up to 1.5M cores and 2M MPI tasks. Detailed timing diagnostics suggest scaling would continue well past that.
Advances in Patch-Based Adaptive Mesh Refinement Scalability
Gunney, Brian T.N.; Anderson, Robert W.
2015-12-18
Patch-based structured adaptive mesh refinement (SAMR) is widely used for high-resolution simu- lations. Combined with modern supercomputers, it could provide simulations of unprecedented size and resolution. A persistent challenge for this com- bination has been managing dynamically adaptive meshes on more and more MPI tasks. The dis- tributed mesh management scheme in SAMRAI has made some progress SAMR scalability, but early al- gorithms still had trouble scaling past the regime of 105 MPI tasks. This work provides two critical SAMR regridding algorithms, which are integrated into that scheme to ensure efficiency of the whole. The clustering algorithm is an extensionmore » of the tile- clustering approach, making it more flexible and efficient in both clustering and parallelism. The partitioner is a new algorithm designed to prevent the network congestion experienced by its prede- cessor. We evaluated performance using weak- and strong-scaling benchmarks designed to be difficult for dynamic adaptivity. Results show good scaling on up to 1.5M cores and 2M MPI tasks. Detailed timing diagnostics suggest scaling would continue well past that.« less
NASA Astrophysics Data System (ADS)
Papadakis, A. P.; Georghiou, G. E.; Metaxas, A. C.
2008-12-01
A new adaptive mesh generator has been developed and used in the analysis of high-pressure gas discharges, such as avalanches and streamers, reducing computational times and computer memory needs significantly. The new adaptive mesh generator developed, uses normalized error indicators, varying from 0 to 1, to guarantee optimal mesh resolution for all carriers involved in the analysis. Furthermore, it uses h- and r-refinement techniques such as mesh jiggling, edge swapping and node addition/removal to develop an element quality improvement algorithm that improves the mesh quality significantly and a fast and accurate algorithm for interpolation between meshes. Finally, the mesh generator is applied in the characterization of the transition from a single electron to the avalanche and streamer discharges in high-voltage, high-pressure gas discharges for dc 1 mm gaps, RF 1 cm point-plane gaps and parallel-plate 40 MHz configurations, in ambient atmospheric air.
Lin, Paul Tinphone; Jameson, Antony, 1934-; Baker, Timothy J.; Martinelli, Luigi
2005-01-01
An implicit multigrid-driven algorithm for two-dimensional incompressible laminar viscous flows has been coupled with a solution adaptation method and a mesh movement method for boundary movement. Time-dependent calculations are performed implicitly by regarding each time step as a steady-state problem in pseudo-time. The method of artificial compressibility is used to solve the flow equations. The solution mesh adaptation method performs local mesh refinement using an incremental Delaunay algorithm and mesh coarsening by means of edge collapse. Mesh movement is achieved by modeling the computational domain as an elastic solid and solving the equilibrium equations for the stress field. The solution adaptation method has been validated by comparison with experimental results and other computational results for low Reynolds number flow over a shedding circular cylinder. Preliminary validation of the mesh movement method has been demonstrated by a comparison with experimental results of an oscillating airfoil and with computational results for an oscillating cylinder.
Dynamic mesh adaption for triangular and tetrahedral grids
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Strawn, Roger
1993-01-01
The following topics are discussed: requirements for dynamic mesh adaption; linked-list data structure; edge-based data structure; adaptive-grid data structure; three types of element subdivision; mesh refinement; mesh coarsening; additional constraints for coarsening; anisotropic error indicator for edges; unstructured-grid Euler solver; inviscid 3-D wing; and mesh quality for solution-adaptive grids. The discussion is presented in viewgraph form.
Block-structured adaptive mesh refinement - theory, implementation and application
Deiterding, Ralf
2011-01-01
Structured adaptive mesh refinement (SAMR) techniques can enable cutting-edge simulations of problems governed by conservation laws. Focusing on the strictly hyperbolic case, these notes explain all algorithmic and mathematical details of a technically relevant implementation tailored for distributed memory computers. An overview of the background of commonly used finite volume discretizations for gas dynamics is included and typical benchmarks to quantify accuracy and performance of the dynamically adaptive code are discussed. Large-scale simulations of shock-induced realistic combustion in non-Cartesian geometry and shock-driven fluid-structure interaction with fully coupled dynamic boundary motion demonstrate the applicability of the discussed techniques for complex scenarios.
Adaptive upscaling with the dual mesh method
Guerillot, D.; Verdiere, S.
1997-08-01
The objective of this paper is to demonstrate that upscaling should be calculated during the flow simulation instead of trying to enhance the a priori upscaling methods. Hence, counter-examples are given to motivate our approach, the so-called Dual Mesh Method. The main steps of this numerical algorithm are recalled. Applications illustrate the necessity to consider different average relative permeability values depending on the direction in space. Moreover, these values could be different for the same average saturation. This proves that an a priori upscaling cannot be the answer even in homogeneous cases because of the {open_quotes}dynamical heterogeneity{close_quotes} created by the saturation profile. Other examples show the efficiency of the Dual Mesh Method applied to heterogeneous medium and to an actual field case in South America.
Sampling and surface reconstruction with adaptive-size meshes
NASA Astrophysics Data System (ADS)
Huang, Wen-Chen; Goldgof, Dmitry B.
1992-03-01
This paper presents a new approach to sampling and surface reconstruction which uses the physically based models. We introduce adaptive-size meshes which automatically update the size of the meshes as the distance between the nodes changes. We have implemented the adaptive-size algorithm to the following three applications: (1) Sampling of the intensity data. (2) Surface reconstruction of the range data. (3) Surface reconstruction of the 3-D computed tomography left ventricle data. The LV data was acquired by the 3-D computed tomography (CT) scanner. It was provided by Dr. Eric Hoffman at University of Pennsylvania Medical school and consists of 16 volumetric (128 X 128 X 118) images taken through the heart cycle.
Efficient triangular adaptive meshes for tsunami simulations
NASA Astrophysics Data System (ADS)
Behrens, J.
2012-04-01
With improving technology and increased sensor density for accurate determination of tsunamogenic earthquake source parameters and consecutively uplift distribution, real-time simulations of even near-field tsunami hazard appears feasible in the near future. In order to support such efforts a new generation of tsunami models is currently under development. These models comprise adaptively refined meshes, in order to save computational resources (in areas of low wave activity) and still represent the inherently multi-scale behavior of a tsunami approaching coastal waters. So far, these methods have been based on oct-tree quadrilateral refinement. The method introduced here is based on binary tree refinement on triangular grids. By utilizing the structure stemming from the refinement strategy, a very efficient method can be achieved, with a triangular mesh, able to accurately represent complex boundaries.
NASA Technical Reports Server (NTRS)
Vemaganti, Gururaja R.; Wieting, Allan R.
1990-01-01
A higher-order streamline upwinding Petrov-Galerkin finite element method is employed for high speed viscous flow analysis using structured and unstructured meshes. For a Mach 8.03 shock interference problem, successive mesh adaptation was performed using an adaptive remeshing method. Results from the finite element algorithm compare well with both experimental data and results from an upwind cell-centered method. Finite element results for a Mach 14.1 flow over a 24 degree compression corner compare well with experimental data and two other numerical algorithms for both structured and unstructured meshes.
A New Approach to Parallel Dynamic Partitioning for Adaptive Unstructured Meshes
NASA Technical Reports Server (NTRS)
Heber, Gerd; Biswas, Rupak; Gao, Guang R.
1999-01-01
Classical mesh partitioning algorithms were designed for rather static situations, and their straightforward application in a dynamical framework may lead to unsatisfactory results, e.g., excessive data migration among processors. Furthermore, special attention should be paid to their amenability to parallelization. In this paper, a novel parallel method for the dynamic partitioning of adaptive unstructured meshes is described. It is based on a linear representation of the mesh using self-avoiding walks.
Elliptic Solvers with Adaptive Mesh Refinement on Complex Geometries
Phillip, B.
2000-07-24
Adaptive Mesh Refinement (AMR) is a numerical technique for locally tailoring the resolution computational grids. Multilevel algorithms for solving elliptic problems on adaptive grids include the Fast Adaptive Composite grid method (FAC) and its parallel variants (AFAC and AFACx). Theory that confirms the independence of the convergence rates of FAC and AFAC on the number of refinement levels exists under certain ellipticity and approximation property conditions. Similar theory needs to be developed for AFACx. The effectiveness of multigrid-based elliptic solvers such as FAC, AFAC, and AFACx on adaptively refined overlapping grids is not clearly understood. Finally, a non-trivial eye model problem will be solved by combining the power of using overlapping grids for complex moving geometries, AMR, and multilevel elliptic solvers.
ROAMing terrain (Real-time Optimally Adapting Meshes)
Duchaineau, M.; Wolinsky, M.; Sigeti, D.E.; Miller, M.C.; Aldrich, C.; Mineev, M.
1997-07-01
Terrain visualization is a difficult problem for applications requiring accurate images of large datasets at high frame rates, such as flight simulation and ground-based aircraft testing using synthetic sensor stimulation. On current graphics hardware, the problem is to maintain dynamic, view-dependent triangle meshes and texture maps that produce good images at the required frame rate. We present an algorithm for constructing triangle meshes that optimizes flexible view-dependent error metrics, produces guaranteed error bounds, achieves specified triangle counts directly, and uses frame-to-frame coherence to operate at high frame rates for thousands of triangles per frame. Our method, dubbed Real-time Optimally Adapting Meshes (ROAM), uses two priority queues to drive split and merge operations that maintain continuous triangulations built from pre-processed bintree triangles. We introduce two additional performance optimizations: incremental triangle stripping and priority-computation deferral lists. ROAM execution time is proportionate to the number of triangle changes per frame, which is typically a few percent of the output mesh size, hence ROAM performance is insensitive to the resolution and extent of the input terrain. Dynamic terrain and simple vertex morphing are supported.
Adaptive Meshing Techniques for Viscous Flow Calculations on Mixed Element Unstructured Meshes
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.
1997-01-01
An adaptive refinement strategy based on hierarchical element subdivision is formulated and implemented for meshes containing arbitrary mixtures of tetrahendra, hexahendra, prisms and pyramids. Special attention is given to keeping memory overheads as low as possible. This procedure is coupled with an algebraic multigrid flow solver which operates on mixed-element meshes. Inviscid flows as well as viscous flows are computed an adaptively refined tetrahedral, hexahedral, and hybrid meshes. The efficiency of the method is demonstrated by generating an adapted hexahedral mesh containing 3 million vertices on a relatively inexpensive workstation.
Adaptive radial basis function mesh deformation using data reduction
NASA Astrophysics Data System (ADS)
Gillebaart, T.; Blom, D. S.; van Zuijlen, A. H.; Bijl, H.
2016-09-01
bandwidth available between CPU and memory. In terms of parallel efficiency/scaling the different studied methods perform similarly, with the greedy algorithm being the bottleneck. In terms of absolute computational work the adaptive methods are better for the cases studied due to their more efficient selection of the control points. By automating most of the RBF mesh deformation, a robust, efficient and almost user-independent mesh deformation method is presented.
Anisotropic Mesh Adaptivity for FE-simulation of cardiovascular flow
NASA Astrophysics Data System (ADS)
Mueller, Jens; Sahni, Onkar; Jansen, Kenneth E.; Shephard, Mark S.; Taylor, Charles A.
2004-11-01
In this study we present an adaptive anisotropic finite element method and demonstrate how computational efficiency can be increased when applying the method to the simulation of blood flow in the cardiovascular system. We use the weak SUPG formulation for the transient 3D incompressible Navier-Stokes equations which are discretized by linear finite elements, both for the pressure and the velocity field. Given the pulsatile nature of the flow in blood vessels we have pursued adaptavity based on the average flow over a cardiac cycle. Error indicators are derived to define an anisotropic mesh metric field. Mesh modification algorithms are used to anisotropically adapt the mesh according to the desired size field. We demonstrate the efficiency of the method by first applying it to pulsatile flow in a straight cylindrical pipe and then to a pig artery with a stenosis bypassed by a graft. The efficiency of the method is measured in terms of computational savings when we compute the wall shear stresses, a quantity identified to be important to understanding arterial disease.
Adaptive Mesh Refinement Simulations of Relativistic Binaries
NASA Astrophysics Data System (ADS)
Motl, Patrick M.; Anderson, M.; Lehner, L.; Olabarrieta, I.; Tohline, J. E.; Liebling, S. L.; Rahman, T.; Hirschman, E.; Neilsen, D.
2006-09-01
We present recent results from our efforts to evolve relativistic binaries composed of compact objects. We simultaneously solve the general relativistic hydrodynamics equations to evolve the material components of the binary and Einstein's equations to evolve the space-time. These two codes are coupled through an adaptive mesh refinement driver (had). One of the ultimate goals of this project is to address the merger of a neutron star and black hole and assess the possible observational signature of such systems as gamma ray bursts. This work has been supported in part by NSF grants AST 04-07070 and PHY 03-26311 and in part through NASA's ATP program grant NAG5-13430. The computations were performed primarily at NCSA through grant MCA98N043 and at LSU's Center for Computation & Technology.
Visualization Tools for Adaptive Mesh Refinement Data
Weber, Gunther H.; Beckner, Vincent E.; Childs, Hank; Ligocki,Terry J.; Miller, Mark C.; Van Straalen, Brian; Bethel, E. Wes
2007-05-09
Adaptive Mesh Refinement (AMR) is a highly effective method for simulations that span a large range of spatiotemporal scales, such as astrophysical simulations that must accommodate ranges from interstellar to sub-planetary. Most mainstream visualization tools still lack support for AMR as a first class data type and AMR code teams use custom built applications for AMR visualization. The Department of Energy's (DOE's) Science Discovery through Advanced Computing (SciDAC) Visualization and Analytics Center for Enabling Technologies (VACET) is currently working on extending VisIt, which is an open source visualization tool that accommodates AMR as a first-class data type. These efforts will bridge the gap between general-purpose visualization applications and highly specialized AMR visual analysis applications. Here, we give an overview of the state of the art in AMR visualization research and tools and describe how VisIt currently handles AMR data.
Visualization of Scalar Adaptive Mesh Refinement Data
VACET; Weber, Gunther; Weber, Gunther H.; Beckner, Vince E.; Childs, Hank; Ligocki, Terry J.; Miller, Mark C.; Van Straalen, Brian; Bethel, E. Wes
2007-12-06
Adaptive Mesh Refinement (AMR) is a highly effective computation method for simulations that span a large range of spatiotemporal scales, such as astrophysical simulations, which must accommodate ranges from interstellar to sub-planetary. Most mainstream visualization tools still lack support for AMR grids as a first class data type and AMR code teams use custom built applications for AMR visualization. The Department of Energy's (DOE's) Science Discovery through Advanced Computing (SciDAC) Visualization and Analytics Center for Enabling Technologies (VACET) is currently working on extending VisIt, which is an open source visualization tool that accommodates AMR as a first-class data type. These efforts will bridge the gap between general-purpose visualization applications and highly specialized AMR visual analysis applications. Here, we give an overview of the state of the art in AMR scalar data visualization research.
AN ALGORITHM FOR PARALLEL SN SWEEPS ON UNSTRUCTURED MESHES
S. D. PAUTZ
2000-12-01
We develop a new algorithm for performing parallel S{sub n} sweeps on unstructured meshes. The algorithm uses a low-complexity list ordering heuristic to determine a sweep ordering on any partitioned mesh. For typical problems and with ''normal'' mesh partitionings we have observed nearly linear speedups on up to 126 processors. This is an important and desirable result, since although analyses of structured meshes indicate that parallel sweeps will not scale with normal partitioning approaches, we do not observe any severe asymptotic degradation in the parallel efficiency with modest ({le}100) levels of parallelism. This work is a fundamental step in the development of parallel S{sub n} methods.
Global Load Balancing with Parallel Mesh Adaption on Distributed-Memory Systems
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Oliker, Leonid; Sohn, Andrew
1996-01-01
Dynamic mesh adaptation on unstructured grids is a powerful tool for efficiently computing unsteady problems to resolve solution features of interest. Unfortunately, this causes load inbalances among processors on a parallel machine. This paper described the parallel implementation of a tetrahedral mesh adaption scheme and a new global load balancing method. A heuristic remapping algorithm is presented that assigns partitions to processors such that the redistribution coast is minimized. Results indicate that the parallel performance of the mesh adaption code depends on the nature of the adaption region and show a 35.5X speedup on 64 processors of an SP2 when 35 percent of the mesh is randomly adapted. For large scale scientific computations, our load balancing strategy gives an almost sixfold reduction in solver execution times over non-balanced loads. Furthermore, our heuristic remappier yields processor assignments that are less than 3 percent of the optimal solutions, but requires only 1 percent of the computational time.
Global Load Balancing with Parallel Mesh Adaption on Distributed-Memory Systems
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Oliker, Leonid; Sohn, Andrew
1996-01-01
Dynamic mesh adaption on unstructured grids is a powerful tool for efficiently computing unsteady problems to resolve solution features of interest. Unfortunately, this causes load imbalance among processors on a parallel machine. This paper describes the parallel implementation of a tetrahedral mesh adaption scheme and a new global load balancing method. A heuristic remapping algorithm is presented that assigns partitions to processors such that the redistribution cost is minimized. Results indicate that the parallel performance of the mesh adaption code depends on the nature of the adaption region and show a 35.5X speedup on 64 processors of an SP2 when 35% of the mesh is randomly adapted. For large-scale scientific computations, our load balancing strategy gives almost a sixfold reduction in solver execution times over non-balanced loads. Furthermore, our heuristic remapper yields processor assignments that are less than 3% off the optimal solutions but requires only 1% of the computational time.
Xia, Kelin; Zhan, Meng; Wan, Decheng; Wei, Guo-Wei
2012-02-01
Mesh deformation methods are a versatile strategy for solving partial differential equations (PDEs) with a vast variety of practical applications. However, these methods break down for elliptic PDEs with discontinuous coefficients, namely, elliptic interface problems. For this class of problems, the additional interface jump conditions are required to maintain the well-posedness of the governing equation. Consequently, in order to achieve high accuracy and high order convergence, additional numerical algorithms are required to enforce the interface jump conditions in solving elliptic interface problems. The present work introduces an interface technique based adaptively deformed mesh strategy for resolving elliptic interface problems. We take the advantages of the high accuracy, flexibility and robustness of the matched interface and boundary (MIB) method to construct an adaptively deformed mesh based interface method for elliptic equations with discontinuous coefficients. The proposed method generates deformed meshes in the physical domain and solves the transformed governed equations in the computational domain, which maintains regular Cartesian meshes. The mesh deformation is realized by a mesh transformation PDE, which controls the mesh redistribution by a source term. The source term consists of a monitor function, which builds in mesh contraction rules. Both interface geometry based deformed meshes and solution gradient based deformed meshes are constructed to reduce the L(∞) and L(2) errors in solving elliptic interface problems. The proposed adaptively deformed mesh based interface method is extensively validated by many numerical experiments. Numerical results indicate that the adaptively deformed mesh based interface method outperforms the original MIB method for dealing with elliptic interface problems. PMID:22586356
Xia, Kelin; Zhan, Meng; Wan, Decheng; Wei, Guo-Wei
2011-01-01
Mesh deformation methods are a versatile strategy for solving partial differential equations (PDEs) with a vast variety of practical applications. However, these methods break down for elliptic PDEs with discontinuous coefficients, namely, elliptic interface problems. For this class of problems, the additional interface jump conditions are required to maintain the well-posedness of the governing equation. Consequently, in order to achieve high accuracy and high order convergence, additional numerical algorithms are required to enforce the interface jump conditions in solving elliptic interface problems. The present work introduces an interface technique based adaptively deformed mesh strategy for resolving elliptic interface problems. We take the advantages of the high accuracy, flexibility and robustness of the matched interface and boundary (MIB) method to construct an adaptively deformed mesh based interface method for elliptic equations with discontinuous coefficients. The proposed method generates deformed meshes in the physical domain and solves the transformed governed equations in the computational domain, which maintains regular Cartesian meshes. The mesh deformation is realized by a mesh transformation PDE, which controls the mesh redistribution by a source term. The source term consists of a monitor function, which builds in mesh contraction rules. Both interface geometry based deformed meshes and solution gradient based deformed meshes are constructed to reduce the L∞ and L2 errors in solving elliptic interface problems. The proposed adaptively deformed mesh based interface method is extensively validated by many numerical experiments. Numerical results indicate that the adaptively deformed mesh based interface method outperforms the original MIB method for dealing with elliptic interface problems. PMID:22586356
Vortex-dominated conical-flow computations using unstructured adaptively-refined meshes
NASA Technical Reports Server (NTRS)
Batina, John T.
1989-01-01
A conical Euler/Navier-Stokes algorithm is presented for the computation of vortex-dominated flows. The flow solver involves a multistage Runge-Kutta time stepping scheme which uses a finite-volume spatial discretization on an unstructured grid made up of triangles. The algorithm also employs an adaptive mesh refinement procedure which enriches the mesh locally to more accurately resolve the vortical flow features. Results are presented for several highly-swept delta wing and circular cone cases at high angles of attack and at supersonic freestream flow conditions. Accurate solutions were obtained more efficiently when adaptive mesh refinement was used in contrast with refining the grid globally. The paper presents descriptions of the conical Euler/Navier-Stokes flow solver and adaptive mesh refinement procedures along with results which demonstrate the capability.
Split Bregman's algorithm for three-dimensional mesh segmentation
NASA Astrophysics Data System (ADS)
Habiba, Nabi; Ali, Douik
2016-05-01
Variational methods have attracted a lot of attention in the literature, especially for image and mesh segmentation. The methods aim at minimizing the energy to optimize both edge and region detections. We propose a spectral mesh decomposition algorithm to obtain disjoint but meaningful regions of an input mesh. The related optimization problem is nonconvex, and it is very difficult to find a good approximation or global optimum, which represents a challenge in computer vision. We propose an alternating split Bregman algorithm for mesh segmentation, where we extended the image-dedicated model to a three-dimensional (3-D) mesh one. By applying our scheme to 3-D mesh segmentation, we obtain fast solvers that can outperform various conventional ones, such as graph-cut and primal dual methods. A consistent evaluation of the proposed method on various public domain 3-D databases for different metrics is elaborated, and a comparison with the state-of-the-art is performed.
Conditional entropy maximization for PET image reconstruction using adaptive mesh model.
Zhu, Hongqing; Shu, Huazhong; Zhou, Jian; Dai, Xiubin; Luo, Limin
2007-04-01
Iterative image reconstruction algorithms have been widely used in the field of positron emission tomography (PET). However, such algorithms are sensitive to noise artifacts so that the reconstruction begins to degrade when the number of iterations is high. In this paper, we propose a new algorithm to reconstruct an image from the PET emission projection data by using the conditional entropy maximization and the adaptive mesh model. In a traditional tomography reconstruction method, the reconstructed image is directly computed in the pixel domain. Unlike this kind of methods, the proposed approach is performed by estimating the nodal values from the observed projection data in a mesh domain. In our method, the initial Delaunay triangulation mesh is generated from a set of randomly selected pixel points, and it is then modified according to the pixel intensity value of the estimated image at each iteration step in which the conditional entropy maximization is used. The advantage of using the adaptive mesh model for image reconstruction is that it provides a natural spatially adaptive smoothness mechanism. In experiments using the synthetic and clinical data, it is found that the proposed algorithm is more robust to noise compared to the common pixel-based MLEM algorithm and mesh-based MLEM with a fixed mesh structure. PMID:17368841
Structured adaptive mesh refinement on the connection machine
Berger, M.J. . Courant Inst. of Mathematical Sciences); Saltzman, J.S. )
1993-01-01
Adaptive mesh refinement has proven itself to be a useful tool in a large collection of applications. By refining only a small portion of the computational domain, computational savings of up to a factor of 80 in 3 dimensional calculations have been obtained on serial machines. A natural question is, can this algorithm be used on massively parallel machines and still achieve the same efficiencies We have designed a data layout scheme for mapping grid points to processors that preserves locality and minimizes global communication for the CM-200. The effect of the data layout scheme is that at the finest level nearby grid points from adjacent grids in physical space are in adjacent memory locations. Furthermore, coarse grid points are arranged in memory to be near their associated fine grid points. We show applications of the algorithm to inviscid compressible fluid flow in two space dimensions.
Local enhancement and denoising algorithms on arbitrary mesh surfaces
NASA Astrophysics Data System (ADS)
Agaian, Sos S.; Sartor, Richard
2012-06-01
In the process of analyzing the surfaces of 3d scanned objects, it is desirable to perform per-vertex calculations on a region of connected vertices, much in the same way that 2d image filters perform per-pixel calculations on a window of adjacent pixels. Operations such as blurring, averaging, and noise reduction would be useful for these applications, and are already well-established in 2d image enhancement. In this paper, we present a method for adapting simple windowed 2d image processing operations to the problem domain of 3d mesh surfaces. The primary obstacle is that mesh surfaces are usually not flat, and their vertices are usually not arranged in a grid, so adapting the 2d algorithms requires a change of analytical models. First we characterize 2d rectangular arrays as a special case of a graph, with edges between adjacent pixels. Next we treat filter windows as a limitation on the walks from a given source node to every other reachable node in the graph. We tested the common windowed average, weighted average, and median operations. We used 3d meshes comprised of sets of vertices and polygons, modeled as weighted undirected graphs. The edge weights are taken as the Euclidean distance between two vertices, calculated from their XYZ coordinates in the usual way. Our method successfully provides a new way to utilize these existing 2d filters. In addition, further generalizations and applications are discussed, including potential applications in any field that uses graph theory, such as social networking, marketing, telecom networks, epidemiology, and others.
Novel biomedical tetrahedral mesh methods: algorithms and applications
NASA Astrophysics Data System (ADS)
Yu, Xiao; Jin, Yanfeng; Chen, Weitao; Huang, Pengfei; Gu, Lixu
2007-12-01
Tetrahedral mesh generation algorithm, as a prerequisite of many soft tissue simulation methods, becomes very important in the virtual surgery programs because of the real-time requirement. Aiming to speed up the computation in the simulation, we propose a revised Delaunay algorithm which makes a good balance of quality of tetrahedra, boundary preservation and time complexity, with many improved methods. Another mesh algorithm named Space-Disassembling is also presented in this paper, and a comparison of Space-Disassembling, traditional Delaunay algorithm and the revised Delaunay algorithm is processed based on clinical soft-tissue simulation projects, including craniofacial plastic surgery and breast reconstruction plastic surgery.
Adaptive mesh fluid simulations on GPU
NASA Astrophysics Data System (ADS)
Wang, Peng; Abel, Tom; Kaehler, Ralf
2010-10-01
We describe an implementation of compressible inviscid fluid solvers with block-structured adaptive mesh refinement on Graphics Processing Units using NVIDIA's CUDA. We show that a class of high resolution shock capturing schemes can be mapped naturally on this architecture. Using the method of lines approach with the second order total variation diminishing Runge-Kutta time integration scheme, piecewise linear reconstruction, and a Harten-Lax-van Leer Riemann solver, we achieve an overall speedup of approximately 10 times faster execution on one graphics card as compared to a single core on the host computer. We attain this speedup in uniform grid runs as well as in problems with deep AMR hierarchies. Our framework can readily be applied to more general systems of conservation laws and extended to higher order shock capturing schemes. This is shown directly by an implementation of a magneto-hydrodynamic solver and comparing its performance to the pure hydrodynamic case. Finally, we also combined our CUDA parallel scheme with MPI to make the code run on GPU clusters. Close to ideal speedup is observed on up to four GPUs.
Lattice Cleaving: A Multimaterial Tetrahedral Meshing Algorithm with Guarantees
Bronson, Jonathan; Levine, Joshua A.; Whitaker, Ross
2014-01-01
We introduce a new algorithm for generating tetrahedral meshes that conform to physical boundaries in volumetric domains consisting of multiple materials. The proposed method allows for an arbitrary number of materials, produces high-quality tetrahedral meshes with upper and lower bounds on dihedral angles, and guarantees geometric fidelity. Moreover, the method is combinatoric so its implementation enables rapid mesh construction. These meshes are structured in a way that also allows grading, to reduce element counts in regions of homogeneity. Additionally, we provide proofs showing that both element quality and geometric fidelity are bounded using this approach. PMID:24356365
Anisotropic Mesh Adaptivity for Turbulent Flows with Boundary Layers
NASA Astrophysics Data System (ADS)
Chitale, Kedar C.
Turbulent flows are found everywhere in nature and are studied, analyzed and simulated using various experimental and numerical tools. For computational analysis, a variety of turbulence models are available and the accuracy of these models in capturing the phenomenon depends largely on the mesh spacings, especially near the walls, in the boundary layer region. Special semi-structured meshes called "mesh boundary layers" are widely used in the CFD community in simulations of turbulent flows, because of their graded and orthogonal layered structure. They provide an efficient way to achieve very fine and highly anisotropic mesh spacings without introducing poorly shaped elements. Since usually the required mesh spacings to accurately resolve the flow are not known a priori to the simulations, an adaptive approach based on a posteriori error indicators is used to achieve an appropriate mesh. In this study, we apply the adaptive meshing techniques to turbulent flows with a focus on boundary layers. We construct a framework to calculate the critical wall normal mesh spacings inside the boundary layers based on the flow physics and the knowledge of the turbulence model. This approach is combined with numerical error indicators to adapt the entire flow region. We illustrate the effectiveness of this hybrid approach by applying it to three aerodynamic flows and studying their superior performance in capturing the flow structures in detail. We also demonstrate the capabilities of the current developments in parallel boundary layer mesh adaptation by applying them to two internal flow problems. We also study the application of adaptive boundary layer meshes to complex geometries like multi element wings. We highlight the advantage of using such techniques for superior wake and tip region resolution by showcasing flow results. We also outline the future direction for the adaptive meshing techniques to be useful to the large scale flow computations.
Importance of dynamic mesh adaptivity for simulation of viscous fingering in porous media
NASA Astrophysics Data System (ADS)
Mostaghimi, P.; Jackson, M.; Pain, C.; Gorman, G.
2014-12-01
Viscous fingering is a major concern in many natural and engineered processes such as water flooding of heavy-oil reservoirs. Common reservoir simulators employ low-order finite volume/difference methods on structured grids to resolve this phenomenon. However, their approach suffers from a significant numerical dispersion error along the fingering patterns due to insufficient mesh resolution and smears out some important features of the flow. We propose use of an unstructured control volume finite element method for simulation of viscous fingering in porous media. Our approach is equipped with anisotropic mesh adaptivity where the mesh resolution is optimized based on the evolving features of flow. The adaptive algorithm uses a metric tensor field based on solution error estimates to locally control the size and shape of elements in the metric. We resolve the viscous fingering patterns accurately and reduce the numerical dispersion error significantly. The mesh optimization, generates an unstructured coarse mesh in other regions of the computational domain which significantly decreases the computational cost. The effect of grid resolution on the resolved fingers is thoroughly investigated. We analyze the computational cost of mesh adaptivty on unstructured mesh and compare it with common finite volume methods. The results of this study suggests that mesh adaptivity is an efficient and accurate approach for resolving complex behaviors and instabilities of flow in porous media such as viscous fingering.
NASA Astrophysics Data System (ADS)
Lee, W. H.; Kim, T.-S.; Cho, M. H.; Ahn, Y. B.; Lee, S. Y.
2006-12-01
In studying bioelectromagnetic problems, finite element analysis (FEA) offers several advantages over conventional methods such as the boundary element method. It allows truly volumetric analysis and incorporation of material properties such as anisotropic conductivity. For FEA, mesh generation is the first critical requirement and there exist many different approaches. However, conventional approaches offered by commercial packages and various algorithms do not generate content-adaptive meshes (cMeshes), resulting in numerous nodes and elements in modelling the conducting domain, and thereby increasing computational load and demand. In this work, we present efficient content-adaptive mesh generation schemes for complex biological volumes of MR images. The presented methodology is fully automatic and generates FE meshes that are adaptive to the geometrical contents of MR images, allowing optimal representation of conducting domain for FEA. We have also evaluated the effect of cMeshes on FEA in three dimensions by comparing the forward solutions from various cMesh head models to the solutions from the reference FE head model in which fine and equidistant FEs constitute the model. The results show that there is a significant gain in computation time with minor loss in numerical accuracy. We believe that cMeshes should be useful in the FEA of bioelectromagnetic problems.
PARAMESH: A Parallel Adaptive Mesh Refinement Community Toolkit
NASA Technical Reports Server (NTRS)
MacNeice, Peter; Olson, Kevin M.; Mobarry, Clark; deFainchtein, Rosalinda; Packer, Charles
1999-01-01
In this paper, we describe a community toolkit which is designed to provide parallel support with adaptive mesh capability for a large and important class of computational models, those using structured, logically cartesian meshes. The package of Fortran 90 subroutines, called PARAMESH, is designed to provide an application developer with an easy route to extend an existing serial code which uses a logically cartesian structured mesh into a parallel code with adaptive mesh refinement. Alternatively, in its simplest use, and with minimal effort, it can operate as a domain decomposition tool for users who want to parallelize their serial codes, but who do not wish to use adaptivity. The package can provide them with an incremental evolutionary path for their code, converting it first to uniformly refined parallel code, and then later if they so desire, adding adaptivity.
Ibrahim, Ahmad M.; Wilson, Paul P.H.; Sawan, Mohamed E.; Mosher, Scott W.; Peplow, Douglas E.; Wagner, John C.; Evans, Thomas M.; Grove, Robert E.
2015-06-30
The CADIS and FW-CADIS hybrid Monte Carlo/deterministic techniques dramatically increase the efficiency of neutronics modeling, but their use in the accurate design analysis of very large and geometrically complex nuclear systems has been limited by the large number of processors and memory requirements for their preliminary deterministic calculations and final Monte Carlo calculation. Three mesh adaptivity algorithms were developed to reduce the memory requirements of CADIS and FW-CADIS without sacrificing their efficiency improvement. First, a macromaterial approach enhances the fidelity of the deterministic models without changing the mesh. Second, a deterministic mesh refinement algorithm generates meshes that capture as muchmore » geometric detail as possible without exceeding a specified maximum number of mesh elements. Finally, a weight window coarsening algorithm decouples the weight window mesh and energy bins from the mesh and energy group structure of the deterministic calculations in order to remove the memory constraint of the weight window map from the deterministic mesh resolution. The three algorithms were used to enhance an FW-CADIS calculation of the prompt dose rate throughout the ITER experimental facility. Using these algorithms resulted in a 23.3% increase in the number of mesh tally elements in which the dose rates were calculated in a 10-day Monte Carlo calculation and, additionally, increased the efficiency of the Monte Carlo simulation by a factor of at least 3.4. The three algorithms enabled this difficult calculation to be accurately solved using an FW-CADIS simulation on a regular computer cluster, eliminating the need for a world-class super computer.« less
Ibrahim, Ahmad M.; Wilson, Paul P.H.; Sawan, Mohamed E.; Mosher, Scott W.; Peplow, Douglas E.; Wagner, John C.; Evans, Thomas M.; Grove, Robert E.
2015-06-30
The CADIS and FW-CADIS hybrid Monte Carlo/deterministic techniques dramatically increase the efficiency of neutronics modeling, but their use in the accurate design analysis of very large and geometrically complex nuclear systems has been limited by the large number of processors and memory requirements for their preliminary deterministic calculations and final Monte Carlo calculation. Three mesh adaptivity algorithms were developed to reduce the memory requirements of CADIS and FW-CADIS without sacrificing their efficiency improvement. First, a macromaterial approach enhances the fidelity of the deterministic models without changing the mesh. Second, a deterministic mesh refinement algorithm generates meshes that capture as much geometric detail as possible without exceeding a specified maximum number of mesh elements. Finally, a weight window coarsening algorithm decouples the weight window mesh and energy bins from the mesh and energy group structure of the deterministic calculations in order to remove the memory constraint of the weight window map from the deterministic mesh resolution. The three algorithms were used to enhance an FW-CADIS calculation of the prompt dose rate throughout the ITER experimental facility. Using these algorithms resulted in a 23.3% increase in the number of mesh tally elements in which the dose rates were calculated in a 10-day Monte Carlo calculation and, additionally, increased the efficiency of the Monte Carlo simulation by a factor of at least 3.4. The three algorithms enabled this difficult calculation to be accurately solved using an FW-CADIS simulation on a regular computer cluster, eliminating the need for a world-class super computer.
Anisotropic adaptive mesh generation in two dimensions for CFD
Borouchaki, H.; Castro-Diaz, M.J.; George, P.L.; Hecht, F.; Mohammadi, B.
1996-12-31
This paper describes the extension of the classical Delaunay method in the case where anisotropic meshes are required such as in CFD when the modelized physic is strongly directional. The way in which such a mesh generation method can be incorporated in an adaptative loop of CFD as well as the case of multicriterium adaptation are discussed. Several concrete application examples are provided to illustrate the capabilities of the proposed method.
Parallel adaptive mesh refinement for electronic structure calculations
Kohn, S.; Weare, J.; Ong, E.; Baden, S.
1996-12-01
We have applied structured adaptive mesh refinement techniques to the solution of the LDA equations for electronic structure calculations. Local spatial refinement concentrates memory resources and numerical effort where it is most needed, near the atomic centers and in regions of rapidly varying charge density. The structured grid representation enables us to employ efficient iterative solver techniques such as conjugate gradients with multigrid preconditioning. We have parallelized our solver using an object-oriented adaptive mesh refinement framework.
A simple adaptive mesh generator for 2-D finite element calculations
Fernandez, F.A.; Yong, Y.C.; Ettinger, R.D. )
1993-03-01
A strategy for adaptive mesh generation is proposed. The method consists of the use of a suitably defined density function', which can either be defined by the user or be calculated from a previous approximate solution, to guide the generation of a new mesh. This new mesh is built starting from a minimal number of triangular elements which are then in several sweeps, repeatedly refined according to the density function. The Delaunay algorithm is used in each stage to keep the shape of the triangles as equilateral as possible.
Parallel algorithms for line detection on a mesh
Guerra, C.; Hambrusch, S. . Dept. of Computer Science)
1989-02-01
The authors consider the problems of detecting lines in an n x n image on an n x n mesh of processors. They present two new and efficient parallel algorithms which detect lines by performing a Hough transform. Both algorithms perform only simple data movement operations over relatively short distances.
Free Mesh Method: fundamental conception, algorithms and accuracy study
YAGAWA, Genki
2011-01-01
The finite element method (FEM) has been commonly employed in a variety of fields as a computer simulation method to solve such problems as solid, fluid, electro-magnetic phenomena and so on. However, creation of a quality mesh for the problem domain is a prerequisite when using FEM, which becomes a major part of the cost of a simulation. It is natural that the concept of meshless method has evolved. The free mesh method (FMM) is among the typical meshless methods intended for particle-like finite element analysis of problems that are difficult to handle using global mesh generation, especially on parallel processors. FMM is an efficient node-based finite element method that employs a local mesh generation technique and a node-by-node algorithm for the finite element calculations. In this paper, FMM and its variation are reviewed focusing on their fundamental conception, algorithms and accuracy. PMID:21558752
Zonal multigrid solution of compressible flow problems on unstructured and adaptive meshes
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1989-01-01
The simultaneous use of adaptive meshing techniques with a multigrid strategy for solving the 2-D Euler equations in the context of unstructured meshes is studied. To obtain optimal efficiency, methods capable of computing locally improved solutions without recourse to global recalculations are pursued. A method for locally refining an existing unstructured mesh, without regenerating a new global mesh is employed, and the domain is automatically partitioned into refined and unrefined regions. Two multigrid strategies are developed. In the first, time-stepping is performed on a global fine mesh covering the entire domain, and convergence acceleration is achieved through the use of zonal coarse grid accelerator meshes, which lie under the adaptively refined regions of the global fine mesh. Both schemes are shown to produce similar convergence rates to each other, and also with respect to a previously developed global multigrid algorithm, which performs time-stepping throughout the entire domain, on each mesh level. However, the present schemes exhibit higher computational efficiency due to the smaller number of operations on each level.
CONSTRAINED-TRANSPORT MAGNETOHYDRODYNAMICS WITH ADAPTIVE MESH REFINEMENT IN CHARM
Miniati, Francesco; Martin, Daniel F. E-mail: DFMartin@lbl.gov
2011-07-01
We present the implementation of a three-dimensional, second-order accurate Godunov-type algorithm for magnetohydrodynamics (MHD) in the adaptive-mesh-refinement (AMR) cosmological code CHARM. The algorithm is based on the full 12-solve spatially unsplit corner-transport-upwind (CTU) scheme. The fluid quantities are cell-centered and are updated using the piecewise-parabolic method (PPM), while the magnetic field variables are face-centered and are evolved through application of the Stokes theorem on cell edges via a constrained-transport (CT) method. The so-called multidimensional MHD source terms required in the predictor step for high-order accuracy are applied in a simplified form which reduces their complexity in three dimensions without loss of accuracy or robustness. The algorithm is implemented on an AMR framework which requires specific synchronization steps across refinement levels. These include face-centered restriction and prolongation operations and a reflux-curl operation, which maintains a solenoidal magnetic field across refinement boundaries. The code is tested against a large suite of test problems, including convergence tests in smooth flows, shock-tube tests, classical two- and three-dimensional MHD tests, a three-dimensional shock-cloud interaction problem, and the formation of a cluster of galaxies in a fully cosmological context. The magnetic field divergence is shown to remain negligible throughout.
Constrained-transport Magnetohydrodynamics with Adaptive Mesh Refinement in CHARM
NASA Astrophysics Data System (ADS)
Miniati, Francesco; Martin, Daniel F.
2011-07-01
We present the implementation of a three-dimensional, second-order accurate Godunov-type algorithm for magnetohydrodynamics (MHD) in the adaptive-mesh-refinement (AMR) cosmological code CHARM. The algorithm is based on the full 12-solve spatially unsplit corner-transport-upwind (CTU) scheme. The fluid quantities are cell-centered and are updated using the piecewise-parabolic method (PPM), while the magnetic field variables are face-centered and are evolved through application of the Stokes theorem on cell edges via a constrained-transport (CT) method. The so-called multidimensional MHD source terms required in the predictor step for high-order accuracy are applied in a simplified form which reduces their complexity in three dimensions without loss of accuracy or robustness. The algorithm is implemented on an AMR framework which requires specific synchronization steps across refinement levels. These include face-centered restriction and prolongation operations and a reflux-curl operation, which maintains a solenoidal magnetic field across refinement boundaries. The code is tested against a large suite of test problems, including convergence tests in smooth flows, shock-tube tests, classical two- and three-dimensional MHD tests, a three-dimensional shock-cloud interaction problem, and the formation of a cluster of galaxies in a fully cosmological context. The magnetic field divergence is shown to remain negligible throughout.
Adaptive mesh refinement and adjoint methods in geophysics simulations
NASA Astrophysics Data System (ADS)
Burstedde, Carsten
2013-04-01
It is an ongoing challenge to increase the resolution that can be achieved by numerical geophysics simulations. This applies to considering sub-kilometer mesh spacings in global-scale mantle convection simulations as well as to using frequencies up to 1 Hz in seismic wave propagation simulations. One central issue is the numerical cost, since for three-dimensional space discretizations, possibly combined with time stepping schemes, a doubling of resolution can lead to an increase in storage requirements and run time by factors between 8 and 16. A related challenge lies in the fact that an increase in resolution also increases the dimensionality of the model space that is needed to fully parametrize the physical properties of the simulated object (a.k.a. earth). Systems that exhibit a multiscale structure in space are candidates for employing adaptive mesh refinement, which varies the resolution locally. An example that we found well suited is the mantle, where plate boundaries and fault zones require a resolution on the km scale, while deeper area can be treated with 50 or 100 km mesh spacings. This approach effectively reduces the number of computational variables by several orders of magnitude. While in this case it is possible to derive the local adaptation pattern from known physical parameters, it is often unclear what are the most suitable criteria for adaptation. We will present the goal-oriented error estimation procedure, where such criteria are derived from an objective functional that represents the observables to be computed most accurately. Even though this approach is well studied, it is rarely used in the geophysics community. A related strategy to make finer resolution manageable is to design methods that automate the inference of model parameters. Tweaking more than a handful of numbers and judging the quality of the simulation by adhoc comparisons to known facts and observations is a tedious task and fundamentally limited by the turnaround times
A flexible unstructured mesh generation algorithm suitable for block partitioning
Karamete, B.K.
1996-12-31
This paper describes the logic of a dynamic algorithm for an arbitrarily prescribed geometry. The generated meshes show Delaunay property both in 2D and 3D. The algorithm requires minimal surface information in 3D. The surface triangles appear as the direct consequence of interior tetrahedration. The adopted successive refinement scheme results in such a node distribution that it is not needed to check boundary conformity. Further computational saving is provided by using a special binary tree (ADT). The generating front can not be determined a-priori as opposed to the moving front techniques. This feature can effectively be used to partition the geometry into equal element sized blocks while generating the mesh for parallel computing purposes. The algorithm shows flexibility to split the geometry into blocks at mesh generation time.
Progress in integrated analysis with adaptive unstructured meshing
NASA Technical Reports Server (NTRS)
Dechaumphai, Pramote
1992-01-01
Design of lightweight structures and thermal protection systems for hypersonic vehicles depend on accurate prediction of aerothermal loads, structural temperatures and their gradients, and structural deformations and stresses. Concentration is on an alternative meshing technique which generates an entirely new adaptive unstructured mesh based on the solution obtained from the earlier mesh. The technique combined with the finite element method has been shown to significantly improve the efficiency and accuracy of the fluid, thermal, and structural analyses. Current capability of the adaptive unstructured meshing technique for the integrated fluid-thermal-structural analysis is described first. The technique was extended to transient thermal analysis of structures with time-dependent adaptive meshing to capture the detailed temperature response with a minimum number of unknowns and computational cost. Both linear and higher-order finite elements are implemented to demonstrate the generality of the technique and to investigate their solution accuracy. Currently, the adaptive meshing technique is being developed for plane structures that can be modeled with membrane elements and built-up structures modeled with membrane and bending elements. The capability of the technique to these different disciplinary problems is demonstrated by several examples.
Structured Adaptive Mesh Refinement Application Infrastructure
Energy Science and Technology Software Center (ESTSC)
2010-07-15
SAMRAI is an object-oriented support library for structured adaptice mesh refinement (SAMR) simulation of computational science problems, modeled by systems of partial differential equations (PDEs). SAMRAI is developed and maintained in the Center for Applied Scientific Computing (CASC) under ASCI ITS and PSE support. SAMRAI is used in a variety of application research efforts at LLNL and in academia. These applications are developed in collaboration with SAMRAI development team members.
Adaptive mesh generation for viscous flows using Delaunay triangulation
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1988-01-01
A method for generating an unstructured triangular mesh in two dimensions, suitable for computing high Reynolds number flows over arbitrary configurations is presented. The method is based on a Delaunay triangulation, which is performed in a locally stretched space, in order to obtain very high aspect ratio triangles in the boundary layer and the wake regions. It is shown how the method can be coupled with an unstructured Navier-Stokes solver to produce a solution adaptive mesh generation procedure for viscous flows.
Patch-based Adaptive Mesh Refinement for Multimaterial Hydrodynamics
Lomov, I; Pember, R; Greenough, J; Liu, B
2005-10-18
We present a patch-based direct Eulerian adaptive mesh refinement (AMR) algorithm for modeling real equation-of-state, multimaterial compressible flow with strength. Our approach to AMR uses a hierarchical, structured grid approach first developed by (Berger and Oliger 1984), (Berger and Oliger 1984). The grid structure is dynamic in time and is composed of nested uniform rectangular grids of varying resolution. The integration scheme on the grid hierarchy is a recursive procedure in which the coarse grids are advanced, then the fine grids are advanced multiple steps to reach the same time, and finally the coarse and fine grids are synchronized to remove conservation errors during the separate advances. The methodology presented here is based on a single grid algorithm developed for multimaterial gas dynamics by (Colella et al. 1993), refined by(Greenough et al. 1995), and extended to the solution of solid mechanics problems with significant strength by (Lomov and Rubin 2003). The single grid algorithm uses a second-order Godunov scheme with an approximate single fluid Riemann solver and a volume-of-fluid treatment of material interfaces. The method also uses a non-conservative treatment of the deformation tensor and an acoustic approximation for shear waves in the Riemann solver. This departure from a strict application of the higher-order Godunov methodology to the equation of solid mechanics is justified due to the fact that highly nonlinear behavior of shear stresses is rare. This algorithm is implemented in two codes, Geodyn and Raptor, the latter of which is a coupled rad-hydro code. The present discussion will be solely concerned with hydrodynamics modeling. Results from a number of simulations for flows with and without strength will be presented.
A Numerical Study of Mesh Adaptivity in Multiphase Flows with Non-Newtonian Fluids
NASA Astrophysics Data System (ADS)
Percival, James; Pavlidis, Dimitrios; Xie, Zhihua; Alberini, Federico; Simmons, Mark; Pain, Christopher; Matar, Omar
2014-11-01
We present an investigation into the computational efficiency benefits of dynamic mesh adaptivity in the numerical simulation of transient multiphase fluid flow problems involving Non-Newtonian fluids. Such fluids appear in a range of industrial applications, from printing inks to toothpastes and introduce new challenges for mesh adaptivity due to the additional ``memory'' of viscoelastic fluids. Nevertheless, the multiscale nature of these flows implies huge potential benefits for a successful implementation. The study is performed using the open source package Fluidity, which couples an unstructured mesh control volume finite element solver for the multiphase Navier-Stokes equations to a dynamic anisotropic mesh adaptivity algorithm, based on estimated solution interpolation error criteria, and conservative mesh-to-mesh interpolation routine. The code is applied to problems involving rheologies ranging from simple Newtonian to shear-thinning to viscoelastic materials and verified against experimental data for various industrial and microfluidic flows. This work was undertaken as part of the EPSRC MEMPHIS programme grant EP/K003976/1.
Multigrid solution of internal flows using unstructured solution adaptive meshes
NASA Astrophysics Data System (ADS)
Smith, Wayne A.; Blake, Kenneth R.
1992-11-01
This is the final report of the NASA Lewis SBIR Phase 2 Contract Number NAS3-25785, Multigrid Solution of Internal Flows Using Unstructured Solution Adaptive Meshes. The objective of this project, as described in the Statement of Work, is to develop and deliver to NASA a general three-dimensional Navier-Stokes code using unstructured solution-adaptive meshes for accuracy and multigrid techniques for convergence acceleration. The code will primarily be applied, but not necessarily limited, to high speed internal flows in turbomachinery.
Conservative Patch Algorithm and Mesh Sequencing for PAB3D
NASA Technical Reports Server (NTRS)
Pao, S. P.; Abdol-Hamid, K. S.
2005-01-01
A mesh-sequencing algorithm and a conservative patched-grid-interface algorithm (hereafter Patch Algorithm ) have been incorporated into the PAB3D code, which is a computer program that solves the Navier-Stokes equations for the simulation of subsonic, transonic, or supersonic flows surrounding an aircraft or other complex aerodynamic shapes. These algorithms are efficient, flexible, and have added tremendously to the capabilities of PAB3D. The mesh-sequencing algorithm makes it possible to perform preliminary computations using only a fraction of the grid cells (provided the original cell count is divisible by an integer) along any grid coordinate axis, independently of the other axes. The patch algorithm addresses another critical need in multi-block grid situation where the cell faces of adjacent grid blocks may not coincide, leading to errors in calculating fluxes of conserved physical quantities across interfaces between the blocks. The patch algorithm, based on the Stokes integral formulation of the applicable conservation laws, effectively matches each of the interfacial cells on one side of the block interface to the corresponding fractional cell area pieces on the other side. This approach is comprehensive and unified such that all interface topology is automatically processed without user intervention. This algorithm is implemented in a preprocessing code that creates a cell-by-cell database that will maintain flux conservation at any level of full or reduced grid density as the user may choose by way of the mesh-sequencing algorithm. These two algorithms have enhanced the numerical accuracy of the code, reduced the time and effort for grid preprocessing, and provided users with the flexibility of performing computations at any desired full or reduced grid resolution to suit their specific computational requirements.
Crane, N K; Parsons, I D; Hjelmstad, K D
2002-03-21
Adaptive mesh refinement selectively subdivides the elements of a coarse user supplied mesh to produce a fine mesh with reduced discretization error. Effective use of adaptive mesh refinement coupled with an a posteriori error estimator can produce a mesh that solves a problem to a given discretization error using far fewer elements than uniform refinement. A geometric multigrid solver uses increasingly finer discretizations of the same geometry to produce a very fast and numerically scalable solution to a set of linear equations. Adaptive mesh refinement is a natural method for creating the different meshes required by the multigrid solver. This paper describes the implementation of a scalable adaptive multigrid method on a distributed memory parallel computer. Results are presented that demonstrate the parallel performance of the methodology by solving a linear elastic rocket fuel deformation problem on an SGI Origin 3000. Two challenges must be met when implementing adaptive multigrid algorithms on massively parallel computing platforms. First, although the fine mesh for which the solution is desired may be large and scaled to the number of processors, the multigrid algorithm must also operate on much smaller fixed-size data sets on the coarse levels. Second, the mesh must be repartitioned as it is adapted to maintain good load balancing. In an adaptive multigrid algorithm, separate mesh levels may require separate partitioning, further complicating the load balance problem. This paper shows that, when the proper optimizations are made, parallel adaptive multigrid algorithms perform well on machines with several hundreds of processors.
PARAMESH V4.1: Parallel Adaptive Mesh Refinement
NASA Astrophysics Data System (ADS)
MacNeice, Peter; Olson, Kevin M.; Mobarry, Clark; de Fainchtein, Rosalinda; Packer, Charles
2011-06-01
PARAMESH is a package of Fortran 90 subroutines designed to provide an application developer with an easy route to extend an existing serial code which uses a logically cartesian structured mesh into a parallel code with adaptive mesh refinement (AMR). Alternatively, in its simplest use, and with minimal effort, it can operate as a domain decomposition tool for users who want to parallelize their serial codes, but who do not wish to use adaptivity. The package builds a hierarchy of sub-grids to cover the computational domain, with spatial resolution varying to satisfy the demands of the application. These sub-grid blocks form the nodes of a tree data-structure (quad-tree in 2D or oct-tree in 3D). Each grid block has a logically cartesian mesh. The package supports 1, 2 and 3D models. PARAMESH is released under the NASA-wide Open-Source software license.
Hornung, R.D.
1996-12-31
An adaptive local mesh refinement (AMR) algorithm originally developed for unsteady gas dynamics is extended to multi-phase flow in porous media. Within the AMR framework, we combine specialized numerical methods to treat the different aspects of the partial differential equations. Multi-level iteration and domain decomposition techniques are incorporated to accommodate elliptic/parabolic behavior. High-resolution shock capturing schemes are used in the time integration of the hyperbolic mass conservation equations. When combined with AMR, these numerical schemes provide high resolution locally in a more efficient manner than if they were applied on a uniformly fine computational mesh. We will discuss the interplay of physical, mathematical, and numerical concerns in the application of adaptive mesh refinement to flow in porous media problems of practical interest.
Numerical study of Taylor bubbles with adaptive unstructured meshes
NASA Astrophysics Data System (ADS)
Xie, Zhihua; Pavlidis, Dimitrios; Percival, James; Pain, Chris; Matar, Omar; Hasan, Abbas; Azzopardi, Barry
2014-11-01
The Taylor bubble is a single long bubble which nearly fills the entire cross section of a liquid-filled circular tube. This type of bubble flow regime often occurs in gas-liquid slug flows in many industrial applications, including oil-and-gas production, chemical and nuclear reactors, and heat exchangers. The objective of this study is to investigate the fluid dynamics of Taylor bubbles rising in a vertical pipe filled with oils of extremely high viscosity (mimicking the ``heavy oils'' found in the oil-and-gas industry). A modelling and simulation framework is presented here which can modify and adapt anisotropic unstructured meshes to better represent the underlying physics of bubble rise and reduce the computational effort without sacrificing accuracy. The numerical framework consists of a mixed control-volume and finite-element formulation, a ``volume of fluid''-type method for the interface capturing based on a compressive control volume advection method, and a force-balanced algorithm for the surface tension implementation. Numerical examples of some benchmark tests and the dynamics of Taylor bubbles are presented to show the capability of this method. EPSRC Programme Grant, MEMPHIS, EP/K0039761/1.
Applications of automatic mesh generation and adaptive methods in computational medicine
Schmidt, J.A.; Macleod, R.S.; Johnson, C.R.; Eason, J.C.
1995-12-31
Important problems in Computational Medicine exist that can benefit from the implementation of adaptive mesh refinement techniques. Biological systems are so inherently complex that only efficient models running on state of the art hardware can begin to simulate reality. To tackle the complex geometries associated with medical applications we present a general purpose mesh generation scheme based upon the Delaunay tessellation algorithm and an iterative point generator. In addition, automatic, two- and three-dimensional adaptive mesh refinement methods are presented that are derived from local and global estimates of the finite element error. Mesh generation and adaptive refinement techniques are utilized to obtain accurate approximations of bioelectric fields within anatomically correct models of the heart and human thorax. Specifically, we explore the simulation of cardiac defibrillation and the general forward and inverse problems in electrocardiography (ECG). Comparisons between uniform and adaptive refinement techniques are made to highlight the computational efficiency and accuracy of adaptive methods in the solution of field problems in computational medicine.
Numerical simulation of immiscible viscous fingering using adaptive unstructured meshes
NASA Astrophysics Data System (ADS)
Adam, A.; Salinas, P.; Percival, J. R.; Pavlidis, D.; Pain, C.; Muggeridge, A. H.; Jackson, M.
2015-12-01
Displacement of one fluid by another in porous media occurs in various settings including hydrocarbon recovery, CO2 storage and water purification. When the invading fluid is of lower viscosity than the resident fluid, the displacement front is subject to a Saffman-Taylor instability and is unstable to transverse perturbations. These instabilities can grow, leading to fingering of the invading fluid. Numerical simulation of viscous fingering is challenging. The physics is controlled by a complex interplay of viscous and diffusive forces and it is necessary to ensure physical diffusion dominates numerical diffusion to obtain converged solutions. This typically requires the use of high mesh resolution and high order numerical methods. This is computationally expensive. We demonstrate here the use of a novel control volume - finite element (CVFE) method along with dynamic unstructured mesh adaptivity to simulate viscous fingering with higher accuracy and lower computational cost than conventional methods. Our CVFE method employs a discontinuous representation for both pressure and velocity, allowing the use of smaller control volumes (CVs). This yields higher resolution of the saturation field which is represented CV-wise. Moreover, dynamic mesh adaptivity allows high mesh resolution to be employed where it is required to resolve the fingers and lower resolution elsewhere. We use our results to re-examine the existing criteria that have been proposed to govern the onset of instability.Mesh adaptivity requires the mapping of data from one mesh to another. Conventional methods such as consistent interpolation do not readily generalise to discontinuous fields and are non-conservative. We further contribute a general framework for interpolation of CV fields by Galerkin projection. The method is conservative, higher order and yields improved results, particularly with higher order or discontinuous elements where existing approaches are often excessively diffusive.
Adaptive mesh refinement for 1-dimensional gas dynamics
Hedstrom, G.; Rodrigue, G.; Berger, M.; Oliger, J.
1982-01-01
We consider the solution of the one-dimensional equation of gas-dynamics. Accurate numerical solutions are difficult to obtain on a given spatial mesh because of the existence of physical regions where components of the exact solution are either discontinuous or have large gradient changes. Numerical methods treat these phenomena in a variety of ways. In this paper, the method of adaptive mesh refinement is used. A thorough description of this method for general hyperbolic systems is given elsewhere and only properties of the method pertinent to the system are elaborated.
PLUM: Parallel Load Balancing for Adaptive Unstructured Meshes
NASA Technical Reports Server (NTRS)
Oliker, Leonid; Biswas, Rupak; Saini, Subhash (Technical Monitor)
1998-01-01
Mesh adaption is a powerful tool for efficient unstructured-grid computations but causes load imbalance among processors on a parallel machine. We present a novel method called PLUM to dynamically balance the processor workloads with a global view. This paper presents the implementation and integration of all major components within our dynamic load balancing strategy for adaptive grid calculations. Mesh adaption, repartitioning, processor assignment, and remapping are critical components of the framework that must be accomplished rapidly and efficiently so as not to cause a significant overhead to the numerical simulation. A data redistribution model is also presented that predicts the remapping cost on the SP2. This model is required to determine whether the gain from a balanced workload distribution offsets the cost of data movement. Results presented in this paper demonstrate that PLUM is an effective dynamic load balancing strategy which remains viable on a large number of processors.
One-node coarse-mesh finite difference algorithm for fine-mesh finite difference operator
Shin, H.C.; Kim, Y.H.; Kim, Y.B.
1999-07-01
This paper is concerned with speeding up the convergence of the fine-mesh finite difference (FMFD) method for the neutron diffusion problem. The basic idea of the new algorithm originates from the two-node coarse-mesh finite difference (CMFD) schemes for nodal methods, where the low-order CMFD operator is iteratively corrected through a global-local iteration so that the final solution of the CMFD problem is equivalent to the high-order nodal solution. Unlike conventional CMFD methods, the new CMFD algorithm is based on one-node local problems, and the high-order solution over the local problem is determined by using the FMFD operator. Nonlinear coupling of CMFD and FMFD operators was previously studied by Aragones and Ahnert. But, in their work, the coarse-mesh operator is corrected by the so-called flux discontinuity factors, and the local problem is defined differently in the sense of boundary conditions and the core dissection scheme.
Adaptive mesh strategies for the spectral element method
NASA Technical Reports Server (NTRS)
Mavriplis, Catherine
1992-01-01
An adaptive spectral method was developed for the efficient solution of time dependent partial differential equations. Adaptive mesh strategies that include resolution refinement and coarsening by three different methods are illustrated on solutions to the 1-D viscous Burger equation and the 2-D Navier-Stokes equations for driven flow in a cavity. Sharp gradients, singularities, and regions of poor resolution are resolved optimally as they develop in time using error estimators which indicate the choice of refinement to be used. The adaptive formulation presents significant increases in efficiency, flexibility, and general capabilities for high order spectral methods.
Parallel 3D Mortar Element Method for Adaptive Nonconforming Meshes
NASA Technical Reports Server (NTRS)
Feng, Huiyu; Mavriplis, Catherine; VanderWijngaart, Rob; Biswas, Rupak
2004-01-01
High order methods are frequently used in computational simulation for their high accuracy. An efficient way to avoid unnecessary computation in smooth regions of the solution is to use adaptive meshes which employ fine grids only in areas where they are needed. Nonconforming spectral elements allow the grid to be flexibly adjusted to satisfy the computational accuracy requirements. The method is suitable for computational simulations of unsteady problems with very disparate length scales or unsteady moving features, such as heat transfer, fluid dynamics or flame combustion. In this work, we select the Mark Element Method (MEM) to handle the non-conforming interfaces between elements. A new technique is introduced to efficiently implement MEM in 3-D nonconforming meshes. By introducing an "intermediate mortar", the proposed method decomposes the projection between 3-D elements and mortars into two steps. In each step, projection matrices derived in 2-D are used. The two-step method avoids explicitly forming/deriving large projection matrices for 3-D meshes, and also helps to simplify the implementation. This new technique can be used for both h- and p-type adaptation. This method is applied to an unsteady 3-D moving heat source problem. With our new MEM implementation, mesh adaptation is able to efficiently refine the grid near the heat source and coarsen the grid once the heat source passes. The savings in computational work resulting from the dynamic mesh adaptation is demonstrated by the reduction of the the number of elements used and CPU time spent. MEM and mesh adaptation, respectively, bring irregularity and dynamics to the computer memory access pattern. Hence, they provide a good way to gauge the performance of computer systems when running scientific applications whose memory access patterns are irregular and unpredictable. We select a 3-D moving heat source problem as the Unstructured Adaptive (UA) grid benchmark, a new component of the NAS Parallel
Parallel Block Structured Adaptive Mesh Refinement on Graphics Processing Units
Beckingsale, D. A.; Gaudin, W. P.; Hornung, R. D.; Gunney, B. T.; Gamblin, T.; Herdman, J. A.; Jarvis, S. A.
2014-11-17
Block-structured adaptive mesh refinement is a technique that can be used when solving partial differential equations to reduce the number of zones necessary to achieve the required accuracy in areas of interest. These areas (shock fronts, material interfaces, etc.) are recursively covered with finer mesh patches that are grouped into a hierarchy of refinement levels. Despite the potential for large savings in computational requirements and memory usage without a corresponding reduction in accuracy, AMR adds overhead in managing the mesh hierarchy, adding complex communication and data movement requirements to a simulation. In this paper, we describe the design and implementation of a native GPU-based AMR library, including: the classes used to manage data on a mesh patch, the routines used for transferring data between GPUs on different nodes, and the data-parallel operators developed to coarsen and refine mesh data. We validate the performance and accuracy of our implementation using three test problems and two architectures: an eight-node cluster, and over four thousand nodes of Oak Ridge National Laboratory’s Titan supercomputer. Our GPU-based AMR hydrodynamics code performs up to 4.87× faster than the CPU-based implementation, and has been scaled to over four thousand GPUs using a combination of MPI and CUDA.
Particle systems for adaptive, isotropic meshing of CAD models
Levine, Joshua A.; Whitaker, Ross T.
2012-01-01
We present a particle-based approach for generating adaptive triangular surface and tetrahedral volume meshes from computer-aided design models. Input shapes are treated as a collection of smooth, parametric surface patches that can meet non-smoothly on boundaries. Our approach uses a hierarchical sampling scheme that places particles on features in order of increasing dimensionality. These particles reach a good distribution by minimizing an energy computed in 3D world space, with movements occurring in the parametric space of each surface patch. Rather than using a pre-computed measure of feature size, our system automatically adapts to both curvature as well as a notion of topological separation. It also enforces a measure of smoothness on these constraints to construct a sizing field that acts as a proxy to piecewise-smooth feature size. We evaluate our technique with comparisons against other popular triangular meshing techniques for this domain. PMID:23162181
Boltzmann Solver with Adaptive Mesh in Velocity Space
Kolobov, Vladimir I.; Arslanbekov, Robert R.; Frolova, Anna A.
2011-05-20
We describe the implementation of direct Boltzmann solver with Adaptive Mesh in Velocity Space (AMVS) using quad/octree data structure. The benefits of the AMVS technique are demonstrated for the charged particle transport in weakly ionized plasmas where the collision integral is linear. We also describe the implementation of AMVS for the nonlinear Boltzmann collision integral. Test computations demonstrate both advantages and deficiencies of the current method for calculations of narrow-kernel distributions.
New methods and astrophysical applications of adaptive mesh fluid simulations
NASA Astrophysics Data System (ADS)
Wang, Peng
The formation of stars, galaxies and supermassive black holes are among the most interesting unsolved problems in astrophysics. Those problems are highly nonlinear and involve enormous dynamical ranges. Thus numerical simulations with spatial adaptivity are crucial in understanding those processes. In this thesis, we discuss the development and application of adaptive mesh refinement (AMR) multi-physics fluid codes to simulate those nonlinear structure formation problems. To simulate the formation of star clusters, we have developed an AMR magnetohydrodynamics (MHD) code, coupled with radiative cooling. We have also developed novel algorithms for sink particle creation, accretion, merging and outflows, all of which are coupled with the fluid algorithms using operator splitting. With this code, we have been able to perform the first AMR-MHD simulation of star cluster formation for several dynamical times, including sink particle and protostellar outflow feedbacks. The results demonstrated that protostellar outflows can drive supersonic turbulence in dense clumps and explain the observed slow and inefficient star formation. We also suggest that global collapse rate is the most important factor in controlling massive star accretion rate. In the topics of galaxy formation, we discuss the results of three projects. In the first project, using cosmological AMR hydrodynamics simulations, we found that isolated massive star still forms in cosmic string wakes even though the mega-parsec scale structure has been perturbed significantly by the cosmic strings. In the second project, we calculated the dynamical heating rate in galaxy formation. We found that by balancing our heating rate with the atomic cooling rate, it gives a critical halo mass which agrees with the result of numerical simulations. This demonstrates that the effect of dynamical heating should be put into semi-analytical works in the future. In the third project, using our AMR-MHD code coupled with radiative
ENZO+MORAY: radiation hydrodynamics adaptive mesh refinement simulations with adaptive ray tracing
NASA Astrophysics Data System (ADS)
Wise, John H.; Abel, Tom
2011-07-01
We describe a photon-conserving radiative transfer algorithm, using a spatially-adaptive ray-tracing scheme, and its parallel implementation into the adaptive mesh refinement cosmological hydrodynamics code ENZO. By coupling the solver with the energy equation and non-equilibrium chemistry network, our radiation hydrodynamics framework can be utilized to study a broad range of astrophysical problems, such as stellar and black hole feedback. Inaccuracies can arise from large time-steps and poor sampling; therefore, we devised an adaptive time-stepping scheme and a fast approximation of the optically-thin radiation field with multiple sources. We test the method with several radiative transfer and radiation hydrodynamics tests that are given in Iliev et al. We further test our method with more dynamical situations, for example, the propagation of an ionization front through a Rayleigh-Taylor instability, time-varying luminosities and collimated radiation. The test suite also includes an expanding H II region in a magnetized medium, utilizing the newly implemented magnetohydrodynamics module in ENZO. This method linearly scales with the number of point sources and number of grid cells. Our implementation is scalable to 512 processors on distributed memory machines and can include the radiation pressure and secondary ionizations from X-ray radiation. It is included in the newest public release of ENZO.
NASA Astrophysics Data System (ADS)
Bajc, Iztok; Hecht, Frédéric; Žumer, Slobodan
2016-09-01
This paper presents a 3D mesh adaptivity strategy on unstructured tetrahedral meshes by a posteriori error estimates based on metrics derived from the Hessian of a solution. The study is made on the case of a nonlinear finite element minimization scheme for the Landau-de Gennes free energy functional of nematic liquid crystals. Newton's iteration for tensor fields is employed with steepest descent method possibly stepping in. Aspects relating the driving of mesh adaptivity within the nonlinear scheme are considered. The algorithmic performance is found to depend on at least two factors: when to trigger each single mesh adaptation, and the precision of the correlated remeshing. Each factor is represented by a parameter, with its values possibly varying for every new mesh adaptation. We empirically show that the time of the overall algorithm convergence can vary considerably when different sequences of parameters are used, thus posing a question about optimality. The extensive testings and debugging done within this work on the simulation of systems of nematic colloids substantially contributed to the upgrade of an open source finite element-oriented programming language to its 3D meshing possibilities, as also to an outer 3D remeshing module.
NASA Astrophysics Data System (ADS)
Calder, A. C.; Curtis, B. C.; Dursi, L. J.; Fryxell, B.; Henry, G.; MacNeice, P.; Olson, K.; Ricker, P.; Rosner, R.; Timmes, F. X.; Tufo, H. M.; Truran, J. W.; Zingale, M.
We present simulations and performance results of nuclear burning fronts in supernovae on the largest domain and at the finest spatial resolution studied to date. These simulations were performed on the Intel ASCI-Red machine at Sandia National Laboratories using FLASH, a code developed at the Center for Astrophysical Thermonuclear Flashes at the University of Chicago. FLASH is a modular, adaptive mesh, parallel simulation code capable of handling compressible, reactive fluid flows in astrophysical environments. FLASH is written primarily in Fortran 90, uses the Message-Passing Interface library for inter-processor communication and portability, and employs the PARAMESH package to manage a block-structured adaptive mesh that places blocks only where the resolution is required and tracks rapidly changing flow features, such as detonation fronts, with ease. We describe the key algorithms and their implementation as well as the optimizations required to achieve sustained performance of 238 GLOPS on 6420 processors of ASCI-Red in 64-bit arithmetic.
Toward parallel, adaptive mesh refinement for chemically reacting flow simulations
Devine, K.D.; Shadid, J.N.; Salinger, A.G. Hutchinson, S.A.; Hennigan, G.L.
1997-12-01
Adaptive numerical methods offer greater efficiency than traditional numerical methods by concentrating computational effort in regions of the problem domain where the solution is difficult to obtain. In this paper, the authors describe progress toward adding mesh refinement to MPSalsa, a computer program developed at Sandia National laboratories to solve coupled three-dimensional fluid flow and detailed reaction chemistry systems for modeling chemically reacting flow on large-scale parallel computers. Data structures that support refinement and dynamic load-balancing are discussed. Results using uniform refinement with mesh sequencing to improve convergence to steady-state solutions are also presented. Three examples are presented: a lid driven cavity, a thermal convection flow, and a tilted chemical vapor deposition reactor.
NASA Technical Reports Server (NTRS)
Stapleton, Scott; Gries, Thomas; Waas, Anthony M.; Pineda, Evan J.
2014-01-01
Enhanced finite elements are elements with an embedded analytical solution that can capture detailed local fields, enabling more efficient, mesh independent finite element analysis. The shape functions are determined based on the analytical model rather than prescribed. This method was applied to adhesively bonded joints to model joint behavior with one element through the thickness. This study demonstrates two methods of maintaining the fidelity of such elements during adhesive non-linearity and cracking without increasing the mesh needed for an accurate solution. The first method uses adaptive shape functions, where the shape functions are recalculated at each load step based on the softening of the adhesive. The second method is internal mesh adaption, where cracking of the adhesive within an element is captured by further discretizing the element internally to represent the partially cracked geometry. By keeping mesh adaptations within an element, a finer mesh can be used during the analysis without affecting the global finite element model mesh. Examples are shown which highlight when each method is most effective in reducing the number of elements needed to capture adhesive nonlinearity and cracking. These methods are validated against analogous finite element models utilizing cohesive zone elements.
Ragusa, Jean C.
2015-01-01
In this paper, we propose a piece-wise linear discontinuous (PWLD) finite element discretization of the diffusion equation for arbitrary polygonal meshes. It is based on the standard diffusion form and uses the symmetric interior penalty technique, which yields a symmetric positive definite linear system matrix. A preconditioned conjugate gradient algorithm is employed to solve the linear system. Piece-wise linear approximations also allow a straightforward implementation of local mesh adaptation by allowing unrefined cells to be interpreted as polygons with an increased number of vertices. Several test cases, taken from the literature on the discretization of the radiation diffusion equation, are presented: random, sinusoidal, Shestakov, and Z meshes are used. The last numerical example demonstrates the application of the PWLD discretization to adaptive mesh refinement.
NASA Astrophysics Data System (ADS)
Yang, Dikun; Oldenburg, Douglas W.; Haber, Eldad
2014-03-01
Airborne electromagnetic (AEM) methods are highly efficient tools for assessing the Earth's conductivity structures in a large area at low cost. However, the configuration of AEM measurements, which typically have widely distributed transmitter-receiver pairs, makes the rigorous modelling and interpretation extremely time-consuming in 3-D. Excessive overcomputing can occur when working on a large mesh covering the entire survey area and inverting all soundings in the data set. We propose two improvements. The first is to use a locally optimized mesh for each AEM sounding for the forward modelling and calculation of sensitivity. This dedicated local mesh is small with fine cells near the sounding location and coarse cells far away in accordance with EM diffusion and the geometric decay of the signals. Once the forward problem is solved on the local meshes, the sensitivity for the inversion on the global mesh is available through quick interpolation. Using local meshes for AEM forward modelling avoids unnecessary computing on fine cells on a global mesh that are far away from the sounding location. Since local meshes are highly independent, the forward modelling can be efficiently parallelized over an array of processors. The second improvement is random and dynamic down-sampling of the soundings. Each inversion iteration only uses a random subset of the soundings, and the subset is reselected for every iteration. The number of soundings in the random subset, determined by an adaptive algorithm, is tied to the degree of model regularization. This minimizes the overcomputing caused by working with redundant soundings. Our methods are compared against conventional methods and tested with a synthetic example. We also invert a field data set that was previously considered to be too large to be practically inverted in 3-D. These examples show that our methodology can dramatically reduce the processing time of 3-D inversion to a practical level without losing resolution
Adaptive Mesh Refinement in Curvilinear Body-Fitted Grid Systems
NASA Technical Reports Server (NTRS)
Steinthorsson, Erlendur; Modiano, David; Colella, Phillip
1995-01-01
To be truly compatible with structured grids, an AMR algorithm should employ a block structure for the refined grids to allow flow solvers to take advantage of the strengths of unstructured grid systems, such as efficient solution algorithms for implicit discretizations and multigrid schemes. One such algorithm, the AMR algorithm of Berger and Colella, has been applied to and adapted for use with body-fitted structured grid systems. Results are presented for a transonic flow over a NACA0012 airfoil (AGARD-03 test case) and a reflection of a shock over a double wedge.
3D Finite Element Trajectory Code with Adaptive Meshing
NASA Astrophysics Data System (ADS)
Ives, Lawrence; Bui, Thuc; Vogler, William; Bauer, Andy; Shephard, Mark; Beal, Mark; Tran, Hien
2004-11-01
Beam Optics Analysis, a new, 3D charged particle program is available and in use for the design of complex, 3D electron guns and charged particle devices. The code reads files directly from most CAD and solid modeling programs, includes an intuitive Graphical User Interface (GUI), and a robust mesh generator that is fully automatic. Complex problems can be set up, and analysis initiated in minutes. The program includes a user-friendly post processor for displaying field and trajectory data using 3D plots and images. The electrostatic solver is based on the standard nodal finite element method. The magnetostatic field solver is based on the vector finite element method and is also called during the trajectory simulation process to solve for self magnetic fields. The user imports the geometry from essentially any commercial CAD program and uses the GUI to assign parameters (voltages, currents, dielectric constant) and designate emitters (including work function, emitter temperature, and number of trajectories). The the mesh is generated automatically and analysis is performed, including mesh adaptation to improve accuracy and optimize computational resources. This presentation will provide information on the basic structure of the code, its operation, and it's capabilities.
Compressible Flows on Adaptive and Unstrucured Meshes with FLUIDITY
NASA Astrophysics Data System (ADS)
Nelson, R.; Piggott, M.; Wilson, C.; Kramer, S.
2011-09-01
Fluidity is an open source, general purpose, multi-phase CFD code capable of solving numerically the Navier-Stokes and accompanying field equations on arbitrary unstructured finite element meshes in one, two and three dimensions. It uses a moving finite element/control volume method which allows arbitrary movement of the mesh in time dependent problems. It has a wide range of finite element/control volume element choices including mixed formulations. Here, continuous Galerkin (CG) and control volumes (CV) solutions of the compressible Navier-Stokes (N-S) equations are presented for the stratified tests cases of the rising thermal bubble and inertia gravity waves. Results show good agreement with previously published literature and novel result presented here is the ability to dynamically adapt the mesh to increase resolution in the region of interest, thus reducing the number of degrees of freedom in the problem without decreasing the accuracy of the result. Finally, results from the case of a fully three dimensional rising thermal bubble are presented.
Thermal-chemical Mantle Convection Models With Adaptive Mesh Refinement
NASA Astrophysics Data System (ADS)
Leng, W.; Zhong, S.
2008-12-01
In numerical modeling of mantle convection, resolution is often crucial for resolving small-scale features. New techniques, adaptive mesh refinement (AMR), allow local mesh refinement wherever high resolution is needed, while leaving other regions with relatively low resolution. Both computational efficiency for large- scale simulation and accuracy for small-scale features can thus be achieved with AMR. Based on the octree data structure [Tu et al. 2005], we implement the AMR techniques into the 2-D mantle convection models. For pure thermal convection models, benchmark tests show that our code can achieve high accuracy with relatively small number of elements both for isoviscous cases (i.e. 7492 AMR elements v.s. 65536 uniform elements) and for temperature-dependent viscosity cases (i.e. 14620 AMR elements v.s. 65536 uniform elements). We further implement tracer-method into the models for simulating thermal-chemical convection. By appropriately adding and removing tracers according to the refinement of the meshes, our code successfully reproduces the benchmark results in van Keken et al. [1997] with much fewer elements and tracers compared with uniform-mesh models (i.e. 7552 AMR elements v.s. 16384 uniform elements, and ~83000 tracers v.s. ~410000 tracers). The boundaries of the chemical piles in our AMR code can be easily refined to the scales of a few kilometers for the Earth's mantle and the tracers are concentrated near the chemical boundaries to precisely trace the evolvement of the boundaries. It is thus very suitable for our AMR code to study the thermal-chemical convection problems which need high resolution to resolve the evolvement of chemical boundaries, such as the entrainment problems [Sleep, 1988].
Simulation of nonpoint source contamination based on adaptive mesh refinement
NASA Astrophysics Data System (ADS)
Kourakos, G.; Harter, T.
2014-12-01
Contamination of groundwater aquifers from nonpoint sources is a worldwide problem. Typical agricultural groundwater basins receive contamination from a large array (in the order of ~10^5-6) of spatially and temporally heterogeneous sources such as fields, crops, dairies etc, while the received contaminants emerge at significantly uncertain time lags to a large array of discharge surfaces such as public supply, domestic and irrigation wells and streams. To support decision making in such complex regimes several approaches have been developed, which can be grouped into 3 categories: i) Index methods, ii)regression methods and iii) physically based methods. Among the three, physically based methods are considered more accurate, but at the cost of computational demand. In this work we present a physically based simulation framework which exploits the latest hardware and software developments to simulate large (>>1,000 km2) groundwater basins. First we simulate groundwater flow using a sufficiently detailed mesh to capture the spatial heterogeneity. To achieve optimal mesh quality we combine adaptive mesh refinement with the nonlinear solution for unconfined flow. Starting from a coarse grid the mesh is refined iteratively in the parts of the domain where the flow heterogeneity appears higher resulting in optimal grid. Secondly we simulate the nonpoint source pollution based on the detailed velocity field computed from the previous step. In our approach we use the streamline model where the 3D transport problem is decomposed into multiple 1D transport problems. The proposed framework is applied to simulate nonpoint source pollution in the Central Valley aquifer system, California.
NASA Technical Reports Server (NTRS)
Steger, J. L.; Dougherty, F. C.; Benek, J. A.
1983-01-01
A mesh system composed of multiple overset body-conforming grids is described for adapting finite-difference procedures to complex aircraft configurations. In this so-called 'chimera mesh,' a major grid is generated about a main component of the configuration and overset minor grids are used to resolve all other features. Methods for connecting overset multiple grids and modifications of flow-simulation algorithms are discussed. Computational tests in two dimensions indicate that the use of multiple overset grids can simplify the task of grid generation without an adverse effect on flow-field algorithms and computer code complexity.
Parallel Processing of Adaptive Meshes with Load Balancing
NASA Technical Reports Server (NTRS)
Das, Sajal K.; Harvey, Daniel J.; Biswas, Rupak; Biegel, Bryan (Technical Monitor)
2001-01-01
Many scientific applications involve grids that lack a uniform underlying structure. These applications are often also dynamic in nature in that the grid structure significantly changes between successive phases of execution. In parallel computing environments, mesh adaptation of unstructured grids through selective refinement/coarsening has proven to be an effective approach. However, achieving load balance while minimizing interprocessor communication and redistribution costs is a difficult problem. Traditional dynamic load balancers are mostly inadequate because they lack a global view of system loads across processors. In this paper, we propose a novel and general-purpose load balancer that utilizes symmetric broadcast networks (SBN) as the underlying communication topology, and compare its performance with a successful global load balancing environment, called PLUM, specifically created to handle adaptive unstructured applications. Our experimental results on an IBM SP2 demonstrate that the SBN-based load balancer achieves lower redistribution costs than that under PLUM by overlapping processing and data migration.
Dynamic Load Balancing for Adaptive Meshes using Symmetric Broadcast Networks
NASA Technical Reports Server (NTRS)
Das, Sajal K.; Harvey, Daniel J.; Biswas, Rupak; Saini, Subhash (Technical Monitor)
1998-01-01
Many scientific applications involve grids that lack a uniform underlying structure. These applications are often dynamic in the sense that the grid structure significantly changes between successive phases of execution. In parallel computing environments, mesh adaptation of grids through selective refinement/coarsening has proven to be an effective approach. However, achieving load balance while minimizing inter-processor communication and redistribution costs is a difficult problem. Traditional dynamic load balancers are mostly inadequate because they lack a global view across processors. In this paper, we compare a novel load balancer that utilizes symmetric broadcast networks (SBN) to a successful global load balancing environment (PLUM) created to handle adaptive unstructured applications. Our experimental results on the IBM SP2 demonstrate that performance of the proposed SBN load balancer is comparable to results achieved under PLUM.
Adaptive protection algorithm and system
Hedrick, Paul [Pittsburgh, PA; Toms, Helen L [Irwin, PA; Miller, Roger M [Mars, PA
2009-04-28
An adaptive protection algorithm and system for protecting electrical distribution systems traces the flow of power through a distribution system, assigns a value (or rank) to each circuit breaker in the system and then determines the appropriate trip set points based on the assigned rank.
Visualization of Octree Adaptive Mesh Refinement (AMR) in Astrophysical Simulations
NASA Astrophysics Data System (ADS)
Labadens, M.; Chapon, D.; Pomaréde, D.; Teyssier, R.
2012-09-01
Computer simulations are important in current cosmological research. Those simulations run in parallel on thousands of processors, and produce huge amount of data. Adaptive mesh refinement is used to reduce the computing cost while keeping good numerical accuracy in regions of interest. RAMSES is a cosmological code developed by the Commissariat à l'énergie atomique et aux énergies alternatives (English: Atomic Energy and Alternative Energies Commission) which uses Octree adaptive mesh refinement. Compared to grid based AMR, the Octree AMR has the advantage to fit very precisely the adaptive resolution of the grid to the local problem complexity. However, this specific octree data type need some specific software to be visualized, as generic visualization tools works on Cartesian grid data type. This is why the PYMSES software has been also developed by our team. It relies on the python scripting language to ensure a modular and easy access to explore those specific data. In order to take advantage of the High Performance Computer which runs the RAMSES simulation, it also uses MPI and multiprocessing to run some parallel code. We would like to present with more details our PYMSES software with some performance benchmarks. PYMSES has currently two visualization techniques which work directly on the AMR. The first one is a splatting technique, and the second one is a custom ray tracing technique. Both have their own advantages and drawbacks. We have also compared two parallel programming techniques with the python multiprocessing library versus the use of MPI run. The load balancing strategy has to be smartly defined in order to achieve a good speed up in our computation. Results obtained with this software are illustrated in the context of a massive, 9000-processor parallel simulation of a Milky Way-like galaxy.
An adaptive mesh-moving and refinement procedure for one-dimensional conservation laws
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Flaherty, Joseph E.; Arney, David C.
1993-01-01
We examine the performance of an adaptive mesh-moving and /or local mesh refinement procedure for the finite difference solution of one-dimensional hyperbolic systems of conservation laws. Adaptive motion of a base mesh is designed to isolate spatially distinct phenomena, and recursive local refinement of the time step and cells of the stationary or moving base mesh is performed in regions where a refinement indicator exceeds a prescribed tolerance. These adaptive procedures are incorporated into a computer code that includes a MacCormack finite difference scheme wih Davis' artificial viscosity model and a discretization error estimate based on Richardson's extrapolation. Experiments are conducted on three problems in order to qualify the advantages of adaptive techniques relative to uniform mesh computations and the relative benefits of mesh moving and refinement. Key results indicate that local mesh refinement, with and without mesh moving, can provide reliable solutions at much lower computational cost than possible on uniform meshes; that mesh motion can be used to improve the results of uniform mesh solutions for a modest computational effort; that the cost of managing the tree data structure associated with refinement is small; and that a combination of mesh motion and refinement reliably produces solutions for the least cost per unit accuracy.
Goffin, Mark A.; Baker, Christopher M.J.; Buchan, Andrew G.; Pain, Christopher C.; Eaton, Matthew D.; Smith, Paul N.
2013-06-01
This article presents a method for goal-based anisotropic adaptive methods for the finite element method applied to the Boltzmann transport equation. The neutron multiplication factor, k{sub eff}, is used as the goal of the adaptive procedure. The anisotropic adaptive algorithm requires error measures for k{sub eff} with directional dependence. General error estimators are derived for any given functional of the flux and applied to k{sub eff} to acquire the driving force for the adaptive procedure. The error estimators require the solution of an appropriately formed dual equation. Forward and dual error indicators are calculated by weighting the Hessian of each solution with the dual and forward residual respectively. The Hessian is used as an approximation of the interpolation error in the solution which gives rise to the directional dependence. The two indicators are combined to form a single error metric that is used to adapt the finite element mesh. The residual is approximated using a novel technique arising from the sub-grid scale finite element discretisation. Two adaptive routes are demonstrated: (i) a single mesh is used to solve all energy groups, and (ii) a different mesh is used to solve each energy group. The second method aims to capture the benefit from representing the flux from each energy group on a specifically optimised mesh. The k{sub eff} goal-based adaptive method was applied to three examples which illustrate the superior accuracy in criticality problems that can be obtained.
A Predictive Model of Fragmentation using Adaptive Mesh Refinement and a Hierarchical Material Model
Koniges, A E; Masters, N D; Fisher, A C; Anderson, R W; Eder, D C; Benson, D; Kaiser, T B; Gunney, B T; Wang, P; Maddox, B R; Hansen, J F; Kalantar, D H; Dixit, P; Jarmakani, H; Meyers, M A
2009-03-03
Fragmentation is a fundamental material process that naturally spans spatial scales from microscopic to macroscopic. We developed a mathematical framework using an innovative combination of hierarchical material modeling (HMM) and adaptive mesh refinement (AMR) to connect the continuum to microstructural regimes. This framework has been implemented in a new multi-physics, multi-scale, 3D simulation code, NIF ALE-AMR. New multi-material volume fraction and interface reconstruction algorithms were developed for this new code, which is leading the world effort in hydrodynamic simulations that combine AMR with ALE (Arbitrary Lagrangian-Eulerian) techniques. The interface reconstruction algorithm is also used to produce fragments following material failure. In general, the material strength and failure models have history vector components that must be advected along with other properties of the mesh during remap stage of the ALE hydrodynamics. The fragmentation models are validated against an electromagnetically driven expanding ring experiment and dedicated laser-based fragmentation experiments conducted at the Jupiter Laser Facility. As part of the exit plan, the NIF ALE-AMR code was applied to a number of fragmentation problems of interest to the National Ignition Facility (NIF). One example shows the added benefit of multi-material ALE-AMR that relaxes the requirement that material boundaries must be along mesh boundaries.
A Spectral Adaptive Mesh Refinement Method for the Burgers equation
NASA Astrophysics Data System (ADS)
Nasr Azadani, Leila; Staples, Anne
2013-03-01
Adaptive mesh refinement (AMR) is a powerful technique in computational fluid dynamics (CFD). Many CFD problems have a wide range of scales which vary with time and space. In order to resolve all the scales numerically, high grid resolutions are required. The smaller the scales the higher the resolutions should be. However, small scales are usually formed in a small portion of the domain or in a special period of time. AMR is an efficient method to solve these types of problems, allowing high grid resolutions where and when they are needed and minimizing memory and CPU time. Here we formulate a spectral version of AMR in order to accelerate simulations of a 1D model for isotropic homogenous turbulence, the Burgers equation, as a first test of this method. Using pseudo spectral methods, we applied AMR in Fourier space. The spectral AMR (SAMR) method we present here is applied to the Burgers equation and the results are compared with the results obtained using standard solution methods performed using a fine mesh.
Patched based methods for adaptive mesh refinement solutions of partial differential equations
Saltzman, J.
1997-09-02
This manuscript contains the lecture notes for a course taught from July 7th through July 11th at the 1997 Numerical Analysis Summer School sponsored by C.E.A., I.N.R.I.A., and E.D.F. The subject area was chosen to support the general theme of that year`s school which is ``Multiscale Methods and Wavelets in Numerical Simulation.`` The first topic covered in these notes is a description of the problem domain. This coverage is limited to classical PDEs with a heavier emphasis on hyperbolic systems and constrained hyperbolic systems. The next topic is difference schemes. These schemes are the foundation for the adaptive methods. After the background material is covered, attention is focused on a simple patched based adaptive algorithm and its associated data structures for square grids and hyperbolic conservation laws. Embellishments include curvilinear meshes, embedded boundary and overset meshes. Next, several strategies for parallel implementations are examined. The remainder of the notes contains descriptions of elliptic solutions on the mesh hierarchy, elliptically constrained flow solution methods and elliptically constrained flow solution methods with diffusion.
Production-quality Tools for Adaptive Mesh RefinementVisualization
Weber, Gunther H.; Childs, Hank; Bonnell, Kathleen; Meredith,Jeremy; Miller, Mark; Whitlock, Brad; Bethel, E. Wes
2007-10-25
Adaptive Mesh Refinement (AMR) is a highly effectivesimulation method for spanning a large range of spatiotemporal scales,such as astrophysical simulations that must accommodate ranges frominterstellar to sub-planetary. Most mainstream visualization tools stilllack support for AMR as a first class data type and AMR code teams usecustom built applications for AMR visualization. The Department ofEnergy's (DOE's) Science Discovery through Advanced Computing (SciDAC)Visualization and Analytics Center for Enabling Technologies (VACET) isextending and deploying VisIt, an open source visualization tool thataccommodates AMR as a first-class data type, for use asproduction-quality, parallel-capable AMR visual data analysisinfrastructure. This effort will help science teams that use AMR-basedsimulations and who develop their own AMR visual data analysis softwareto realize cost and labor savings.
Adaptive color image watermarking algorithm
NASA Astrophysics Data System (ADS)
Feng, Gui; Lin, Qiwei
2008-03-01
As a major method for intellectual property right protecting, digital watermarking techniques have been widely studied and used. But due to the problems of data amount and color shifted, watermarking techniques on color image was not so widespread studied, although the color image is the principal part for multi-medium usages. Considering the characteristic of Human Visual System (HVS), an adaptive color image watermarking algorithm is proposed in this paper. In this algorithm, HSI color model was adopted both for host and watermark image, the DCT coefficient of intensity component (I) of the host color image was used for watermark date embedding, and while embedding watermark the amount of embedding bit was adaptively changed with the complex degree of the host image. As to the watermark image, preprocessing is applied first, in which the watermark image is decomposed by two layer wavelet transformations. At the same time, for enhancing anti-attack ability and security of the watermarking algorithm, the watermark image was scrambled. According to its significance, some watermark bits were selected and some watermark bits were deleted as to form the actual embedding data. The experimental results show that the proposed watermarking algorithm is robust to several common attacks, and has good perceptual quality at the same time.
3D Compressible Melt Transport with Adaptive Mesh Refinement
NASA Astrophysics Data System (ADS)
Dannberg, Juliane; Heister, Timo
2015-04-01
Melt generation and migration have been the subject of numerous investigations, but their typical time and length-scales are vastly different from mantle convection, which makes it difficult to study these processes in a unified framework. The equations that describe coupled Stokes-Darcy flow have been derived a long time ago and they have been successfully implemented and applied in numerical models (Keller et al., 2013). However, modelling magma dynamics poses the challenge of highly non-linear and spatially variable material properties, in particular the viscosity. Applying adaptive mesh refinement to this type of problems is particularly advantageous, as the resolution can be increased in mesh cells where melt is present and viscosity gradients are high, whereas a lower resolution is sufficient in regions without melt. In addition, previous models neglect the compressibility of both the solid and the fluid phase. However, experiments have shown that the melt density change from the depth of melt generation to the surface leads to a volume increase of up to 20%. Considering these volume changes in both phases also ensures self-consistency of models that strive to link melt generation to processes in the deeper mantle, where the compressibility of the solid phase becomes more important. We describe our extension of the finite-element mantle convection code ASPECT (Kronbichler et al., 2012) that allows for solving additional equations describing the behaviour of silicate melt percolating through and interacting with a viscously deforming host rock. We use the original compressible formulation of the McKenzie equations, augmented by an equation for the conservation of energy. This approach includes both melt migration and melt generation with the accompanying latent heat effects. We evaluate the functionality and potential of this method using a series of simple model setups and benchmarks, comparing results of the compressible and incompressible formulation and
Unstructured and adaptive mesh generation for high Reynolds number viscous flows
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1991-01-01
A method for generating and adaptively refining a highly stretched unstructured mesh suitable for the computation of high-Reynolds-number viscous flows about arbitrary two-dimensional geometries was developed. The method is based on the Delaunay triangulation of a predetermined set of points and employs a local mapping in order to achieve the high stretching rates required in the boundary-layer and wake regions. The initial mesh-point distribution is determined in a geometry-adaptive manner which clusters points in regions of high curvature and sharp corners. Adaptive mesh refinement is achieved by adding new points in regions of large flow gradients, and locally retriangulating; thus, obviating the need for global mesh regeneration. Initial and adapted meshes about complex multi-element airfoil geometries are shown and compressible flow solutions are computed on these meshes.
Adaptive Mesh Expansion Model (AMEM) for Liver Segmentation from CT Image
Wang, Xuehu; Yang, Jian; Ai, Danni; Zheng, Yongchang; Tang, Songyuan; Wang, Yongtian
2015-01-01
This study proposes a novel adaptive mesh expansion model (AMEM) for liver segmentation from computed tomography images. The virtual deformable simplex model (DSM) is introduced to represent the mesh, in which the motion of each vertex can be easily manipulated. The balloon, edge, and gradient forces are combined with the binary image to construct the external force of the deformable model, which can rapidly drive the DSM to approach the target liver boundaries. Moreover, tangential and normal forces are combined with the gradient image to control the internal force, such that the DSM degree of smoothness can be precisely controlled. The triangular facet of the DSM is adaptively decomposed into smaller triangular components, which can significantly improve the segmentation accuracy of the irregularly sharp corners of the liver. The proposed method is evaluated on the basis of different criteria applied to 10 clinical data sets. Experiments demonstrate that the proposed AMEM algorithm is effective and robust and thus outperforms six other up-to-date algorithms. Moreover, AMEM can achieve a mean overlap error of 6.8% and a mean volume difference of 2.7%, whereas the average symmetric surface distance and the root mean square symmetric surface distance can reach 1.3 mm and 2.7 mm, respectively. PMID:25769030
Implicit adaptive mesh refinement for 2D reduced resistive magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Philip, Bobby; Chacón, Luis; Pernice, Michael
2008-10-01
An implicit structured adaptive mesh refinement (SAMR) solver for 2D reduced magnetohydrodynamics (MHD) is described. The time-implicit discretization is able to step over fast normal modes, while the spatial adaptivity resolves thin, dynamically evolving features. A Jacobian-free Newton-Krylov method is used for the nonlinear solver engine. For preconditioning, we have extended the optimal "physics-based" approach developed in [L. Chacón, D.A. Knoll, J.M. Finn, An implicit, nonlinear reduced resistive MHD solver, J. Comput. Phys. 178 (2002) 15-36] (which employed multigrid solver technology in the preconditioner for scalability) to SAMR grids using the well-known Fast Adaptive Composite grid (FAC) method [S. McCormick, Multilevel Adaptive Methods for Partial Differential Equations, SIAM, Philadelphia, PA, 1989]. A grid convergence study demonstrates that the solver performance is independent of the number of grid levels and only depends on the finest resolution considered, and that it scales well with grid refinement. The study of error generation and propagation in our SAMR implementation demonstrates that high-order (cubic) interpolation during regridding, combined with a robustly damping second-order temporal scheme such as BDF2, is required to minimize impact of grid errors at coarse-fine interfaces on the overall error of the computation for this MHD application. We also demonstrate that our implementation features the desired property that the overall numerical error is dependent only on the finest resolution level considered, and not on the base-grid resolution or on the number of refinement levels present during the simulation. We demonstrate the effectiveness of the tool on several challenging problems.
Curved Mesh Correction And Adaptation Tool to Improve COMPASS Electromagnetic Analyses
Luo, X.; Shephard, M.; Lee, L.Q.; Ng, C.; Ge, L.; /SLAC
2011-11-14
SLAC performs large-scale simulations for the next-generation accelerator design using higher-order finite elements. This method requires using valid curved meshes and adaptive mesh refinement in complex 3D curved domains to achieve its fast rate of convergence. ITAPS has developed a procedure to address those mesh requirements to enable petascale electromagnetic accelerator simulations by SLAC. The results demonstrate that those correct valid curvilinear meshes can not only make the simulation more reliable but also improve computational efficiency up to 30%. This paper presents a procedure to track moving adaptive mesh refinement in curved domains. The procedure is capable of generating suitable curvilinear meshes to enable large-scale accelerator simulations. The procedure can generate valid curved meshes with substantially fewer elements to improve the computational efficiency and reliability of the COMPASS electromagnetic analyses. Future work will focus on the scalable parallelization of all steps for petascale simulations.
Block structured adaptive mesh and time refinement for hybrid, hyperbolic + N-body systems
NASA Astrophysics Data System (ADS)
Miniati, Francesco; Colella, Phillip
2007-11-01
We present a new numerical algorithm for the solution of coupled collisional and collisionless systems, based on the block structured adaptive mesh and time refinement strategy (AMR). We describe the issues associated with the discretization of the system equations and the synchronization of the numerical solution on the hierarchy of grid levels. We implement a code based on a higher order, conservative and directionally unsplit Godunov’s method for hydrodynamics; a symmetric, time centered modified symplectic scheme for collisionless component; and a multilevel, multigrid relaxation algorithm for the elliptic equation coupling the two components. Numerical results that illustrate the accuracy of the code and the relative merit of various implemented schemes are also presented.
A processor-time-minimal systolic array for cubical mesh algorithms
Cappello, P. . Dept. of Computer Science)
1992-01-01
Using a directed acyclic graph (dag) model of algorithms, the paper focuses on time-minimal multiprocessor schedules that use as few processors as possible. Such a processor-time-minimal scheduling of an algorithm's dag first is illustrated using a triangular shaped 2-D directed mesh (representing, for example, an algorithm for solving a triangular system of linear equations). Then, algorithms represented by an n {times} n {times} n directed mesh are investigated. This cubical directed mesh is fundamental; it represents the standard algorithm for computing matrix product as well as many other algorithms. Completion of the cubical mesh requires 3n - 2 steps. It is shown that the number of processing elements needed to achieve this time bound is at least (3n{sup 2/4}). A systolic array for the cubical directed mesh is then presented. It completes the mesh using the minimum number of steps and exactly (3n{sup 2/4}) processing elements: it is processor-time-minimal. The systolic array's topology is that of a hexagonally shaped, cylindrically- connected, 2-D directed mesh.
A new adaptive mesh refinement data structure with an application to detonation
NASA Astrophysics Data System (ADS)
Ji, Hua; Lien, Fue-Sang; Yee, Eugene
2010-11-01
A new Cell-based Structured Adaptive Mesh Refinement (CSAMR) data structure is developed. In our CSAMR data structure, Cartesian-like indices are used to identify each cell. With these stored indices, the information on the parent, children and neighbors of a given cell can be accessed simply and efficiently. Owing to the usage of these indices, the computer memory required for storage of the proposed AMR data structure is only {5}/{8} word per cell, in contrast to the conventional oct-tree [P. MacNeice, K.M. Olson, C. Mobary, R. deFainchtein, C. Packer, PARAMESH: a parallel adaptive mesh refinement community toolkit, Comput. Phys. Commun. 330 (2000) 126] and the fully threaded tree (FTT) [A.M. Khokhlov, Fully threaded tree algorithms for adaptive mesh fluid dynamics simulations, J. Comput. Phys. 143 (1998) 519] data structures which require, respectively, 19 and 2{3}/{8} words per cell for storage of the connectivity information. Because the connectivity information (e.g., parent, children and neighbors) of a cell in our proposed AMR data structure can be accessed using only the cell indices, a tree structure which was required in previous approaches for the organization of the AMR data is no longer needed for this new data structure. Instead, a much simpler hash table structure is used to maintain the AMR data, with the entry keys in the hash table obtained directly from the explicitly stored cell indices. The proposed AMR data structure simplifies the implementation and parallelization of an AMR code. Two three-dimensional test cases are used to illustrate and evaluate the computational performance of the new CSAMR data structure.
NASA Astrophysics Data System (ADS)
Lian, Y.-Y.; Hsu, K.-H.; Shao, Y.-L.; Lee, Y.-M.; Jeng, Y.-W.; Wu, J.-S.
2006-12-01
The development of a parallel three-dimensional (3-D) adaptive mesh refinement (PAMR) scheme for an unstructured tetrahedral mesh using dynamic domain decomposition on a memory-distributed machine is presented in detail. A memory-saving cell-based data structure is designed such that the resulting mesh information can be readily utilized in both node- or cell-based numerical methods. The general procedures include isotropic refinement from one parent cell into eight child cells and then followed by anisotropic refinement which effectively removes hanging nodes. A simple but effective mesh-quality control mechanism is employed to preserve the mesh quality. The resulting parallel performance of this PAMR is found to scale approximately as N for N⩽32. Two test cases, including a particle method (parallel DSMC solver for rarefied gas dynamics) and an equation-based method (parallel Poisson-Boltzmann equation solver for electrostatic field), are used to demonstrate the generality of the PAMR module. It is argued that this PAMR scheme can be applied in any numerical method if the unstructured tetrahedral mesh is adopted.
An object-oriented approach for parallel self adaptive mesh refinement on block structured grids
NASA Technical Reports Server (NTRS)
Lemke, Max; Witsch, Kristian; Quinlan, Daniel
1993-01-01
Self-adaptive mesh refinement dynamically matches the computational demands of a solver for partial differential equations to the activity in the application's domain. In this paper we present two C++ class libraries, P++ and AMR++, which significantly simplify the development of sophisticated adaptive mesh refinement codes on (massively) parallel distributed memory architectures. The development is based on our previous research in this area. The C++ class libraries provide abstractions to separate the issues of developing parallel adaptive mesh refinement applications into those of parallelism, abstracted by P++, and adaptive mesh refinement, abstracted by AMR++. P++ is a parallel array class library to permit efficient development of architecture independent codes for structured grid applications, and AMR++ provides support for self-adaptive mesh refinement on block-structured grids of rectangular non-overlapping blocks. Using these libraries, the application programmers' work is greatly simplified to primarily specifying the serial single grid application and obtaining the parallel and self-adaptive mesh refinement code with minimal effort. Initial results for simple singular perturbation problems solved by self-adaptive multilevel techniques (FAC, AFAC), being implemented on the basis of prototypes of the P++/AMR++ environment, are presented. Singular perturbation problems frequently arise in large applications, e.g. in the area of computational fluid dynamics. They usually have solutions with layers which require adaptive mesh refinement and fast basic solvers in order to be resolved efficiently.
Algebraic turbulence modeling for unstructured and adaptive meshes
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1990-01-01
An algebraic turbulence model based on the Baldwin-Lomax model, has been implemented for use on unstructured grids. The implementation is based on the use of local background structured turbulence meshes. At each time-step, flow variables are interpolated from the unstructured mesh onto the background structured meshes, the turbulence model is executed on these meshes, and the resulting eddy viscosity values are interpolated back to the unstructured mesh. Modifications to the algebraic model were required to enable the treatment of more complicated flows, such as confluent boundary layers and wakes. The model is used in conjuction with an efficient unstructured multigrid finite-element Navier-Stokes solver in order to compute compressible turbulent flows on fully unstructured meshes. Solutions about single and multiple element airfoils are obtained and compared with experimental data.
AMR++: Object-oriented design for adaptive mesh refinement
Quinlan, D.
1998-12-01
The development of object-oriented libraries for scientific computing is complicated by the wide range of applications that are targeted and the complexity and wide range of numerical methods that are used. A problem is to design a library that can be customized to handle a wide range of target applications and increasingly complex numerical methods while maintaining a sufficiently useful library for simple problems. These problems have been classically at odds with one another and have compromised the design of many object-oriented library solutions. In this paper the authors detail the mechanisms used within AMR**, and object-oriented library for Adaptive Mesh Refinement (AMR), to provide the level of extensibility that is required to make AMR++ easily customizable for the more obscure applications while remaining small and simple for less complex applications. The goal has been to have a complex applications. The goal has been to have a complexity that matches the complexity of the target application. These mechanisms are general and extend to other libraries as well.
Adaptive Numerical Algorithms in Space Weather Modeling
NASA Technical Reports Server (NTRS)
Toth, Gabor; vanderHolst, Bart; Sokolov, Igor V.; DeZeeuw, Darren; Gombosi, Tamas I.; Fang, Fang; Manchester, Ward B.; Meng, Xing; Nakib, Dalal; Powell, Kenneth G.; Stout, Quentin F.; Glocer, Alex; Ma, Ying-Juan; Opher, Merav
2010-01-01
Space weather describes the various processes in the Sun-Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different physics in different domains. A multi-physics system can be modeled by a software framework comprising of several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models. Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solar wind Roe Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamics (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems. BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit numerical
Adaptive numerical algorithms in space weather modeling
NASA Astrophysics Data System (ADS)
Tóth, Gábor; van der Holst, Bart; Sokolov, Igor V.; De Zeeuw, Darren L.; Gombosi, Tamas I.; Fang, Fang; Manchester, Ward B.; Meng, Xing; Najib, Dalal; Powell, Kenneth G.; Stout, Quentin F.; Glocer, Alex; Ma, Ying-Juan; Opher, Merav
2012-02-01
Space weather describes the various processes in the Sun-Earth system that present danger to human health and technology. The goal of space weather forecasting is to provide an opportunity to mitigate these negative effects. Physics-based space weather modeling is characterized by disparate temporal and spatial scales as well as by different relevant physics in different domains. A multi-physics system can be modeled by a software framework comprising several components. Each component corresponds to a physics domain, and each component is represented by one or more numerical models. The publicly available Space Weather Modeling Framework (SWMF) can execute and couple together several components distributed over a parallel machine in a flexible and efficient manner. The framework also allows resolving disparate spatial and temporal scales with independent spatial and temporal discretizations in the various models. Several of the computationally most expensive domains of the framework are modeled by the Block-Adaptive Tree Solarwind Roe-type Upwind Scheme (BATS-R-US) code that can solve various forms of the magnetohydrodynamic (MHD) equations, including Hall, semi-relativistic, multi-species and multi-fluid MHD, anisotropic pressure, radiative transport and heat conduction. Modeling disparate scales within BATS-R-US is achieved by a block-adaptive mesh both in Cartesian and generalized coordinates. Most recently we have created a new core for BATS-R-US: the Block-Adaptive Tree Library (BATL) that provides a general toolkit for creating, load balancing and message passing in a 1, 2 or 3 dimensional block-adaptive grid. We describe the algorithms of BATL and demonstrate its efficiency and scaling properties for various problems. BATS-R-US uses several time-integration schemes to address multiple time-scales: explicit time stepping with fixed or local time steps, partially steady-state evolution, point-implicit, semi-implicit, explicit/implicit, and fully implicit
NASA Astrophysics Data System (ADS)
Fromang, S.; Hennebelle, P.; Teyssier, R.
2006-10-01
Aims. In this paper, we present a new method to perform numerical simulations of astrophysical MHD flows using the Adaptive Mesh Refinement framework and Constrained Transport. Methods: . The algorithm is based on a previous work in which the MUSCL-Hancock scheme was used to evolve the induction equation. In this paper, we detail the extension of this scheme to the full MHD equations and discuss its properties. Results: . Through a series of test problems, we illustrate the performances of this new code using two different MHD Riemann solvers (Lax-Friedrich and Roe) and the need of the Adaptive Mesh Refinement capabilities in some cases. Finally, we show its versatility by applying it to two completely different astrophysical situations well studied in the past years: the growth of the magnetorotational instability in the shearing box and the collapse of magnetized cloud cores. Conclusions: . We have implemented a new Godunov scheme to solve the ideal MHD equations in the AMR code RAMSES. We have shown that it results in a powerful tool that can be applied to a great variety of astrophysical problems, ranging from galaxies formation in the early universe to high resolution studies of molecular cloud collapse in our galaxy.
A Robust and Scalable Software Library for Parallel Adaptive Refinement on Unstructured Meshes
NASA Technical Reports Server (NTRS)
Lou, John Z.; Norton, Charles D.; Cwik, Thomas A.
1999-01-01
The design and implementation of Pyramid, a software library for performing parallel adaptive mesh refinement (PAMR) on unstructured meshes, is described. This software library can be easily used in a variety of unstructured parallel computational applications, including parallel finite element, parallel finite volume, and parallel visualization applications using triangular or tetrahedral meshes. The library contains a suite of well-designed and efficiently implemented modules that perform operations in a typical PAMR process. Among these are mesh quality control during successive parallel adaptive refinement (typically guided by a local-error estimator), parallel load-balancing, and parallel mesh partitioning using the ParMeTiS partitioner. The Pyramid library is implemented in Fortran 90 with an interface to the Message-Passing Interface (MPI) library, supporting code efficiency, modularity, and portability. An EM waveguide filter application, adaptively refined using the Pyramid library, is illustrated.
Adaptive mesh refinement with spectral accuracy for magnetohydrodynamics in two space dimensions
NASA Astrophysics Data System (ADS)
Rosenberg, D.; Pouquet, A.; Mininni, P. D.
2007-08-01
We examine the effect of accuracy of high-order spectral element methods, with or without adaptive mesh refinement (AMR), in the context of a classical configuration of magnetic reconnection in two space dimensions, the so-called Orszag-Tang (OT) vortex made up of a magnetic X-point centred on a stagnation point of the velocity. A recently developed spectral-element adaptive refinement incompressible magnetohydrodynamic (MHD) code is applied to simulate this problem. The MHD solver is explicit, and uses the Elsässer formulation on high-order elements. It automatically takes advantage of the adaptive grid mechanics that have been described elsewhere in the fluid context (Rosenberg et al 2006 J. Comput. Phys. 215 59-80) the code allows both statically refined and dynamically refined grids. Tests of the algorithm using analytic solutions are described, and comparisons of the OT solutions with pseudo-spectral computations are performed. We demonstrate for moderate Reynolds numbers that the algorithms using both static and refined grids reproduce the pseudo-spectral solutions quite well. We show that low-order truncation—even with a comparable number of global degrees of freedom—fails to correctly model some strong (sup-norm) quantities in this problem, even though it satisfies adequately the weak (integrated) balance diagnostics.
RAM: a Relativistic Adaptive Mesh Refinement Hydrodynamics Code
Zhang, Wei-Qun; MacFadyen, Andrew I.; /Princeton, Inst. Advanced Study
2005-06-06
The authors have developed a new computer code, RAM, to solve the conservative equations of special relativistic hydrodynamics (SRHD) using adaptive mesh refinement (AMR) on parallel computers. They have implemented a characteristic-wise, finite difference, weighted essentially non-oscillatory (WENO) scheme using the full characteristic decomposition of the SRHD equations to achieve fifth-order accuracy in space. For time integration they use the method of lines with a third-order total variation diminishing (TVD) Runge-Kutta scheme. They have also implemented fourth and fifth order Runge-Kutta time integration schemes for comparison. The implementation of AMR and parallelization is based on the FLASH code. RAM is modular and includes the capability to easily swap hydrodynamics solvers, reconstruction methods and physics modules. In addition to WENO they have implemented a finite volume module with the piecewise parabolic method (PPM) for reconstruction and the modified Marquina approximate Riemann solver to work with TVD Runge-Kutta time integration. They examine the difficulty of accurately simulating shear flows in numerical relativistic hydrodynamics codes. They show that under-resolved simulations of simple test problems with transverse velocity components produce incorrect results and demonstrate the ability of RAM to correctly solve these problems. RAM has been tested in one, two and three dimensions and in Cartesian, cylindrical and spherical coordinates. they have demonstrated fifth-order accuracy for WENO in one and two dimensions and performed detailed comparison with other schemes for which they show significantly lower convergence rates. Extensive testing is presented demonstrating the ability of RAM to address challenging open questions in relativistic astrophysics.
Vectorizable algorithms for adaptive schemes for rapid analysis of SSME flows
NASA Technical Reports Server (NTRS)
Oden, J. Tinsley
1987-01-01
An initial study into vectorizable algorithms for use in adaptive schemes for various types of boundary value problems is described. The focus is on two key aspects of adaptive computational methods which are crucial in the use of such methods (for complex flow simulations such as those in the Space Shuttle Main Engine): the adaptive scheme itself and the applicability of element-by-element matrix computations in a vectorizable format for rapid calculations in adaptive mesh procedures.
NASA Technical Reports Server (NTRS)
Barnard, Stephen T.; Simon, Horst; Lasinski, T. A. (Technical Monitor)
1994-01-01
The design of a parallel implementation of multilevel recursive spectral bisection is described. The goal is to implement a code that is fast enough to enable dynamic repartitioning of adaptive meshes.
Kohn, S.; Weare, J.; Ong, E.; Baden, S.
1997-05-01
We have applied structured adaptive mesh refinement techniques to the solution of the LDA equations for electronic structure calculations. Local spatial refinement concentrates memory resources and numerical effort where it is most needed, near the atomic centers and in regions of rapidly varying charge density. The structured grid representation enables us to employ efficient iterative solver techniques such as conjugate gradient with FAC multigrid preconditioning. We have parallelized our solver using an object- oriented adaptive mesh refinement framework.
Fast animation of lightning using an adaptive mesh.
Kim, Theodore; Lin, Ming C
2007-01-01
We present a fast method for simulating, animating, and rendering lightning using adaptive grids. The "dielectric breakdown model" is an elegant algorithm for electrical pattern formation that we extend to enable animation of lightning. The simulation can be slow, particularly in 3D, because it involves solving a large Poisson problem. Losasso et al. recently proposed an octree data structure for simulating water and smoke, and we show that this discretization can be applied to the problem of lightning simulation as well. However, implementing the incomplete Cholesky conjugate gradient (ICCG) solver for this problem can be daunting, so we provide an extensive discussion of implementation issues. ICCG solvers can usually be accelerated using "Eisenstat's trick," but the trick cannot be directly applied to the adaptive case. Fortunately, we show that an "almost incomplete Cholesky" factorization can be computed so that Eisenstat's trick can still be used. We then present a fast rendering method based on convolution that is competitive with Monte Carlo ray tracing but orders of magnitude faster, and we also show how to further improve the visual results using jittering. PMID:17218754
NASA Astrophysics Data System (ADS)
Todarello, Giovanni; Vonck, Floris; Bourasseau, Sébastien; Peter, Jacques; Désidéri, Jean-Antoine
2016-05-01
A new goal-oriented mesh adaptation method for finite volume/finite difference schemes is extended from the structured mesh framework to a more suitable setting for adaptation of unstructured meshes. The method is based on the total derivative of the goal with respect to volume mesh nodes that is computable after the solution of the goal discrete adjoint equation. The asymptotic behaviour of this derivative is assessed on regularly refined unstructured meshes. A local refinement criterion is derived from the requirement of limiting the first order change in the goal that an admissible node displacement may cause. Mesh adaptations are then carried out for classical test cases of 2D Euler flows. Efficiency and local density of the adapted meshes are presented. They are compared with those obtained with a more classical mesh adaptation method in the framework of finite volume/finite difference schemes [46]. Results are very close although the present method only makes usage of the current grid.
Star formation with adaptive mesh refinement and magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Collins, David C.
2009-01-01
In this thesis, we develop an adaptive mesh refinement (AMR) code including magnetic fields, and use it to perform high resolution simulations of magnetized molecular clouds. The purpose of these simulations is to study present day star formation in the presence of turbulence and magnetic fields. We first present MHDEnzo, the extension of the cosmology and astrophysics code Enzo to include the effects magnetic fields. We use a higher order Godunov Riemann solver for the computation of interface fluxes; constrained transport to compute the electric field from those interface fluxes, which advances the induction equation in a divergence free manner; divergence free reconstruction technique to interpolate the magnetic fields to fine grids; operator splitting to include gravity and cosmological expansion. We present a series of test problems to demonstrate the quality of solution achieved. Additionally, we present several other solvers that were developed along the way. Finally we present the results from several AMR simulations that study isothermal turbulence in the presence of magnetic fields and self gravity. Ten simulations with initial Mach number 8.9 were studied varying several parameters; virial parameter a from 0.52 to 3.1; whether they were continuously stirred or allowed to decay; and the number of refinement levels (4 or 6). Measurements of the density probability density function (PDF) were made, showing both the expected log normal distribution and an additional power law. Measurements of the line of sight magnetic field vs. column density are done, giving excellent agreement with recent observations. The line width vs. size relationship is measured and compared with good agreement to observations, reproducing both turbulent and collapse signatures The core mass distribution is measured and agrees well with observations of Serpens and Perseus core samples, but the power-law distribution in Ophiuchus is not reproduced by our simulations. Finally we
Feature edge extraction from 3D triangular meshes using a thinning algorithm
NASA Astrophysics Data System (ADS)
Nomura, Masaru; Hamada, Nozomu
2001-11-01
Highly detailed geometric models, which are represented as dense triangular meshes are becoming popular in computer graphics. Since such 3D meshes often have huge information, we require some methods to treat them efficiently in the 3D mesh processing such as, surface simplification, subdivision surface, curved surface approximation and morphing. In these applications, we often extract features of 3D meshes such as feature vertices and feature edges in preprocessing step. An automatic extraction method of feature edges is treated in this study. In order to realize the feature edge extraction method, we first introduce the concavity and convexity evaluation value. Then the histogram of the concavity and convexity evaluation value is used to separate the feature edge region. We apply a thinning algorithm, which is used in 2D binary image processing. It is shown that the proposed method can extract appropriate feature edges from 3D meshes.
Ying, Wenjun; Henriquez, Craig S.
2015-01-01
A both space and time adaptive algorithm is presented for simulating electrical wave propagation in the Purkinje system of the heart. The equations governing the distribution of electric potential over the system are solved in time with the method of lines. At each timestep, by an operator splitting technique, the space-dependent but linear diffusion part and the nonlinear but space-independent reactions part in the partial differential equations are integrated separately with implicit schemes, which have better stability and allow larger timesteps than explicit ones. The linear diffusion equation on each edge of the system is spatially discretized with the continuous piecewise linear finite element method. The adaptive algorithm can automatically recognize when and where the electrical wave starts to leave or enter the computational domain due to external current/voltage stimulation, self-excitation, or local change of membrane properties. Numerical examples demonstrating efficiency and accuracy of the adaptive algorithm are presented. PMID:26581455
SU-D-207-04: GPU-Based 4D Cone-Beam CT Reconstruction Using Adaptive Meshing Method
Zhong, Z; Gu, X; Iyengar, P; Mao, W; Wang, J; Guo, X
2015-06-15
Purpose: Due to the limited number of projections at each phase, the image quality of a four-dimensional cone-beam CT (4D-CBCT) is often degraded, which decreases the accuracy of subsequent motion modeling. One of the promising methods is the simultaneous motion estimation and image reconstruction (SMEIR) approach. The objective of this work is to enhance the computational speed of the SMEIR algorithm using adaptive feature-based tetrahedral meshing and GPU-based parallelization. Methods: The first step is to generate the tetrahedral mesh based on the features of a reference phase 4D-CBCT, so that the deformation can be well captured and accurately diffused from the mesh vertices to voxels of the image volume. After the mesh generation, the updated motion model and other phases of 4D-CBCT can be obtained by matching the 4D-CBCT projection images at each phase with the corresponding forward projections of the deformed reference phase of 4D-CBCT. The entire process of this 4D-CBCT reconstruction method is implemented on GPU, resulting in significantly increasing the computational efficiency due to its tremendous parallel computing ability. Results: A 4D XCAT digital phantom was used to test the proposed mesh-based image reconstruction algorithm. The image Result shows both bone structures and inside of the lung are well-preserved and the tumor position can be well captured. Compared to the previous voxel-based CPU implementation of SMEIR, the proposed method is about 157 times faster for reconstructing a 10 -phase 4D-CBCT with dimension 256×256×150. Conclusion: The GPU-based parallel 4D CBCT reconstruction method uses the feature-based mesh for estimating motion model and demonstrates equivalent image Result with previous voxel-based SMEIR approach, with significantly improved computational speed.
NASA Astrophysics Data System (ADS)
Wang, Cheng; Dong, XinZhuang; Shu, Chi-Wang
2015-10-01
For numerical simulation of detonation, computational cost using uniform meshes is large due to the vast separation in both time and space scales. Adaptive mesh refinement (AMR) is advantageous for problems with vastly different scales. This paper aims to propose an AMR method with high order accuracy for numerical investigation of multi-dimensional detonation. A well-designed AMR method based on finite difference weighted essentially non-oscillatory (WENO) scheme, named as AMR&WENO is proposed. A new cell-based data structure is used to organize the adaptive meshes. The new data structure makes it possible for cells to communicate with each other quickly and easily. In order to develop an AMR method with high order accuracy, high order prolongations in both space and time are utilized in the data prolongation procedure. Based on the message passing interface (MPI) platform, we have developed a workload balancing parallel AMR&WENO code using the Hilbert space-filling curve algorithm. Our numerical experiments with detonation simulations indicate that the AMR&WENO is accurate and has a high resolution. Moreover, we evaluate and compare the performance of the uniform mesh WENO scheme and the parallel AMR&WENO method. The comparison results provide us further insight into the high performance of the parallel AMR&WENO method.
The adaptive GRP scheme for compressible fluid flows over unstructured meshes
NASA Astrophysics Data System (ADS)
Li, Jiequan; Zhang, Yongjin
2013-06-01
Unstructured mesh methods have attracted much attention in CFD community due to the flexibility for dealing with complex geometries and the ability to easily incorporate adaptive (moving) mesh strategies. When the finite volume framework is applied, a reliable solver is crucial for the construction of numerical fluxes, for which the generalized Riemann problem (GRP) scheme undertakes such a task in the sense of second order accuracy. Combining these techniques yields a second order accurate adaptive generalized Riemann problem (AGRP) scheme for two dimensional compressible fluid flows over unstructured triangular meshes. Besides the generation of meshes, the main process of this combination consists of two ingredients: Fluid dynamical evolution and mesh redistribution. The fluid dynamical evolution ingredient serves to evolve the compressible fluid flows on a fixed nonuniform triangular mesh with the direct Eulerian GRP solver. The role of the mesh redistribution is to redistribute mesh points on which a conservative interpolation formula is adopted to calculate the cell-averages for the conservative variables, and the gradients of primitive variables are reconstructed using the least squares method. Several examples are taken from various contexts to demonstrate the performance of such a program.
Parallel adaptive simplical re-meshing for deforming domain CFD computations
NASA Astrophysics Data System (ADS)
Menon, Sandeep; Mooney, Kyle G.; Stapf, K. G.; Schmidt, David P.
2015-10-01
Deforming domains occur in many fields of computational fluid dynamics (CFD), such as interface tracking, simulation of pumps and engines, and fluid/structure interaction. The deformation of the domain presents a challenge to the integrity of the computational mesh; substantial motion of the domain boundaries requires vertex motion and changes in mesh connectivity. For cases of simple boundary motion or structured meshes, predetermined changes to the mesh structure can be sufficient. However, without a priori knowledge of how the domain will change, a more robust solution is required. The present work offers a parallelized solution for simplical meshes that is well-suited to extremely complex geometry. The mesh continuously evolves without user intervention or the use of target meshes. Varying length scales imposed by evolving boundary curvatures and narrow gaps are resolved with a fast length-scale algorithm. The set of algorithms are incorporated into an object-oriented code structure that permits broad application to a range of CFD problems. The robustness and versatility of the algorithm is demonstrated in several examples, representing motion of internal and external boundaries, where the boundary motion may or may not be known a priori.
Single-pass GPU-raycasting for structured adaptive mesh refinement data
NASA Astrophysics Data System (ADS)
Kaehler, Ralf; Abel, Tom
2013-01-01
Structured Adaptive Mesh Refinement (SAMR) is a popular numerical technique to study processes with high spatial and temporal dynamic range. It reduces computational requirements by adapting the lattice on which the underlying differential equations are solved to most efficiently represent the solution. Particularly in astrophysics and cosmology such simulations now can capture spatial scales ten orders of magnitude apart and more. The irregular locations and extensions of the refined regions in the SAMR scheme and the fact that different resolution levels partially overlap, poses a challenge for GPU-based direct volume rendering methods. kD-trees have proven to be advantageous to subdivide the data domain into non-overlapping blocks of equally sized cells, optimal for the texture units of current graphics hardware, but previous GPU-supported raycasting approaches for SAMR data using this data structure required a separate rendering pass for each node, preventing the application of many advanced lighting schemes that require simultaneous access to more than one block of cells. In this paper we present the first single-pass GPU-raycasting algorithm for SAMR data that is based on a kD-tree. The tree is efficiently encoded by a set of 3D-textures, which allows to adaptively sample complete rays entirely on the GPU without any CPU interaction. We discuss two different data storage strategies to access the grid data on the GPU and apply them to several datasets to prove the benefits of the proposed method.
Radiation hydrodynamics including irradiation and adaptive mesh refinement with AZEuS. I. Methods
NASA Astrophysics Data System (ADS)
Ramsey, J. P.; Dullemond, C. P.
2015-02-01
Aims: The importance of radiation to the physical structure of protoplanetary disks cannot be understated. However, protoplanetary disks evolve with time, and so to understand disk evolution and by association, disk structure, one should solve the combined and time-dependent equations of radiation hydrodynamics. Methods: We implement a new implicit radiation solver in the AZEuS adaptive mesh refinement magnetohydrodynamics fluid code. Based on a hybrid approach that combines frequency-dependent ray-tracing for stellar irradiation with non-equilibrium flux limited diffusion, we solve the equations of radiation hydrodynamics while preserving the directionality of the stellar irradiation. The implementation permits simulations in Cartesian, cylindrical, and spherical coordinates, on both uniform and adaptive grids. Results: We present several hydrostatic and hydrodynamic radiation tests which validate our implementation on uniform and adaptive grids as appropriate, including benchmarks specifically designed for protoplanetary disks. Our results demonstrate that the combination of a hybrid radiation algorithm with AZEuS is an effective tool for radiation hydrodynamics studies, and produces results which are competitive with other astrophysical radiation hydrodynamics codes.
Yaqi Wang; Jean C. Ragusa
2011-02-01
Standard and goal-oriented adaptive mesh refinement (AMR) techniques are presented for the linear Boltzmann transport equation. A posteriori error estimates are employed to drive the AMR process and are based on angular-moment information rather than on directional information, leading to direction-independent adapted meshes. An error estimate based on a two-mesh approach and a jump-based error indicator are compared for various test problems. In addition to the standard AMR approach, where the global error in the solution is diminished, a goal-oriented AMR procedure is devised and aims at reducing the error in user-specified quantities of interest. The quantities of interest are functionals of the solution and may include, for instance, point-wise flux values or average reaction rates in a subdomain. A high-order (up to order 4) Discontinuous Galerkin technique with standard upwinding is employed for the spatial discretization; the discrete ordinates method is used to treat the angular variable.
Huang, W.; Zheng, Lingyun; Zhan, X.
2002-01-01
Accurate modelling of groundwater flow and transport with sharp moving fronts often involves high computational cost, when a fixed/uniform mesh is used. In this paper, we investigate the modelling of groundwater problems using a particular adaptive mesh method called the moving mesh partial differential equation approach. With this approach, the mesh is dynamically relocated through a partial differential equation to capture the evolving sharp fronts with a relatively small number of grid points. The mesh movement and physical system modelling are realized by solving the mesh movement and physical partial differential equations alternately. The method is applied to the modelling of a range of groundwater problems, including advection dominated chemical transport and reaction, non-linear infiltration in soil, and the coupling of density dependent flow and transport. Numerical results demonstrate that sharp moving fronts can be accurately and efficiently captured by the moving mesh approach. Also addressed are important implementation strategies, e.g. the construction of the monitor function based on the interpolation error, control of mesh concentration, and two-layer mesh movement. Copyright ?? 2002 John Wiley and Sons, Ltd.
NASA Astrophysics Data System (ADS)
Slattery, Stuart R.
2016-02-01
In this paper we analyze and extend mesh-free algorithms for three-dimensional data transfer problems in partitioned multiphysics simulations. We first provide a direct comparison between a mesh-based weighted residual method using the common-refinement scheme and two mesh-free algorithms leveraging compactly supported radial basis functions: one using a spline interpolation and one using a moving least square reconstruction. Through the comparison we assess both the conservation and accuracy of the data transfer obtained from each of the methods. We do so for a varying set of geometries with and without curvature and sharp features and for functions with and without smoothness and with varying gradients. Our results show that the mesh-based and mesh-free algorithms are complementary with cases where each was demonstrated to perform better than the other. We then focus on the mesh-free methods by developing a set of algorithms to parallelize them based on sparse linear algebra techniques. This includes a discussion of fast parallel radius searching in point clouds and restructuring the interpolation algorithms to leverage data structures and linear algebra services designed for large distributed computing environments. The scalability of our new algorithms is demonstrated on a leadership class computing facility using a set of basic scaling studies. These scaling studies show that for problems with reasonable load balance, our new algorithms for both spline interpolation and moving least square reconstruction demonstrate both strong and weak scalability using more than 100,000 MPI processes with billions of degrees of freedom in the data transfer operation.
Slattery, Stuart R.
2015-12-02
In this study we analyze and extend mesh-free algorithms for three-dimensional data transfer problems in partitioned multiphysics simulations. We first provide a direct comparison between a mesh-based weighted residual method using the common-refinement scheme and two mesh-free algorithms leveraging compactly supported radial basis functions: one using a spline interpolation and one using a moving least square reconstruction. Through the comparison we assess both the conservation and accuracy of the data transfer obtained from each of the methods. We do so for a varying set of geometries with and without curvature and sharp features and for functions with and without smoothnessmore » and with varying gradients. Our results show that the mesh-based and mesh-free algorithms are complementary with cases where each was demonstrated to perform better than the other. We then focus on the mesh-free methods by developing a set of algorithms to parallelize them based on sparse linear algebra techniques. This includes a discussion of fast parallel radius searching in point clouds and restructuring the interpolation algorithms to leverage data structures and linear algebra services designed for large distributed computing environments. The scalability of our new algorithms is demonstrated on a leadership class computing facility using a set of basic scaling studies. Finally, these scaling studies show that for problems with reasonable load balance, our new algorithms for both spline interpolation and moving least square reconstruction demonstrate both strong and weak scalability using more than 100,000 MPI processes with billions of degrees of freedom in the data transfer operation.« less
Slattery, Stuart R.
2015-12-02
In this study we analyze and extend mesh-free algorithms for three-dimensional data transfer problems in partitioned multiphysics simulations. We first provide a direct comparison between a mesh-based weighted residual method using the common-refinement scheme and two mesh-free algorithms leveraging compactly supported radial basis functions: one using a spline interpolation and one using a moving least square reconstruction. Through the comparison we assess both the conservation and accuracy of the data transfer obtained from each of the methods. We do so for a varying set of geometries with and without curvature and sharp features and for functions with and without smoothness and with varying gradients. Our results show that the mesh-based and mesh-free algorithms are complementary with cases where each was demonstrated to perform better than the other. We then focus on the mesh-free methods by developing a set of algorithms to parallelize them based on sparse linear algebra techniques. This includes a discussion of fast parallel radius searching in point clouds and restructuring the interpolation algorithms to leverage data structures and linear algebra services designed for large distributed computing environments. The scalability of our new algorithms is demonstrated on a leadership class computing facility using a set of basic scaling studies. Finally, these scaling studies show that for problems with reasonable load balance, our new algorithms for both spline interpolation and moving least square reconstruction demonstrate both strong and weak scalability using more than 100,000 MPI processes with billions of degrees of freedom in the data transfer operation.
Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme
NASA Astrophysics Data System (ADS)
Yabe, Takashi; Mizoe, Hiroki; Takizawa, Kenji; Moriki, Hiroshi; Im, Hyo-Nam; Ogata, Youichi
2004-02-01
A new class of body-fitted grid system that can keep the third-order accuracy in time and space is proposed with the help of the CIP (constrained interpolation profile/cubic interpolated propagation) method. The grid system consists of the straight lines and grid points moving along these lines like abacus - Soroban in Japanese. The length of each line and the number of grid points in each line can be different. The CIP scheme is suitable to this mesh system and the calculation of large CFL (>10) at locally refined mesh is easily performed. Mesh generation and searching of upstream departure point are very simple and almost mesh-free treatment is possible. Adaptive grid movement and local mesh refinement are demonstrated.
An Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods.
Li, Zhilin; Song, Peng
2012-01-01
An adaptive mesh refinement strategy is proposed in this paper for the Immersed Boundary and Immersed Interface methods for two-dimensional elliptic interface problems involving singular sources. The interface is represented by the zero level set of a Lipschitz function φ(x,y). Our adaptive mesh refinement is done within a small tube of |φ(x,y)|≤ δ with finer Cartesian meshes. The discrete linear system of equations is solved by a multigrid solver. The AMR methods could obtain solutions with accuracy that is similar to those on a uniform fine grid by distributing the mesh more economically, therefore, reduce the size of the linear system of the equations. Numerical examples presented show the efficiency of the grid refinement strategy. PMID:22670155
QPSO-Based Adaptive DNA Computing Algorithm
Karakose, Mehmet; Cigdem, Ugur
2013-01-01
DNA (deoxyribonucleic acid) computing that is a new computation model based on DNA molecules for information storage has been increasingly used for optimization and data analysis in recent years. However, DNA computing algorithm has some limitations in terms of convergence speed, adaptability, and effectiveness. In this paper, a new approach for improvement of DNA computing is proposed. This new approach aims to perform DNA computing algorithm with adaptive parameters towards the desired goal using quantum-behaved particle swarm optimization (QPSO). Some contributions provided by the proposed QPSO based on adaptive DNA computing algorithm are as follows: (1) parameters of population size, crossover rate, maximum number of operations, enzyme and virus mutation rate, and fitness function of DNA computing algorithm are simultaneously tuned for adaptive process, (2) adaptive algorithm is performed using QPSO algorithm for goal-driven progress, faster operation, and flexibility in data, and (3) numerical realization of DNA computing algorithm with proposed approach is implemented in system identification. Two experiments with different systems were carried out to evaluate the performance of the proposed approach with comparative results. Experimental results obtained with Matlab and FPGA demonstrate ability to provide effective optimization, considerable convergence speed, and high accuracy according to DNA computing algorithm. PMID:23935409
Novel irregular mesh tagging algorithm for wound synthesis on a 3D face.
Lee, Sangyong; Chin, Seongah
2015-01-01
Recently, advanced visualizing techniques in computer graphics have considerably enhanced the visual appearance of synthetic models. To realize enhanced visual graphics for synthetic medical effects, the first step followed by rendering techniques involves attaching albedo textures to the region where a certain graphic is to be rendered. For instance, in order to render wound textures efficiently, the first step is to recognize the area where the user wants to attach a wound. However, in general, face indices are not stored in sequential order, which makes sub-texturing difficult. In this paper, we present a novel mesh tagging algorithm that utilizes a task for mesh traversals and level extension in the general case of a wound sub-texture mapping and a selected region deformation in a three-dimensional (3D) model. This method works automatically on both regular and irregular mesh surfaces. The approach consists of mesh selection (MS), mesh leveling (ML), and mesh tagging (MT). To validate our approach, we performed experiments for synthesizing wounds on a 3D face model and on a simulated mesh. PMID:26405904
AMR++: A design for parallel object-oriented adaptive mesh refinement
Quinlan, D.
1997-11-01
Adaptive mesh refinement computations are complicated by their dynamic nature. In the serial environment they require substantial infrastructures to support the regridding processes, intergrid operations, and local bookkeeping of positions of grids relative to one another. In the parallel environment the dynamic behavior is more problematic because it requires dynamic distribution support and load balancing. Parallel AMR is further complicated by the substantial task parallelism, in addition to the obvious data parallelism, this task parallelism requires additional infrastructure to support efficiently. The degree of parallelism is typically dependent upon the algorithms in use and the equations being solved. Different algorithms have significant compromises between computation and communication. Substantial research work is often required to define efficient methods and suitable infrastructure. The purpose of this paper is to introduce AMR++ as an object-oriented library which forms a part of the OVERTURE framework, a much larger object-oriented numerical framework developed and supported at Los Alamos National Laboratory and distributed on the Web for the last several years.
CRASH: A BLOCK-ADAPTIVE-MESH CODE FOR RADIATIVE SHOCK HYDRODYNAMICS-IMPLEMENTATION AND VERIFICATION
Van der Holst, B.; Toth, G.; Sokolov, I. V.; Myra, E. S.; Fryxell, B.; Drake, R. P.; Powell, K. G.; Holloway, J. P.; Stout, Q.; Adams, M. L.; Morel, J. E.; Karni, S.
2011-06-01
We describe the Center for Radiative Shock Hydrodynamics (CRASH) code, a block-adaptive-mesh code for multi-material radiation hydrodynamics. The implementation solves the radiation diffusion model with a gray or multi-group method and uses a flux-limited diffusion approximation to recover the free-streaming limit. Electrons and ions are allowed to have different temperatures and we include flux-limited electron heat conduction. The radiation hydrodynamic equations are solved in the Eulerian frame by means of a conservative finite-volume discretization in either one-, two-, or three-dimensional slab geometry or in two-dimensional cylindrical symmetry. An operator-split method is used to solve these equations in three substeps: (1) an explicit step of a shock-capturing hydrodynamic solver; (2) a linear advection of the radiation in frequency-logarithm space; and (3) an implicit solution of the stiff radiation diffusion, heat conduction, and energy exchange. We present a suite of verification test problems to demonstrate the accuracy and performance of the algorithms. The applications are for astrophysics and laboratory astrophysics. The CRASH code is an extension of the Block-Adaptive Tree Solarwind Roe Upwind Scheme (BATS-R-US) code with a new radiation transfer and heat conduction library and equation-of-state and multi-group opacity solvers. Both CRASH and BATS-R-US are part of the publicly available Space Weather Modeling Framework.
CRASH: A Block-adaptive-mesh Code for Radiative Shock Hydrodynamics—Implementation and Verification
NASA Astrophysics Data System (ADS)
van der Holst, B.; Tóth, G.; Sokolov, I. V.; Powell, K. G.; Holloway, J. P.; Myra, E. S.; Stout, Q.; Adams, M. L.; Morel, J. E.; Karni, S.; Fryxell, B.; Drake, R. P.
2011-06-01
We describe the Center for Radiative Shock Hydrodynamics (CRASH) code, a block-adaptive-mesh code for multi-material radiation hydrodynamics. The implementation solves the radiation diffusion model with a gray or multi-group method and uses a flux-limited diffusion approximation to recover the free-streaming limit. Electrons and ions are allowed to have different temperatures and we include flux-limited electron heat conduction. The radiation hydrodynamic equations are solved in the Eulerian frame by means of a conservative finite-volume discretization in either one-, two-, or three-dimensional slab geometry or in two-dimensional cylindrical symmetry. An operator-split method is used to solve these equations in three substeps: (1) an explicit step of a shock-capturing hydrodynamic solver; (2) a linear advection of the radiation in frequency-logarithm space; and (3) an implicit solution of the stiff radiation diffusion, heat conduction, and energy exchange. We present a suite of verification test problems to demonstrate the accuracy and performance of the algorithms. The applications are for astrophysics and laboratory astrophysics. The CRASH code is an extension of the Block-Adaptive Tree Solarwind Roe Upwind Scheme (BATS-R-US) code with a new radiation transfer and heat conduction library and equation-of-state and multi-group opacity solvers. Both CRASH and BATS-R-US are part of the publicly available Space Weather Modeling Framework.
CRASH: A Block-Adaptive-Mesh Code for Radiative Shock Hydrodynamics
NASA Astrophysics Data System (ADS)
van der Holst, B.; Toth, G.; Sokolov, I. V.; Powell, K. G.; Holloway, J. P.; Myra, E. S.; Stout, Q.; Adams, M. L.; Morel, J. E.; Drake, R. P.
2011-01-01
We describe the CRASH (Center for Radiative Shock Hydrodynamics) code, a block adaptive mesh code for multi-material radiation hydrodynamics. The implementation solves the radiation diffusion model with the gray or multigroup method and uses a flux limited diffusion approximation to recover the free-streaming limit. The electrons and ions are allowed to have different temperatures and we include a flux limited electron heat conduction. The radiation hydrodynamic equations are solved in the Eulerian frame by means of a conservative finite volume discretization in either one, two, or three-dimensional slab geometry or in two-dimensional cylindrical symmetry. An operator split method is used to solve these equations in three substeps: (1) solve the hydrodynamic equations with shock-capturing schemes, (2) a linear advection of the radiation in frequency-logarithm space, and (3) an implicit solve of the stiff radiation diffusion, heat conduction, and energy exchange. We present a suite of verification test problems to demonstrate the accuracy and performance of the algorithms. The CRASH code is an extension of the Block-Adaptive Tree Solarwind Roe Upwind Scheme (BATS-R-US) code with this new radiation transfer and heat conduction library and equation-of-state and multigroup opacity solvers. Both CRASH and BATS-R-US are part of the publicly available Space Weather Modeling Framework (SWMF).
NASA Technical Reports Server (NTRS)
Steinthorsson, E.; Modiano, David; Colella, Phillip
1994-01-01
A methodology for accurate and efficient simulation of unsteady, compressible flows is presented. The cornerstones of the methodology are a special discretization of the Navier-Stokes equations on structured body-fitted grid systems and an efficient solution-adaptive mesh refinement technique for structured grids. The discretization employs an explicit multidimensional upwind scheme for the inviscid fluxes and an implicit treatment of the viscous terms. The mesh refinement technique is based on the AMR algorithm of Berger and Colella. In this approach, cells on each level of refinement are organized into a small number of topologically rectangular blocks, each containing several thousand cells. The small number of blocks leads to small overhead in managing data, while their size and regular topology means that a high degree of optimization can be achieved on computers with vector processors.
Adaptive sensor fusion using genetic algorithms
Fitzgerald, D.S.; Adams, D.G.
1994-08-01
Past attempts at sensor fusion have used some form of Boolean logic to combine the sensor information. As an alteniative, an adaptive ``fuzzy`` sensor fusion technique is described in this paper. This technique exploits the robust capabilities of fuzzy logic in the decision process as well as the optimization features of the genetic algorithm. This paper presents a brief background on fuzzy logic and genetic algorithms and how they are used in an online implementation of adaptive sensor fusion.
An adaptive mesh finite volume method for the Euler equations of gas dynamics
NASA Astrophysics Data System (ADS)
Mungkasi, Sudi
2016-06-01
The Euler equations have been used to model gas dynamics for decades. They consist of mathematical equations for the conservation of mass, momentum, and energy of the gas. For a large time value, the solution may contain discontinuities, even when the initial condition is smooth. A standard finite volume numerical method is not able to give accurate solutions to the Euler equations around discontinuities. Therefore we solve the Euler equations using an adaptive mesh finite volume method. In this paper, we present a new construction of the adaptive mesh finite volume method with an efficient computation of the refinement indicator. The adaptive method takes action automatically at around places having inaccurate solutions. Inaccurate solutions are reconstructed to reduce the error by refining the mesh locally up to a certain level. On the other hand, if the solution is already accurate, then the mesh is coarsened up to another certain level to minimize computational efforts. We implement the numerical entropy production as the mesh refinement indicator. As a test problem, we take the Sod shock tube problem. Numerical results show that the adaptive method is more promising than the standard one in solving the Euler equations of gas dynamics.
NASA Astrophysics Data System (ADS)
Rastigejev, Y.; Semakin, A. N.
2013-12-01
Accurate numerical simulations of global scale three-dimensional atmospheric chemical transport models (CTMs) are essential for studies of many important atmospheric chemistry problems such as adverse effect of air pollutants on human health, ecosystems and the Earth's climate. These simulations usually require large CPU time due to numerical difficulties associated with a wide range of spatial and temporal scales, nonlinearity and large number of reacting species. In our previous work we have shown that in order to achieve adequate convergence rate and accuracy, the mesh spacing in numerical simulation of global synoptic-scale pollution plume transport must be decreased to a few kilometers. This resolution is difficult to achieve for global CTMs on uniform or quasi-uniform grids. To address the described above difficulty we developed a three-dimensional Wavelet-based Adaptive Mesh Refinement (WAMR) algorithm. The method employs a highly non-uniform adaptive grid with fine resolution over the areas of interest without requiring small grid-spacing throughout the entire domain. The method uses multi-grid iterative solver that naturally takes advantage of a multilevel structure of the adaptive grid. In order to represent the multilevel adaptive grid efficiently, a dynamic data structure based on indirect memory addressing has been developed. The data structure allows rapid access to individual points, fast inter-grid operations and re-gridding. The WAMR method has been implemented on parallel computer architectures. The parallel algorithm is based on run-time partitioning and load-balancing scheme for the adaptive grid. The partitioning scheme maintains locality to reduce communications between computing nodes. The parallel scheme was found to be cost-effective. Specifically we obtained an order of magnitude increase in computational speed for numerical simulations performed on a twelve-core single processor workstation. We have applied the WAMR method for numerical
Adaptive unstructured meshing for thermal stress analysis of built-up structures
NASA Technical Reports Server (NTRS)
Dechaumphai, Pramote
1992-01-01
An adaptive unstructured meshing technique for mechanical and thermal stress analysis of built-up structures has been developed. A triangular membrane finite element and a new plate bending element are evaluated on a panel with a circular cutout and a frame stiffened panel. The adaptive unstructured meshing technique, without a priori knowledge of the solution to the problem, generates clustered elements only where needed. An improved solution accuracy is obtained at a reduced problem size and analysis computational time as compared to the results produced by the standard finite element procedure.
Using Multi-threading for the Automatic Load Balancing of 2D Adaptive Finite Element Meshes
NASA Technical Reports Server (NTRS)
Heber, Gerd; Biswas, Rupak; Thulasiraman, Parimala; Gao, Guang R.; Saini, Subhash (Technical Monitor)
1998-01-01
In this paper, we present a multi-threaded approach for the automatic load balancing of adaptive finite element (FE) meshes The platform of our choice is the EARTH multi-threaded system which offers sufficient capabilities to tackle this problem. We implement the adaption phase of FE applications oil triangular meshes and exploit the EARTH token mechanism to automatically balance the resulting irregular and highly nonuniform workload. We discuss the results of our experiments oil EARTH-SP2, on implementation of EARTH on the IBM SP2 with different load balancing strategies that are built into the runtime system.
Parallelization of Unsteady Adaptive Mesh Refinement for Unstructured Navier-Stokes Solvers
NASA Technical Reports Server (NTRS)
Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.
2014-01-01
This paper explores the implementation of the MPI parallelization in a Navier-Stokes solver using adaptive mesh re nement. Viscous and inviscid test problems are considered for the purpose of benchmarking, as are implicit and explicit time advancement methods. The main test problem for comparison includes e ects from boundary layers and other viscous features and requires a large number of grid points for accurate computation. Ex- perimental validation against double cone experiments in hypersonic ow are shown. The adaptive mesh re nement shows promise for a staple test problem in the hypersonic com- munity. Extension to more advanced techniques for more complicated ows is described.
Thickness-based adaptive mesh refinement methods for multi-phase flow simulations with thin regions
Chen, Xiaodong; Yang, Vigor
2014-07-15
In numerical simulations of multi-scale, multi-phase flows, grid refinement is required to resolve regions with small scales. A notable example is liquid-jet atomization and subsequent droplet dynamics. It is essential to characterize the detailed flow physics with variable length scales with high fidelity, in order to elucidate the underlying mechanisms. In this paper, two thickness-based mesh refinement schemes are developed based on distance- and topology-oriented criteria for thin regions with confining wall/plane of symmetry and in any situation, respectively. Both techniques are implemented in a general framework with a volume-of-fluid formulation and an adaptive-mesh-refinement capability. The distance-oriented technique compares against a critical value, the ratio of an interfacial cell size to the distance between the mass center of the cell and a reference plane. The topology-oriented technique is developed from digital topology theories to handle more general conditions. The requirement for interfacial mesh refinement can be detected swiftly, without the need of thickness information, equation solving, variable averaging or mesh repairing. The mesh refinement level increases smoothly on demand in thin regions. The schemes have been verified and validated against several benchmark cases to demonstrate their effectiveness and robustness. These include the dynamics of colliding droplets, droplet motions in a microchannel, and atomization of liquid impinging jets. Overall, the thickness-based refinement technique provides highly adaptive meshes for problems with thin regions in an efficient and fully automatic manner.
NASA Astrophysics Data System (ADS)
Tang, Qiuyan; Wang, Jing; Lv, Pin; Sun, Quan
2015-10-01
Propagation simulation method and choosing mesh grid are both very important to get the correct propagation results in wave optics simulation. A new angular spectrum propagation method with alterable mesh grid based on the traditional angular spectrum method and the direct FFT method is introduced. With this method, the sampling space after propagation is not limited to propagation methods no more, but freely alterable. However, choosing mesh grid on target board influences the validity of simulation results directly. So an adaptive mesh choosing method based on wave characteristics is proposed with the introduced propagation method. We can calculate appropriate mesh grids on target board to get satisfying results. And for complex initial wave field or propagation through inhomogeneous media, we can also calculate and set the mesh grid rationally according to above method. Finally, though comparing with theoretical results, it's shown that the simulation result with the proposed method coinciding with theory. And by comparing with the traditional angular spectrum method and the direct FFT method, it's known that the proposed method is able to adapt to a wider range of Fresnel number conditions. That is to say, the method can simulate propagation results efficiently and correctly with propagation distance of almost zero to infinity. So it can provide better support for more wave propagation applications such as atmospheric optics, laser propagation and so on.
NASA Astrophysics Data System (ADS)
Rastigejev, Y.; Semakin, A. N.
2012-12-01
In this work we present a multilevel Wavelet-based Adaptive Mesh Refinement (WAMR) method for numerical modeling of global atmospheric chemical transport problems. An accurate numerical simulation of such problems presents an enormous challenge. Atmospheric Chemical Transport Models (CTMs) combine chemical reactions with meteorologically predicted atmospheric advection and turbulent mixing. The resulting system of multi-scale advection-reaction-diffusion equations is extremely stiff, nonlinear and involves a large number of chemically interacting species. As a consequence, the need for enormous computational resources for solving these equations imposes severe limitations on the spatial resolution of the CTMs implemented on uniform or quasi-uniform grids. In turn, this relatively crude spatial resolution results in significant numerical diffusion introduced into the system. This numerical diffusion is shown to noticeably distort the pollutant mixing and transport dynamics for typically used grid resolutions. The developed WAMR method for numerical modeling of atmospheric chemical evolution equations presented in this work provides a significant reduction in the computational cost, without upsetting numerical accuracy, therefore it addresses the numerical difficulties described above. WAMR method introduces a fine grid in the regions where sharp transitions occur and cruder grid in the regions of smooth solution behavior. Therefore WAMR results in much more accurate solutions than conventional numerical methods implemented on uniform or quasi-uniform grids. The algorithm allows one to provide error estimates of the solution that are used in conjunction with appropriate threshold criteria to adapt the non-uniform grid. The method has been tested for a variety of problems including numerical simulation of traveling pollution plumes. It was shown that pollution plumes in the remote troposphere can propagate as well-defined layered structures for two weeks or more as
A boundary recovery algorithm for Delaunay tetrahedral meshing
Sharov, D.; Nakahashi, K.
1996-12-31
A method for automatic generation of unstructured grids comprised of tetrahedra is discussed. Delaunay approach for tetrahedral grid generation is used. Particular attention is given to the boundary constraining problem. A simple and robust algorithm for the boundary constraining by successive use of boundary edge swapping, tetrahedral edge swapping and direct subdivision of tetrahedra is used. Small modifications allow to apply the method for viscous grid generation as well. Grid examples demonstrate efficiency of the method.
A parallel, volume-tracking algorithm for unstructured meshes
Mosso, S.J.; Swartz, B.K.; Kothe, D.B.; Ferrell, R.C.
1996-10-01
Many diverse areas of industry benefit from the use of volume of fluid methods to predict the movement of materials. Casting is a common method of part fabrication. The accurate prediction of the casting process is pivotal to industry. Mold design and casting is currently considered an art by industry. It typically involves many trial mold designs, and the rejection of defective parts is costly. Failure of cast parts, because residual stresses reduce the part`s strength, can be catastrophic. Cast parts should have precise geometric details that reduce or eliminate the need for machining after casting. Volume of fluid codes will help designers predict how the molten metal fills a mold and where ay trapped voids remain. Prediction of defects due to thermal contraction or expansion will eliminate defective, trial mold designs and speed the parts to market with fewer rejections. Increasing the predictability and therefore the accuracy of the casting process will reduce the art that is involved in mold design and parts casting. Here, recent enhancements to multidimensional volume-tracking algorithms are presented. Illustrations in two dimensions are given. The improvements include new, local algorithms for interface normal constructions and a new full remapping algorithm for time integration. These methods are used on structured and unstructured grids.
Henshaw, W; Schwendeman, D
2007-11-15
This paper describes an approach for the numerical solution of time-dependent partial differential equations in complex three-dimensional domains. The domains are represented by overlapping structured grids, and block-structured adaptive mesh refinement (AMR) is employed to locally increase the grid resolution. In addition, the numerical method is implemented on parallel distributed-memory computers using a domain-decomposition approach. The implementation is flexible so that each base grid within the overlapping grid structure and its associated refinement grids can be independently partitioned over a chosen set of processors. A modified bin-packing algorithm is used to specify the partition for each grid so that the computational work is evenly distributed amongst the processors. All components of the AMR algorithm such as error estimation, regridding, and interpolation are performed in parallel. The parallel time-stepping algorithm is illustrated for initial-boundary-value problems involving a linear advection-diffusion equation and the (nonlinear) reactive Euler equations. Numerical results are presented for both equations to demonstrate the accuracy and correctness of the parallel approach. Exact solutions of the advection-diffusion equation are constructed, and these are used to check the corresponding numerical solutions for a variety of tests involving different overlapping grids, different numbers of refinement levels and refinement ratios, and different numbers of processors. The problem of planar shock diffraction by a sphere is considered as an illustration of the numerical approach for the Euler equations, and a problem involving the initiation of a detonation from a hot spot in a T-shaped pipe is considered to demonstrate the numerical approach for the reactive case. For both problems, the solutions are shown to be well resolved on the finest grid. The parallel performance of the approach is examined in detail for the shock diffraction problem.
Multilevel Error Estimation and Adaptive h-Refinement for Cartesian Meshes with Embedded Boundaries
NASA Technical Reports Server (NTRS)
Aftosmis, M. J.; Berger, M. J.; Kwak, Dochan (Technical Monitor)
2002-01-01
This paper presents the development of a mesh adaptation module for a multilevel Cartesian solver. While the module allows mesh refinement to be driven by a variety of different refinement parameters, a central feature in its design is the incorporation of a multilevel error estimator based upon direct estimates of the local truncation error using tau-extrapolation. This error indicator exploits the fact that in regions of uniform Cartesian mesh, the spatial operator is exactly the same on the fine and coarse grids, and local truncation error estimates can be constructed by evaluating the residual on the coarse grid of the restricted solution from the fine grid. A new strategy for adaptive h-refinement is also developed to prevent errors in smooth regions of the flow from being masked by shocks and other discontinuous features. For certain classes of error histograms, this strategy is optimal for achieving equidistribution of the refinement parameters on hierarchical meshes, and therefore ensures grid converged solutions will be achieved for appropriately chosen refinement parameters. The robustness and accuracy of the adaptation module is demonstrated using both simple model problems and complex three dimensional examples using meshes with from 10(exp 6), to 10(exp 7) cells.
Self-adaptive parameters in genetic algorithms
NASA Astrophysics Data System (ADS)
Pellerin, Eric; Pigeon, Luc; Delisle, Sylvain
2004-04-01
Genetic algorithms are powerful search algorithms that can be applied to a wide range of problems. Generally, parameter setting is accomplished prior to running a Genetic Algorithm (GA) and this setting remains unchanged during execution. The problem of interest to us here is the self-adaptive parameters adjustment of a GA. In this research, we propose an approach in which the control of a genetic algorithm"s parameters can be encoded within the chromosome of each individual. The parameters" values are entirely dependent on the evolution mechanism and on the problem context. Our preliminary results show that a GA is able to learn and evaluate the quality of self-set parameters according to their degree of contribution to the resolution of the problem. These results are indicative of a promising approach to the development of GAs with self-adaptive parameter settings that do not require the user to pre-adjust parameters at the outset.
Modeling, mesh generation, and adaptive numerical methods for partial differential equations
Babuska, I.; Henshaw, W.D.; Oliger, J.E.; Flaherty, J.E.; Hopcroft, J.E.; Tezduyar, T.
1995-12-31
Mesh generation is one of the most time consuming aspects of computational solutions of problems involving partial differential equations. It is, furthermore, no longer acceptable to compute solutions without proper verification that specified accuracy criteria are being satisfied. Mesh generation must be related to the solution through computable estimates of discretization errors. Thus, an iterative process of alternate mesh and solution generation evolves in an adaptive manner with the end result that the solution is computed to prescribed specifications in an optimal, or at least efficient, manner. While mesh generation and adaptive strategies are becoming available, major computational challenges remain. One, in particular, involves moving boundaries and interfaces, such as free-surface flows and fluid-structure interactions. A 3-week program was held from July 5 to July 23, 1993 with 173 participants and 66 keynote, invited, and contributed presentations. This volume represents written versions of 21 of these lectures. These proceedings are organized roughly in order of their presentation at the workshop. Thus, the initial papers are concerned with geometry and mesh generation and discuss the representation of physical objects and surfaces on a computer and techniques to use this data to generate, principally, unstructured meshes of tetrahedral or hexahedral elements. The remainder of the papers cover adaptive strategies, error estimation, and applications. Several submissions deal with high-order p- and hp-refinement methods where mesh refinement/coarsening (h-refinement) is combined with local variation of method order (p-refinement). Combinations of mathematically verified and physically motivated approaches to error estimation are represented. Applications center on fluid mechanics. Selected papers are indexed separately for inclusion in the Energy Science and Technology Database.
Rebay, S. )
1993-05-01
This work is devoted to the description of an efficient unstructured mesh generation method entirely based on the Delaunay triangulation. The distinctive characteristic of the proposed method is that point positions and connections are computed simultaneously. This result is achieved by taking advantage of the sequential way in which the Bowyer-Watson algorithm computes the Delaunay triangulation. Two methods are proposed which have great geometrical flexibility, in that they allow us to treat domains of arbitrary shape and topology and to generate arbitrarily nonuniform meshes. The methods are computationally efficient and are applicable both in two and three dimensions. 11 refs., 20 figs., 1 tab.
Implementation of a mesh adaptive scheme based on an element-level error indicator
NASA Technical Reports Server (NTRS)
Keating, Scott; Felippa, Carlos A.; Militello, Carmelo
1993-01-01
We investigate the formulation and application of element-level error indicators based on parametrized variational principles. The qualifier 'element-level' means that no information from adjacent elements is used for error estimation. This property is ideally suited to drive adaptive mesh refinement on parallel computers where access to neighboring elements resident on different processors may incur significant computational overhead. Furthermore, such indicators are not affected by physical jumps at junctures or interfaces. An element-level indicator has been derived from the higher-order element energy and applied to r and h mesh adaptation of meshes in plates and shell structures. We report on our initial experiments with a cylindrical shell that intersects with fist plates forming a simplified 'wing-body intersection' benchmark problem.
Adaptive mesh refinement techniques for the immersed interface method applied to flow problems.
Li, Zhilin; Song, Peng
2013-06-01
In this paper, we develop an adaptive mesh refinement strategy of the Immersed Interface Method for flow problems with a moving interface. The work is built on the AMR method developed for two-dimensional elliptic interface problems in the paper [12] (CiCP, 12(2012), 515-527). The interface is captured by the zero level set of a Lipschitz continuous function φ(x, y, t). Our adaptive mesh refinement is built within a small band of |φ(x, y, t)| ≤ δ with finer Cartesian meshes. The AMR-IIM is validated for Stokes and Navier-Stokes equations with exact solutions, moving interfaces driven by the surface tension, and classical bubble deformation problems. A new simple area preserving strategy is also proposed in this paper for the level set method. PMID:23794763
Parallel, Gradient-Based Anisotropic Mesh Adaptation for Re-entry Vehicle Configurations
NASA Technical Reports Server (NTRS)
Bibb, Karen L.; Gnoffo, Peter A.; Park, Michael A.; Jones, William T.
2006-01-01
Two gradient-based adaptation methodologies have been implemented into the Fun3d refine GridEx infrastructure. A spring-analogy adaptation which provides for nodal movement to cluster mesh nodes in the vicinity of strong shocks has been extended for general use within Fun3d, and is demonstrated for a 70 sphere cone at Mach 2. A more general feature-based adaptation metric has been developed for use with the adaptation mechanics available in Fun3d, and is applicable to any unstructured, tetrahedral, flow solver. The basic functionality of general adaptation is explored through a case of flow over the forebody of a 70 sphere cone at Mach 6. A practical application of Mach 10 flow over an Apollo capsule, computed with the Felisa flow solver, is given to compare the adaptive mesh refinement with uniform mesh refinement. The examples of the paper demonstrate that the gradient-based adaptation capability as implemented can give an improvement in solution quality.
Failure of Anisotropic Unstructured Mesh Adaption Based on Multidimensional Residual Minimization
NASA Technical Reports Server (NTRS)
Wood, William A.; Kleb, William L.
2003-01-01
An automated anisotropic unstructured mesh adaptation strategy is proposed, implemented, and assessed for the discretization of viscous flows. The adaption criteria is based upon the minimization of the residual fluctuations of a multidimensional upwind viscous flow solver. For scalar advection, this adaption strategy has been shown to use fewer grid points than gradient based adaption, naturally aligning mesh edges with discontinuities and characteristic lines. The adaption utilizes a compact stencil and is local in scope, with four fundamental operations: point insertion, point deletion, edge swapping, and nodal displacement. Evaluation of the solution-adaptive strategy is performed for a two-dimensional blunt body laminar wind tunnel case at Mach 10. The results demonstrate that the strategy suffers from a lack of robustness, particularly with regard to alignment of the bow shock in the vicinity of the stagnation streamline. In general, constraining the adaption to such a degree as to maintain robustness results in negligible improvement to the solution. Because the present method fails to consistently or significantly improve the flow solution, it is rejected in favor of simple uniform mesh refinement.
3D Boltzmann Simulation of the Io's Plasma Environment with Adaptive Mesh and Particle Refinement
NASA Astrophysics Data System (ADS)
Lipatov, A. S.; Combi, M. R.
2002-12-01
The global dynamics of the ionized and neutral components in the environment of Io plays an important role in the interaction of Jupiter's corotating magnetospheric plasma with Io [Combi et al., 2002; 1998; Kabin et al., 2001]. The stationary simulation of this problem was done in the MHD [Combi et al., 1998; Linker et al, 1998; Kabin et al., 2001] and the electrodynamic [Saur et al., 1999] approaches. In this report, we develop a method of kinetic ion-neutral simulation, which is based on a multiscale adaptive mesh, particle and algorithm refinement. This method employs the fluid description for electrons whereas for ions the drift-kinetic and particle approaches are used. This method takes into account charge-exchange and photoionization processes. The first results of such simulation of the dynamics of ions in the Io's environment are discussed in this report. ~ M R Combi et al., J. Geophys. Res., 103, 9071, 1998. M R Combi, T I Gombosi, K Kabin, Atmospheres in the Solar System: Comparative\\ Aeronomy. Geophys. Monograph Series, 130, 151, 2002. K Kabin et al., Planetary and Space Sci., 49, 337, 2001. J A Linker et al., J. Geophys. Res., 103(E9), 19867, 1998. J Saur et al., J. Geophys. Res., 104, 25105, 1999.
Relativistic Flows Using Spatial And Temporal Adaptive Structured Mesh Refinement. I. Hydrodynamics
Wang, Peng; Abel, Tom; Zhang, Weiqun; /KIPAC, Menlo Park
2007-04-02
Astrophysical relativistic flow problems require high resolution three-dimensional numerical simulations. In this paper, we describe a new parallel three-dimensional code for simulations of special relativistic hydrodynamics (SRHD) using both spatially and temporally structured adaptive mesh refinement (AMR). We used method of lines to discrete SRHD equations spatially and used a total variation diminishing (TVD) Runge-Kutta scheme for time integration. For spatial reconstruction, we have implemented piecewise linear method (PLM), piecewise parabolic method (PPM), third order convex essentially non-oscillatory (CENO) and third and fifth order weighted essentially non-oscillatory (WENO) schemes. Flux is computed using either direct flux reconstruction or approximate Riemann solvers including HLL, modified Marquina flux, local Lax-Friedrichs flux formulas and HLLC. The AMR part of the code is built on top of the cosmological Eulerian AMR code enzo, which uses the Berger-Colella AMR algorithm and is parallel with dynamical load balancing using the widely available Message Passing Interface library. We discuss the coupling of the AMR framework with the relativistic solvers and show its performance on eleven test problems.
Towards a large-scale scalable adaptive heart model using shallow tree meshes
NASA Astrophysics Data System (ADS)
Krause, Dorian; Dickopf, Thomas; Potse, Mark; Krause, Rolf
2015-10-01
Electrophysiological heart models are sophisticated computational tools that place high demands on the computing hardware due to the high spatial resolution required to capture the steep depolarization front. To address this challenge, we present a novel adaptive scheme for resolving the deporalization front accurately using adaptivity in space. Our adaptive scheme is based on locally structured meshes. These tensor meshes in space are organized in a parallel forest of trees, which allows us to resolve complicated geometries and to realize high variations in the local mesh sizes with a minimal memory footprint in the adaptive scheme. We discuss both a non-conforming mortar element approximation and a conforming finite element space and present an efficient technique for the assembly of the respective stiffness matrices using matrix representations of the inclusion operators into the product space on the so-called shallow tree meshes. We analyzed the parallel performance and scalability for a two-dimensional ventricle slice as well as for a full large-scale heart model. Our results demonstrate that the method has good performance and high accuracy.
Laser ray tracing in a parallel arbitrary Lagrangian-Eulerian adaptive mesh refinement hydrocode
NASA Astrophysics Data System (ADS)
Masters, N. D.; Kaiser, T. B.; Anderson, R. W.; Eder, D. C.; Fisher, A. C.; Koniges, A. E.
2010-08-01
ALE-AMR is a new hydrocode that we are developing as a predictive modeling tool for debris and shrapnel formation in high-energy laser experiments. In this paper we present our approach to implementing laser ray tracing in ALE-AMR. We present the basic concepts of laser ray tracing and our approach to efficiently traverse the adaptive mesh hierarchy.
A moving mesh algorithm for 3-D regional groundwater flow with water table and seepage face
NASA Astrophysics Data System (ADS)
Knupp, P.
A numerical algorithm is described for solving the free-surface groundwater flow equations in 3-D large-scale unconfined aquifers with strongly heterogeneous conductivity and surface recharge. The algorithm uses a moving mesh to track the water-table as it evolves according to kinematic and seepage face boundary conditions. Both steady-state and transient algorithms are implemented in the SECO-Flow 3-D code and demonstrated on stratigraphy based on the Delaware Basin of south-eastern New Mexico.
Adaptive link selection algorithms for distributed estimation
NASA Astrophysics Data System (ADS)
Xu, Songcen; de Lamare, Rodrigo C.; Poor, H. Vincent
2015-12-01
This paper presents adaptive link selection algorithms for distributed estimation and considers their application to wireless sensor networks and smart grids. In particular, exhaustive search-based least mean squares (LMS) / recursive least squares (RLS) link selection algorithms and sparsity-inspired LMS / RLS link selection algorithms that can exploit the topology of networks with poor-quality links are considered. The proposed link selection algorithms are then analyzed in terms of their stability, steady-state, and tracking performance and computational complexity. In comparison with the existing centralized or distributed estimation strategies, the key features of the proposed algorithms are as follows: (1) more accurate estimates and faster convergence speed can be obtained and (2) the network is equipped with the ability of link selection that can circumvent link failures and improve the estimation performance. The performance of the proposed algorithms for distributed estimation is illustrated via simulations in applications of wireless sensor networks and smart grids.
The geometry of r-adaptive meshes generated using optimal transport methods
NASA Astrophysics Data System (ADS)
Budd, C. J.; Russell, R. D.; Walsh, E.
2015-02-01
The principles of mesh equidistribution and alignment play a fundamental role in the design of adaptive methods, and a metric tensor and mesh metric are useful theoretical tools for understanding a method's level of mesh alignment, or anisotropy. We consider a mesh redistribution method based on the Monge-Ampère equation which combines equidistribution of a given scalar density function with optimal transport. It does not involve explicit use of a metric tensor, although such a tensor must exist for the method, and an interesting question to ask is whether or not the alignment produced by the metric gives an anisotropic mesh. For model problems with a linear feature and with a radially symmetric feature, we derive the exact form of the metric, which involves expressions for its eigenvalues and eigenvectors. The eigenvectors are shown to be orthogonal and tangential to the feature, and the ratio of the eigenvalues (corresponding to the level of anisotropy) is shown to depend, both locally and globally, on the value of the density function and the amount of curvature. We thereby demonstrate how the optimal transport method produces an anisotropic mesh along a given feature while equidistributing a suitably chosen scalar density function. Numerical results are given to verify these results and to demonstrate how the analysis is useful for problems involving more complex features, including for a non-trivial time dependant nonlinear PDE which evolves narrow and curved reaction fronts.
Adaptive Cuckoo Search Algorithm for Unconstrained Optimization
2014-01-01
Modification of the intensification and diversification approaches in the recently developed cuckoo search algorithm (CSA) is performed. The alteration involves the implementation of adaptive step size adjustment strategy, and thus enabling faster convergence to the global optimal solutions. The feasibility of the proposed algorithm is validated against benchmark optimization functions, where the obtained results demonstrate a marked improvement over the standard CSA, in all the cases. PMID:25298971
Adaptive cuckoo search algorithm for unconstrained optimization.
Ong, Pauline
2014-01-01
Modification of the intensification and diversification approaches in the recently developed cuckoo search algorithm (CSA) is performed. The alteration involves the implementation of adaptive step size adjustment strategy, and thus enabling faster convergence to the global optimal solutions. The feasibility of the proposed algorithm is validated against benchmark optimization functions, where the obtained results demonstrate a marked improvement over the standard CSA, in all the cases. PMID:25298971
Performance Evaluation of Various STL File Mesh Refining Algorithms Applied for FDM-RP Process
NASA Astrophysics Data System (ADS)
Ledalla, Siva Rama Krishna; Tirupathi, Balaji; Sriram, Venkatesh
2016-06-01
Layered manufacturing machines use the stereolithography (STL) file to build parts. When a curved surface is converted from a computer aided design (CAD) file to STL, it results in a geometrical distortion and chordal error. Parts manufactured with this file, might not satisfy geometric dimensioning and tolerance requirements due to approximated geometry. Current algorithms built in CAD packages have export options to globally reduce this distortion, which leads to an increase in the file size and pre-processing time. In this work, different mesh subdivision algorithms are applied on STL file of a complex geometric features using MeshLab software. The mesh subdivision algorithms considered in this work are modified butterfly subdivision technique, loops sub division technique and general triangular midpoint sub division technique. A comparative study is made with respect to volume and the build time using the above techniques. It is found that triangular midpoint sub division algorithm is more suitable for the geometry under consideration. Only the wheel cap part is then manufactured on Stratasys MOJO FDM machine. The surface roughness of the part is measured on Talysurf surface roughness tester.
Time-dependent grid adaptation for meshes of triangles and tetrahedra
NASA Technical Reports Server (NTRS)
Rausch, Russ D.
1993-01-01
This paper presents in viewgraph form a method of optimizing grid generation for unsteady CFD flow calculations that distributes the numerical error evenly throughout the mesh. Adaptive meshing is used to locally enrich in regions of relatively large errors and to locally coarsen in regions of relatively small errors. The enrichment/coarsening procedures are robust for isotropic cells; however, enrichment of high aspect ratio cells may fail near boundary surfaces with relatively large curvature. The enrichment indicator worked well for the cases shown, but in general requires user supervision for a more efficient solution.
Using Multithreading for the Automatic Load Balancing of 2D Adaptive Finite Element Meshes
NASA Technical Reports Server (NTRS)
Heber, Gerd; Biswas, Rupak; Thulasiraman, Parimala; Gao, Guang R.; Bailey, David H. (Technical Monitor)
1998-01-01
In this paper, we present a multi-threaded approach for the automatic load balancing of adaptive finite element (FE) meshes. The platform of our choice is the EARTH multi-threaded system which offers sufficient capabilities to tackle this problem. We implement the question phase of FE applications on triangular meshes, and exploit the EARTH token mechanism to automatically balance the resulting irregular and highly nonuniform workload. We discuss the results of our experiments on EARTH-SP2, an implementation of EARTH on the IBM SP2, with different load balancing strategies that are built into the runtime system.
NASA Astrophysics Data System (ADS)
Burago, N. G.; Nikitin, I. S.; Yakushev, V. L.
2016-06-01
Techniques that improve the accuracy of numerical solutions and reduce their computational costs are discussed as applied to continuum mechanics problems with complex time-varying geometry. The approach combines shock-capturing computations with the following methods: (1) overlapping meshes for specifying complex geometry; (2) elastic arbitrarily moving adaptive meshes for minimizing the approximation errors near shock waves, boundary layers, contact discontinuities, and moving boundaries; (3) matrix-free implementation of efficient iterative and explicit-implicit finite element schemes; (4) balancing viscosity (version of the stabilized Petrov-Galerkin method); (5) exponential adjustment of physical viscosity coefficients; and (6) stepwise correction of solutions for providing their monotonicity and conservativeness.
Laser Ray Tracing in a Parallel Arbitrary Lagrangian-Eulerian Adaptive Mesh Refinement Hydrocode
Masters, N D; Kaiser, T B; Anderson, R W; Eder, D C; Fisher, A C; Koniges, A E
2009-09-28
ALE-AMR is a new hydrocode that we are developing as a predictive modeling tool for debris and shrapnel formation in high-energy laser experiments. In this paper we present our approach to implementing laser ray-tracing in ALE-AMR. We present the equations of laser ray tracing, our approach to efficient traversal of the adaptive mesh hierarchy in which we propagate computational rays through a virtual composite mesh consisting of the finest resolution representation of the modeled space, and anticipate simulations that will be compared to experiments for code validation.
Spatially adaptive bases in wavelet-based coding of semi-regular meshes
NASA Astrophysics Data System (ADS)
Denis, Leon; Florea, Ruxandra; Munteanu, Adrian; Schelkens, Peter
2010-05-01
In this paper we present a wavelet-based coding approach for semi-regular meshes, which spatially adapts the employed wavelet basis in the wavelet transformation of the mesh. The spatially-adaptive nature of the transform requires additional information to be stored in the bit-stream in order to allow the reconstruction of the transformed mesh at the decoder side. In order to limit this overhead, the mesh is first segmented into regions of approximately equal size. For each spatial region, a predictor is selected in a rate-distortion optimal manner by using a Lagrangian rate-distortion optimization technique. When compared against the classical wavelet transform employing the butterfly subdivision filter, experiments reveal that the proposed spatially-adaptive wavelet transform significantly decreases the energy of the wavelet coefficients for all subbands. Preliminary results show also that employing the proposed transform for the lowest-resolution subband systematically yields improved compression performance at low-to-medium bit-rates. For the Venus and Rabbit test models the compression improvements add up to 1.47 dB and 0.95 dB, respectively.
PLUM: Parallel Load Balancing for Unstructured Adaptive Meshes. Degree awarded by Colorado Univ.
NASA Technical Reports Server (NTRS)
Oliker, Leonid
1998-01-01
Dynamic mesh adaption on unstructured grids is a powerful tool for computing large-scale problems that require grid modifications to efficiently resolve solution features. By locally refining and coarsening the mesh to capture physical phenomena of interest, such procedures make standard computational methods more cost effective. Unfortunately, an efficient parallel implementation of these adaptive methods is rather difficult to achieve, primarily due to the load imbalance created by the dynamically-changing nonuniform grid. This requires significant communication at runtime, leading to idle processors and adversely affecting the total execution time. Nonetheless, it is generally thought that unstructured adaptive- grid techniques will constitute a significant fraction of future high-performance supercomputing. Various dynamic load balancing methods have been reported to date; however, most of them either lack a global view of loads across processors or do not apply their techniques to realistic large-scale applications.
An adaptive embedded mesh procedure for leading-edge vortex flows
NASA Technical Reports Server (NTRS)
Powell, Kenneth G.; Beer, Michael A.; Law, Glenn W.
1989-01-01
A procedure for solving the conical Euler equations on an adaptively refined mesh is presented, along with a method for determining which cells to refine. The solution procedure is a central-difference cell-vertex scheme. The adaptation procedure is made up of a parameter on which the refinement decision is based, and a method for choosing a threshold value of the parameter. The refinement parameter is a measure of mesh-convergence, constructed by comparison of locally coarse- and fine-grid solutions. The threshold for the refinement parameter is based on the curvature of the curve relating the number of cells flagged for refinement to the value of the refinement threshold. Results for three test cases are presented. The test problem is that of a delta wing at angle of attack in a supersonic free-stream. The resulting vortices and shocks are captured efficiently by the adaptive code.
Spatial adaptation procedures on tetrahedral meshes for unsteady aerodynamic flow calculations
NASA Technical Reports Server (NTRS)
Rausch, Russ D.; Batina, John T.; Yang, Henry T. Y.
1993-01-01
Spatial adaptation procedures for the accurate and efficient solution of steady and unsteady inviscid flow problems are described. The adaptation procedures were developed and implemented within a three-dimensional, unstructured-grid, upwind-type Euler code. These procedures involve mesh enrichment and mesh coarsening to either add points in high gradient regions of the flow or remove points where they are not needed, respectively, to produce solutions of high spatial accuracy at minimal computational cost. A detailed description of the enrichment and coarsening procedures are presented and comparisons with experimental data for an ONERA M6 wing and an exact solution for a shock-tube problem are presented to provide an assessment of the accuracy and efficiency of the capability. Steady and unsteady results, obtained using spatial adaptation procedures, are shown to be of high spatial accuracy, primarily in that discontinuities such as shock waves are captured very sharply.
NASA Astrophysics Data System (ADS)
Wang, Tianyang; Wüchner, Roland; Sicklinger, Stefan; Bletzinger, Kai-Uwe
2016-05-01
This paper investigates data mapping between non-matching meshes and geometries in fluid-structure interaction. Mapping algorithms for surface meshes including nearest element interpolation, the standard mortar method and the dual mortar method are studied and comparatively assessed. The inconsistency problem of mortar methods at curved edges of fluid-structure-interfaces is solved by a newly developed enforcing consistency approach, which is robust enough to handle even the case that fluid boundary facets are totally not in contact with structure boundary elements due to high fluid refinement. Besides, tests with representative geometries show that the mortar methods are suitable for conservative mapping but it is better to use the nearest element interpolation in a direct way, and moreover, the dual mortar method can give slight oscillations. This work also develops a co-rotating mapping algorithm for 1D beam elements. Its novelty lies in the ability of handling large displacements and rotations.
Algorithm for protecting light-trees in survivable mesh wavelength-division-multiplexing networks
NASA Astrophysics Data System (ADS)
Luo, Hongbin; Li, Lemin; Yu, Hongfang
2006-12-01
Wavelength-division-multiplexing (WDM) technology is expected to facilitate bandwidth-intensive multicast applications such as high-definition television. A single fiber cut in a WDM mesh network, however, can disrupt the dissemination of information to several destinations on a light-tree based multicast session. Thus it is imperative to protect multicast sessions by reserving redundant resources. We propose a novel and efficient algorithm for protecting light-trees in survivable WDM mesh networks. The algorithm is called segment-based protection with sister node first (SSNF), whose basic idea is to protect a light-tree using a set of backup segments with a higher priority to protect the segments from a branch point to its children (sister nodes). The SSNF algorithm differs from the segment protection scheme proposed in the literature in how the segments are identified and protected. Our objective is to minimize the network resources used for protecting each primary light-tree such that the blocking probability can be minimized. To verify the effectiveness of the SSNF algorithm, we conduct extensive simulation experiments. The simulation results demonstrate that the SSNF algorithm outperforms existing algorithms for the same problem.
Kolobov, Vladimir; Arslanbekov, Robert; Frolova, Anna
2014-12-09
The paper describes an Adaptive Mesh in Phase Space (AMPS) technique for solving kinetic equations with deterministic mesh-based methods. The AMPS technique allows automatic generation of adaptive Cartesian mesh in both physical and velocity spaces using a Tree-of-Trees data structure. We illustrate advantages of AMPS for simulations of rarefied gas dynamics and electron kinetics on low temperature plasmas. In particular, we consider formation of the velocity distribution functions in hypersonic flows, particle kinetics near oscillating boundaries, and electron kinetics in a radio-frequency sheath. AMPS provide substantial savings in computational cost and increased efficiency of the mesh-based kinetic solvers.
NASA Astrophysics Data System (ADS)
Kolobov, Vladimir; Arslanbekov, Robert; Frolova, Anna
2014-12-01
The paper describes an Adaptive Mesh in Phase Space (AMPS) technique for solving kinetic equations with deterministic mesh-based methods. The AMPS technique allows automatic generation of adaptive Cartesian mesh in both physical and velocity spaces using a Tree-of-Trees data structure. We illustrate advantages of AMPS for simulations of rarefied gas dynamics and electron kinetics on low temperature plasmas. In particular, we consider formation of the velocity distribution functions in hypersonic flows, particle kinetics near oscillating boundaries, and electron kinetics in a radio-frequency sheath. AMPS provide substantial savings in computational cost and increased efficiency of the mesh-based kinetic solvers.
Practical improvements of multi-grid iteration for adaptive mesh refinement method
NASA Astrophysics Data System (ADS)
Miyashita, Hisashi; Yamada, Yoshiyuki
2005-03-01
Adaptive mesh refinement(AMR) is a powerful tool to efficiently solve multi-scaled problems. However, the vanilla AMR method has a well-known critical demerit, i.e., it cannot be applied to non-local problems. Although multi-grid iteration (MGI) can be regarded as a good remedy for a non-local problem such as the Poisson equation, we observed fundamental difficulties in applying the MGI technique in AMR to realistic problems under complicated mesh layouts because it does not converge or it requires too many iterations even if it does converge. To cope with the problem, when updating the next approximation in the MGI process, we calculate the precise total corrections that are relatively accurate to the current residual by introducing a new iteration for such a total correction. This procedure greatly accelerates the MGI convergence speed especially under complicated mesh layouts.
Genetic algorithms in adaptive fuzzy control
NASA Technical Reports Server (NTRS)
Karr, C. Lucas; Harper, Tony R.
1992-01-01
Researchers at the U.S. Bureau of Mines have developed adaptive process control systems in which genetic algorithms (GA's) are used to augment fuzzy logic controllers (FLC's). GA's are search algorithms that rapidly locate near-optimum solutions to a wide spectrum of problems by modeling the search procedures of natural genetics. FLC's are rule based systems that efficiently manipulate a problem environment by modeling the 'rule-of-thumb' strategy used in human decision making. Together, GA's and FLC's possess the capabilities necessary to produce powerful, efficient, and robust adaptive control systems. To perform efficiently, such control systems require a control element to manipulate the problem environment, an analysis element to recognize changes in the problem environment, and a learning element to adjust fuzzy membership functions in response to the changes in the problem environment. Details of an overall adaptive control system are discussed. A specific computer-simulated chemical system is used to demonstrate the ideas presented.
Ray, Jaideep; Lefantzi, Sophia; Najm, Habib N.; Kennedy, Christopher A.
2006-01-01
Block-structured adaptively refined meshes (SAMR) strive for efficient resolution of partial differential equations (PDEs) solved on large computational domains by clustering mesh points only where required by large gradients. Previous work has indicated that fourth-order convergence can be achieved on such meshes by using a suitable combination of high-order discretizations, interpolations, and filters and can deliver significant computational savings over conventional second-order methods at engineering error tolerances. In this paper, we explore the interactions between the errors introduced by discretizations, interpolations and filters. We develop general expressions for high-order discretizations, interpolations, and filters, in multiple dimensions, using a Fourier approach, facilitating the high-order SAMR implementation. We derive a formulation for the necessary interpolation order for given discretization and derivative orders. We also illustrate this order relationship empirically using one and two-dimensional model problems on refined meshes. We study the observed increase in accuracy with increasing interpolation order. We also examine the empirically observed order of convergence, as the effective resolution of the mesh is increased by successively adding levels of refinement, with different orders of discretization, interpolation, or filtering.
NASA Astrophysics Data System (ADS)
Foks, Nathan Leon
The interpretation of geophysical data plays an important role in the analysis of potential field data in resource exploration industries. Two categories of interpretation techniques are discussed in this thesis; boundary detection and geophysical inversion. Fault or boundary detection is a method to interpret the locations of subsurface boundaries from measured data, while inversion is a computationally intensive method that provides 3D information about subsurface structure. My research focuses on these two aspects of interpretation techniques. First, I develop a method to aid in the interpretation of faults and boundaries from magnetic data. These processes are traditionally carried out using raster grid and image processing techniques. Instead, I use unstructured meshes of triangular facets that can extract inferred boundaries using mesh edges. Next, to address the computational issues of geophysical inversion, I develop an approach to reduce the number of data in a data set. The approach selects the data points according to a user specified proxy for its signal content. The approach is performed in the data domain and requires no modification to existing inversion codes. This technique adds to the existing suite of compressive inversion algorithms. Finally, I develop an algorithm to invert gravity data for an interfacing surface using an unstructured mesh of triangular facets. A pertinent property of unstructured meshes is their flexibility at representing oblique, or arbitrarily oriented structures. This flexibility makes unstructured meshes an ideal candidate for geometry based interface inversions. The approaches I have developed provide a suite of algorithms geared towards large-scale interpretation of potential field data, by using an unstructured representation of both the data and model parameters.
Implementation of Implicit Adaptive Mesh Refinement in an Unstructured Finite-Volume Flow Solver
NASA Technical Reports Server (NTRS)
Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.
2013-01-01
This paper explores the implementation of adaptive mesh refinement in an unstructured, finite-volume solver. Unsteady and steady problems are considered. The effect on the recovery of high-order numerics is explored and the results are favorable. Important to this work is the ability to provide a path for efficient, implicit time advancement. A method using a simple refinement sensor based on undivided differences is discussed and applied to a practical problem: a shock-shock interaction on a hypersonic, inviscid double-wedge. Cases are compared to uniform grids without the use of adapted meshes in order to assess error and computational expense. Discussion of difficulties, advances, and future work prepare this method for additional research. The potential for this method in more complicated flows is described.
Anderson, R W; Pember, R B; Elliott, N S
2001-10-22
A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. This method facilitates the solution of problems currently at and beyond the boundary of soluble problems by traditional ALE methods by focusing computational resources where they are required through dynamic adaption. Many of the core issues involved in the development of the combined ALEAMR method hinge upon the integration of AMR with a staggered grid Lagrangian integration method. The novel components of the method are mainly driven by the need to reconcile traditional AMR techniques, which are typically employed on stationary meshes with cell-centered quantities, with the staggered grids and grid motion employed by Lagrangian methods. Numerical examples are presented which demonstrate the accuracy and efficiency of the method.
NASA Astrophysics Data System (ADS)
De Colle, Fabio; Granot, Jonathan; López-Cámara, Diego; Ramirez-Ruiz, Enrico
2012-02-01
We report on the development of Mezcal-SRHD, a new adaptive mesh refinement, special relativistic hydrodynamics (SRHD) code, developed with the aim of studying the highly relativistic flows in gamma-ray burst sources. The SRHD equations are solved using finite-volume conservative solvers, with second-order interpolation in space and time. The correct implementation of the algorithms is verified by one-dimensional (1D) and multi-dimensional tests. The code is then applied to study the propagation of 1D spherical impulsive blast waves expanding in a stratified medium with ρvpropr -k , bridging between the relativistic and Newtonian phases (which are described by the Blandford-McKee and Sedov-Taylor self-similar solutions, respectively), as well as to a two-dimensional (2D) cylindrically symmetric impulsive jet propagating in a constant density medium. It is shown that the deceleration to nonrelativistic speeds in one dimension occurs on scales significantly larger than the Sedov length. This transition is further delayed with respect to the Sedov length as the degree of stratification of the ambient medium is increased. This result, together with the scaling of position, Lorentz factor, and the shock velocity as a function of time and shock radius, is explained here using a simple analytical model based on energy conservation. The method used for calculating the afterglow radiation by post-processing the results of the simulations is described in detail. The light curves computed using the results of 1D numerical simulations during the relativistic stage correctly reproduce those calculated assuming the self-similar Blandford-McKee solution for the evolution of the flow. The jet dynamics from our 2D simulations and the resulting afterglow light curves, including the jet break, are in good agreement with those presented in previous works. Finally, we show how the details of the dynamics critically depend on properly resolving the structure of the relativistic flow.
Turner, C. David; Kotulski, Joseph Daniel; Pasik, Michael Francis
2005-12-01
This report investigates the feasibility of applying Adaptive Mesh Refinement (AMR) techniques to a vector finite element formulation for the wave equation in three dimensions. Possible error estimators are considered first. Next, approaches for refining tetrahedral elements are reviewed. AMR capabilities within the Nevada framework are then evaluated. We summarize our conclusions on the feasibility of AMR for time-domain vector finite elements and identify a path forward.
An adaptive guidance algorithm for aerospace vehicles
NASA Astrophysics Data System (ADS)
Bradt, J. E.; Hardtla, J. W.; Cramer, E. J.
The specifications for proposed space transportation systems are placing more emphasis on developing reusable avionics subsystems which have the capability to respond to vehicle evolution and diverse missions while at the same time reducing the cost of ground support for mission planning, contingency response and verification and validation. An innovative approach to meeting these goals is to specify the guidance problem as a multi-point boundary value problen and solve that problem using modern control theory and nonlinear constrained optimization techniques. This approach has been implemented as Gamma Guidance (Hardtla, 1978) and has been successfully flown in the Inertial Upper Stage. The adaptive guidance algorithm described in this paper is a generalized formulation of Gamma Guidance. The basic equations are presented and then applied to four diverse aerospace vehicles to demonstrate the feasibility of using a reusable, explicit, adaptive guidance algorithm for diverse applications and vehicles.
NASA Astrophysics Data System (ADS)
Wallin, John
1996-01-01
Particle-mesh calculations treat forces and potentials as field quantities which are represented approximately on a mesh. A system of particles is mapped onto this mesh as a density distribution of mass or charge. The Fourier transform is used to convolve this distribution with the Green's function of the potential, and a finite difference scheme is used to calculate the forces acting on the particles. The computation time scales as the Ng log Ng, where Ng is the size of the computational grid. In contrast, the particle-particle method's computing time relies on direct summation, so the time for each calculation is given by Np2, where Np is the number of particles. The particle-mesh method is best suited for simulations with a fixed minimum resolution and for collisionless systems, while hierarchical tree codes have proven to be superior for collisional systems where two-body interactions are important. Particle mesh methods still dominate in plasma physics where collisionless systems are modeled. The CM-200 Connection Machine produced by Thinking Machines Corp. is a data parallel system. On this system, the front-end computer controls the timing and execution of the parallel processing units. The programming paradigm is Single-Instruction, Multiple Data (SIMD). The processors on the CM-200 are connected in an N-dimensional hypercube; the largest number of links a message will ever have to make is N. As in all parallel computing, the efficiency of an algorithm is primarily determined by the fraction of the time spent communicating compared to that spent computing. Because of the topology of the processors, nearest neighbor communication is more efficient than general communication.
Turbo LMS algorithm: supercharger meets adaptive filter
NASA Astrophysics Data System (ADS)
Meyer-Baese, Uwe
2006-04-01
Adaptive digital filters (ADFs) are, in general, the most sophisticated and resource intensive components of modern digital signal processing (DSP) and communication systems. Improvements in performance or the complexity of ADFs can have a significant impact on the overall size, speed, and power properties of a complete system. The least mean square (LMS) algorithm is a popular algorithm for coefficient adaptation in ADF because it is robust, easy to implement, and a close approximation to the optimal Wiener-Hopf least mean square solution. The main weakness of the LMS algorithm is the slow convergence, especially for non Markov-1 colored noise input signals with high eigenvalue ratios (EVRs). Since its introduction in 1993, the turbo (supercharge) principle has been successfully applied in error correction decoding and has become very popular because it reaches the theoretical limits of communication capacity predicted 5 decades ago by Shannon. The turbo principle applied to LMS ADF is analogous to the turbo principle used for error correction decoders: First, an "interleaver" is used to minimize crosscorrelation, secondly, an iterative improvement which uses the same data set several times is implemented using the standard LMS algorithm. Results for 6 different interleaver schemes for EVR in the range 1-100 are presented.
Adjoint-Based Algorithms for Adaptation and Design Optimizations on Unstructured Grids
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.
2006-01-01
Schemes based on discrete adjoint algorithms present several exciting opportunities for significantly advancing the current state of the art in computational fluid dynamics. Such methods provide an extremely efficient means for obtaining discretely consistent sensitivity information for hundreds of design variables, opening the door to rigorous, automated design optimization of complex aerospace configuration using the Navier-Stokes equation. Moreover, the discrete adjoint formulation provides a mathematically rigorous foundation for mesh adaptation and systematic reduction of spatial discretization error. Error estimates are also an inherent by-product of an adjoint-based approach, valuable information that is virtually non-existent in today's large-scale CFD simulations. An overview of the adjoint-based algorithm work at NASA Langley Research Center is presented, with examples demonstrating the potential impact on complex computational problems related to design optimization as well as mesh adaptation.
Impact of space-time mesh adaptation on solute transport modeling in porous media
NASA Astrophysics Data System (ADS)
Esfandiar, Bahman; Porta, Giovanni; Perotto, Simona; Guadagnini, Alberto
2015-02-01
We implement a space-time grid adaptation procedure to efficiently improve the accuracy of numerical simulations of solute transport in porous media in the context of model parameter estimation. We focus on the Advection Dispersion Equation (ADE) for the interpretation of nonreactive transport experiments in laboratory-scale heterogeneous porous media. When compared to a numerical approximation based on a fixed space-time discretization, our approach is grounded on a joint automatic selection of the spatial grid and the time step to capture the main (space-time) system dynamics. Spatial mesh adaptation is driven by an anisotropic recovery-based error estimator which enables us to properly select the size, shape, and orientation of the mesh elements. Adaptation of the time step is performed through an ad hoc local reconstruction of the temporal derivative of the solution via a recovery-based approach. The impact of the proposed adaptation strategy on the ability to provide reliable estimates of the key parameters of an ADE model is assessed on the basis of experimental solute breakthrough data measured following tracer injection in a nonuniform porous system. Model calibration is performed in a Maximum Likelihood (ML) framework upon relying on the representation of the ADE solution through a generalized Polynomial Chaos Expansion (gPCE). Our results show that the proposed anisotropic space-time grid adaptation leads to ML parameter estimates and to model results of markedly improved quality when compared to classical inversion approaches based on a uniform space-time discretization.
Armstrong, Jerawan C.; Favorite, Jeffrey A.
2012-06-20
The Levenberg-Marquardt (or simply Marquardt) and differential evolution (DE) optimization methods were recently applied to solve inverse transport problems. The Marquardt method is fast but convergence of the method is dependent on the initial guess. While it has been shown to work extremely well at finding an optimum independent of the initial guess, the DE method does not provide a global optimal solution in some problems. In this paper, we apply the Mesh Adaptive Direct Search (MADS) algorithm to solve the inverse problem of material interface location identification in one-dimensional spherical radiation source/shield systems, and we compare the results obtained by MADS to those obtained by Levenberg-Marquardt and DE.
Mesh quality control for multiply-refined tetrahedral grids
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Strawn, Roger
1994-01-01
A new algorithm for controlling the quality of multiply-refined tetrahedral meshes is presented in this paper. The basic dynamic mesh adaption procedure allows localized grid refinement and coarsening to efficiently capture aerodynamic flow features in computational fluid dynamics problems; however, repeated application of the procedure may significantly deteriorate the quality of the mesh. Results presented show the effectiveness of this mesh quality algorithm and its potential in the area of helicopter aerodynamics and acoustics.
MediaMesh: an architecture for integrating isochronous processing algorithms into media servers
NASA Astrophysics Data System (ADS)
Amini, Lisa D.; Lepre, Jorge; Kienzle, Martin G.
1999-12-01
Current media servers do not provide the generality required to easily integrate arbitrary isochronous processing algorithms into streams of continuous media. Specifically, present day video server architectures primarily focus on disk and network strategies for efficiently managing available resources under stringent QoS guarantees. However, they do not fully consider the problems of integrating the wide variety of algorithms required for interactive multimedia applications. Examples of applications benefiting from a more flexible server environment include watermarking, encrypting or scrambling streams, visual VCR operations, and multiplexing or demultiplexing of live presentations. In this paper, we detail the MediaMesh architecture for integrating arbitrary isochronous processing algorithms into general purpose media servers. Our framework features a programming model through which user-written modules can be dynamically loaded and interconnected in self-managing graphs of stream processing components. Design highlights include novel techniques for distributed stream control, efficient buffer management and QoS management. To demonstrate its applicability, we have implemented the MediaMesh architecture in the context of a commercial video server. We illustrate the viability of the architecture through performance data collected from four processing modules that were implemented to facilitate new classes of applications on our video server.
Parallel CFD Algorithms for Aerodynamical Flow Solvers on Unstructured Meshes. Parts 1 and 2
NASA Technical Reports Server (NTRS)
Barth, Timothy J.; Kwak, Dochan (Technical Monitor)
1995-01-01
The Advisory Group for Aerospace Research and Development (AGARD) has requested my participation in the lecture series entitled Parallel Computing in Computational Fluid Dynamics to be held at the von Karman Institute in Brussels, Belgium on May 15-19, 1995. In addition, a request has been made from the US Coordinator for AGARD at the Pentagon for NASA Ames to hold a repetition of the lecture series on October 16-20, 1995. I have been asked to be a local coordinator for the Ames event. All AGARD lecture series events have attendance limited to NATO allied countries. A brief of the lecture series is provided in the attached enclosure. Specifically, I have been asked to give two lectures of approximately 75 minutes each on the subject of parallel solution techniques for the fluid flow equations on unstructured meshes. The title of my lectures is "Parallel CFD Algorithms for Aerodynamical Flow Solvers on Unstructured Meshes" (Parts I-II). The contents of these lectures will be largely review in nature and will draw upon previously published work in this area. Topics of my lectures will include: (1) Mesh partitioning algorithms. Recursive techniques based on coordinate bisection, Cuthill-McKee level structures, and spectral bisection. (2) Newton's method for large scale CFD problems. Size and complexity estimates for Newton's method, modifications for insuring global convergence. (3) Techniques for constructing the Jacobian matrix. Analytic and numerical techniques for Jacobian matrix-vector products, constructing the transposed matrix, extensions to optimization and homotopy theories. (4) Iterative solution algorithms. Practical experience with GIVIRES and BICG-STAB matrix solvers. (5) Parallel matrix preconditioning. Incomplete Lower-Upper (ILU) factorization, domain-decomposed ILU, approximate Schur complement strategies.
Adaptive path planning: Algorithm and analysis
Chen, Pang C.
1993-03-01
Path planning has to be fast to support real-time robot programming. Unfortunately, current planning techniques are still too slow to be effective, as they often require several minutes, if not hours of computation. To alleviate this problem, we present a learning algorithm that uses past experience to enhance future performance. The algorithm relies on an existing path planner to provide solutions to difficult tasks. From these solutions, an evolving sparse network of useful subgoals is learned to support faster planning. The algorithm is suitable for both stationary and incrementally-changing environments. To analyze our algorithm, we use a previously developed stochastic model that quantifies experience utility. Using this model, we characterize the situations in which the adaptive planner is useful, and provide quantitative bounds to predict its behavior. The results are demonstrated with problems in manipulator planning. Our algorithm and analysis are sufficiently general that they may also be applied to task planning or other planning domains in which experience is useful.
Error estimation and adaptive mesh refinement for parallel analysis of shell structures
NASA Technical Reports Server (NTRS)
Keating, Scott C.; Felippa, Carlos A.; Park, K. C.
1994-01-01
The formulation and application of element-level, element-independent error indicators is investigated. This research culminates in the development of an error indicator formulation which is derived based on the projection of element deformation onto the intrinsic element displacement modes. The qualifier 'element-level' means that no information from adjacent elements is used for error estimation. This property is ideally suited for obtaining error values and driving adaptive mesh refinements on parallel computers where access to neighboring elements residing on different processors may incur significant overhead. In addition such estimators are insensitive to the presence of physical interfaces and junctures. An error indicator qualifies as 'element-independent' when only visible quantities such as element stiffness and nodal displacements are used to quantify error. Error evaluation at the element level and element independence for the error indicator are highly desired properties for computing error in production-level finite element codes. Four element-level error indicators have been constructed. Two of the indicators are based on variational formulation of the element stiffness and are element-dependent. Their derivations are retained for developmental purposes. The second two indicators mimic and exceed the first two in performance but require no special formulation of the element stiffness mesh refinement which we demonstrate for two dimensional plane stress problems. The parallelizing of substructures and adaptive mesh refinement is discussed and the final error indicator using two-dimensional plane-stress and three-dimensional shell problems is demonstrated.
Numerical modelling of tsunami generation by deformable submarine slides using mesh adaptivity
NASA Astrophysics Data System (ADS)
Smith, Rebecca; Parkinson, Samuel; Hill, Jon; Collins, Gareth; Piggott, Matthew
2014-05-01
Tsunamis generated by submarine slides are often under considered in comparison to earthquake generated tsunami, despite several recent examples. Tsunamigenic slides have generated waves that have caused significant damage and loss of life, for example the 1998 Papua New Guinea submarine mass failure resulted in a tsunami that devastated coastal villages and killed over 2,100 people. Numerical simulations of submarine slide generated waves can help us understand the nature of the waves that are generated, and identify the important factors in determining wave characteristics. There have not been many studies of tsunami generation by deformable submarine slides, largely because of the complexities and computational expense involved in modelling these large scale events. At large, real world, scales modelling of tsunami waves by the generation of slides is computationally challenging. Fluidity is an open source finite element code that is ideally suited to tackle this type of problem as it uses unstructured, adaptive meshes, which help to reduce the computational expense without losing accuracy in the results. Adaptive meshes change topology and resolution based on the current simulation state and as such can focus or reduce resolution when and where it is required. The model also allows a number of different numerical approaches to be taken to simulate the same problem within the same numerical framework. In this example we use multi-material approach, with both two materials (slide and water) and three materials (slide, water and air), alongside a density-driven sediment model approach. We will present results of validating Fluidity against benchmarks from experimental and other numerical studies, at different scales, for deformable underwater slides, and consider the utility of mesh adaptivity. We show good agreement to both laboratory results and other numerical models, both with a fixed mesh and a dynamically adaptive mesh, tracking important features of the
Application of adaptive mesh refinement to particle-in-cell simulations of plasmas and beams
Vay, J.-L.; Colella, P.; Kwan, J.W.; McCorquodale, P.; Serafini, D.B.; Friedman, A.; Grote, D.P.; Westenskow, G.; Adam, J.-C.; Heron, A.; Haber, I.
2003-11-04
Plasma simulations are often rendered challenging by the disparity of scales in time and in space which must be resolved. When these disparities are in distinctive zones of the simulation domain, a method which has proven to be effective in other areas (e.g. fluid dynamics simulations) is the mesh refinement technique. We briefly discuss the challenges posed by coupling this technique with plasma Particle-In-Cell simulations, and present examples of application in Heavy Ion Fusion and related fields which illustrate the effectiveness of the approach. We also report on the status of a collaboration under way at Lawrence Berkeley National Laboratory between the Applied Numerical Algorithms Group (ANAG) and the Heavy Ion Fusion group to upgrade ANAG's mesh refinement library Chombo to include the tools needed by Particle-In-Cell simulation codes.
Delanaye, M.; Essers, J.A.
1997-04-01
This paper presents a new finite volume cell-centered scheme for solving the two-dimensional Euler equations. The technique for computing the advective derivatives is based on a high-order Gauss quadrature and an original quadratic reconstruction of the conservative variables for each control volume. A very sensitive detector identifying discontinuity regions switches the scheme to a TVD scheme, and ensures the monotonicity of the solution. The code uses unstructured meshes whose cells are polygons with any number of edges. A mesh adaptation based on cell division is performed in order to increase the resolution of shocks. The accuracy, insensitivity to grid distortions, and shock capturing properties of the scheme are demonstrated for different cascade flow computations.
Adaptive Trajectory Prediction Algorithm for Climbing Flights
NASA Technical Reports Server (NTRS)
Schultz, Charles Alexander; Thipphavong, David P.; Erzberger, Heinz
2012-01-01
Aircraft climb trajectories are difficult to predict, and large errors in these predictions reduce the potential operational benefits of some advanced features for NextGen. The algorithm described in this paper improves climb trajectory prediction accuracy by adjusting trajectory predictions based on observed track data. It utilizes rate-of-climb and airspeed measurements derived from position data to dynamically adjust the aircraft weight modeled for trajectory predictions. In simulations with weight uncertainty, the algorithm is able to adapt to within 3 percent of the actual gross weight within two minutes of the initial adaptation. The root-mean-square of altitude errors for five-minute predictions was reduced by 73 percent. Conflict detection performance also improved, with a 15 percent reduction in missed alerts and a 10 percent reduction in false alerts. In a simulation with climb speed capture intent and weight uncertainty, the algorithm improved climb trajectory prediction accuracy by up to 30 percent and conflict detection performance, reducing missed and false alerts by up to 10 percent.
Designing efficient parallel algorithms on mesh-connected computers with multiple broadcasting
Chen, Y.C.; Chen, W.T. ); Chen, G.H. ); Sheu, J.P. )
1990-04-01
Semigroup and prefix computations on two-dimensional mesh-connected computers with multiple broadcasting (2-MCCMB's) are studied in this paper. Previously, only square 2-MCCMB's with N processing elements were considered or semigroup computations of N data items, and O(N{sup 1/6}) time was required. It is found that square machines are not the best form for semigroup computations, and an O(N{sup 1/8}) time algorithm is thus derived on an N{sup 5/8} {times} N{sup 3/8} rectangular 2-MCCMB. This time complexity can be further reduced to O(N{sup 1/9}) if fewer PE's are used. Following the same way, parallel algorithms for prefix computations are also derived with the same time complexities.
Numerical modeling of landslide-generated tsunami using adaptive unstructured meshes
NASA Astrophysics Data System (ADS)
Wilson, Cian; Collins, Gareth; Desousa Costa, Patrick; Piggott, Matthew
2010-05-01
Landslides impacting into or occurring under water generate waves, which can have devastating environmental consequences. Depending on the characteristics of the landslide the waves can have significant amplitude and potentially propagate over large distances. Linear models of classical earthquake-generated tsunamis cannot reproduce the highly nonlinear generation mechanisms required to accurately predict the consequences of landslide-generated tsunamis. Also, laboratory-scale experimental investigation is limited to simple geometries and short time-scales before wave reflections contaminate the data. Computational fluid dynamics models based on the nonlinear Navier-Stokes equations can simulate landslide-tsunami generation at realistic scales. However, traditional chessboard-like structured meshes introduce superfluous resolution and hence the computing power required for such a simulation can be prohibitively high, especially in three dimensions. Unstructured meshes allow the grid spacing to vary rapidly from high resolution in the vicinity of small scale features to much coarser, lower resolution in other areas. Combining this variable resolution with dynamic mesh adaptivity allows such high resolution zones to follow features like the interface between the landslide and the water whilst minimising the computational costs. Unstructured meshes are also better suited to representing complex geometries and bathymetries allowing more realistic domains to be simulated. Modelling multiple materials, like water, air and a landslide, on an unstructured adaptive mesh poses significant numerical challenges. Novel methods of interface preservation must be considered and coupled to a flow model in such a way that ensures conservation of the different materials. Furthermore this conservation property must be maintained during successive stages of mesh optimisation and interpolation. In this paper we validate a new multi-material adaptive unstructured fluid dynamics model
NASA Astrophysics Data System (ADS)
Shi, Lei; Wang, Z. J.
2015-08-01
Adjoint-based mesh adaptive methods are capable of distributing computational resources to areas which are important for predicting an engineering output. In this paper, we develop an adjoint-based h-adaptation approach based on the high-order correction procedure via reconstruction formulation (CPR) to minimize the output or functional error. A dual-consistent CPR formulation of hyperbolic conservation laws is developed and its dual consistency is analyzed. Super-convergent functional and error estimate for the output with the CPR method are obtained. Factors affecting the dual consistency, such as the solution point distribution, correction functions, boundary conditions and the discretization approach for the non-linear flux divergence term, are studied. The presented method is then used to perform simulations for the 2D Euler and Navier-Stokes equations with mesh adaptation driven by the adjoint-based error estimate. Several numerical examples demonstrate the ability of the presented method to dramatically reduce the computational cost comparing with uniform grid refinement.
An adaptive mesh method for phase-field simulation of alloy solidification in three dimensions
NASA Astrophysics Data System (ADS)
Bollada, P. C.; Jimack, P. K.; Mullis, A. M.
2015-06-01
We present our computational method for binary alloy solidification which takes advantage of high performance computing where up to 1024 cores are employed. Much of the simulation at a sufficiently fine resolution is possible on a modern 12 core PC and the 1024 core simulation is only necessary for very mature dendrite and convergence testing where high resolution puts extreme demands on memory. In outline, the method uses implicit time stepping in conjunction with an iterative solver, adaptive meshing and a scheme for dividing the work load across processors. We include three dimensional results for a Lewis number of 100 and a snapshot for a mature dendrite for a Lewis number of 40.
Development of a Godunov method for Maxwell's equations with Adaptive Mesh Refinement
NASA Astrophysics Data System (ADS)
Barbas, Alfonso; Velarde, Pedro
2015-11-01
In this paper we present a second order 3D method for Maxwell's equations based on a Godunov scheme with Adaptive Mesh Refinement (AMR). In order to achieve it, we apply a limiter which better preserves extrema and boundary conditions based on a characteristic fields decomposition. Despite being more complex, simplifications in the boundary conditions make the resulting method competitive in computer time consumption and accuracy compared to FDTD. AMR allows us to simulate systems with a sharp step in material properties with negligible rebounds and also large domains with accuracy in small wavelengths.
Compact integration factor methods for complex domains and adaptive mesh refinement
Liu, Xinfeng; Nie, Qing
2010-01-01
Implicit integration factor (IIF) method, a class of efficient semi-implicit temporal scheme, was introduced recently for stiff reaction-diffusion equations. To reduce cost of IIF, compact implicit integration factor (cIIF) method was later developed for efficient storage and calculation of exponential matrices associated with the diffusion operators in two and three spatial dimensions for Cartesian coordinates with regular meshes. Unlike IIF, cIIF cannot be directly extended to other curvilinear coordinates, such as polar and spherical coordinate, due to the compact representation for the diffusion terms in cIIF. In this paper, we present a method to generalize cIIF for other curvilinear coordinates through examples of polar and spherical coordinates. The new cIIF method in polar and spherical coordinates has similar computational efficiency and stability properties as the cIIF in Cartesian coordinate. In addition, we present a method for integrating cIIF with adaptive mesh refinement (AMR) to take advantage of the excellent stability condition for cIIF. Because the second order cIIF is unconditionally stable, it allows large time steps for AMR, unlike a typical explicit temporal scheme whose time step is severely restricted by the smallest mesh size in the entire spatial domain. Finally, we apply those methods to simulating a cell signaling system described by a system of stiff reaction-diffusion equations in both two and three spatial dimensions using AMR, curvilinear and Cartesian coordinates. Excellent performance of the new methods is observed. PMID:20543883
Earthquake Rupture Dynamics using Adaptive Mesh Refinement and High-Order Accurate Numerical Methods
NASA Astrophysics Data System (ADS)
Kozdon, J. E.; Wilcox, L.
2013-12-01
Our goal is to develop scalable and adaptive (spatial and temporal) numerical methods for coupled, multiphysics problems using high-order accurate numerical methods. To do so, we are developing an opensource, parallel library known as bfam (available at http://bfam.in). The first application to be developed on top of bfam is an earthquake rupture dynamics solver using high-order discontinuous Galerkin methods and summation-by-parts finite difference methods. In earthquake rupture dynamics, wave propagation in the Earth's crust is coupled to frictional sliding on fault interfaces. This coupling is two-way, required the simultaneous simulation of both processes. The use of laboratory-measured friction parameters requires near-fault resolution that is 4-5 orders of magnitude higher than that needed to resolve the frequencies of interest in the volume. This, along with earlier simulations using a low-order, finite volume based adaptive mesh refinement framework, suggest that adaptive mesh refinement is ideally suited for this problem. The use of high-order methods is motivated by the high level of resolution required off the fault in earlier the low-order finite volume simulations; we believe this need for resolution is a result of the excessive numerical dissipation of low-order methods. In bfam spatial adaptivity is handled using the p4est library and temporal adaptivity will be accomplished through local time stepping. In this presentation we will present the guiding principles behind the library as well as verification of code against the Southern California Earthquake Center dynamic rupture code validation test problems.
Synaptic dynamics: linear model and adaptation algorithm.
Yousefi, Ali; Dibazar, Alireza A; Berger, Theodore W
2014-08-01
In this research, temporal processing in brain neural circuitries is addressed by a dynamic model of synaptic connections in which the synapse model accounts for both pre- and post-synaptic processes determining its temporal dynamics and strength. Neurons, which are excited by the post-synaptic potentials of hundred of the synapses, build the computational engine capable of processing dynamic neural stimuli. Temporal dynamics in neural models with dynamic synapses will be analyzed, and learning algorithms for synaptic adaptation of neural networks with hundreds of synaptic connections are proposed. The paper starts by introducing a linear approximate model for the temporal dynamics of synaptic transmission. The proposed linear model substantially simplifies the analysis and training of spiking neural networks. Furthermore, it is capable of replicating the synaptic response of the non-linear facilitation-depression model with an accuracy better than 92.5%. In the second part of the paper, a supervised spike-in-spike-out learning rule for synaptic adaptation in dynamic synapse neural networks (DSNN) is proposed. The proposed learning rule is a biologically plausible process, and it is capable of simultaneously adjusting both pre- and post-synaptic components of individual synapses. The last section of the paper starts with presenting the rigorous analysis of the learning algorithm in a system identification task with hundreds of synaptic connections which confirms the learning algorithm's accuracy, repeatability and scalability. The DSNN is utilized to predict the spiking activity of cortical neurons and pattern recognition tasks. The DSNN model is demonstrated to be a generative model capable of producing different cortical neuron spiking patterns and CA1 Pyramidal neurons recordings. A single-layer DSNN classifier on a benchmark pattern recognition task outperforms a 2-Layer Neural Network and GMM classifiers while having fewer numbers of free parameters and
NASA Astrophysics Data System (ADS)
Grosges, T.; Borouchaki, H.; Barchiesi, D.
2010-12-01
We present an improved adaptive mesh process based on Riemannian transformation to control the accuracy in high field gradient representation for diffraction problems. Such an adaptive meshing is applied in representing the electromagnetic intensity around a metallic submicronic spherical particle, which is known to present high gradients in limited zones of space including the interference pattern of the electromagnetic field. We show that, the precision of the field variation being controlled, this improved scheme permits drastically decreasing the computational time as well as the memory requirements by adapting the number and the position of nodes where the electromagnetic field must be computed and represented.
NASA Astrophysics Data System (ADS)
Sarkis, C.; Silva, L.; Gandin, Ch-A.; Plapp, M.
2016-03-01
Dendritic growth is computed with automatic adaptation of an anisotropic and unstructured finite element mesh. The energy conservation equation is formulated for solid and liquid phases considering an interface balance that includes the Gibbs-Thomson effect. An equation for a diffuse interface is also developed by considering a phase field function with constant negative value in the liquid and constant positive value in the solid. Unknowns are the phase field function and a dimensionless temperature, as proposed by [1]. Linear finite element interpolation is used for both variables, and discretization stabilization techniques ensure convergence towards a correct non-oscillating solution. In order to perform quantitative computations of dendritic growth on a large domain, two additional numerical ingredients are necessary: automatic anisotropic unstructured adaptive meshing [2,[3] and parallel implementations [4], both made available with the numerical platform used (CimLib) based on C++ developments. Mesh adaptation is found to greatly reduce the number of degrees of freedom. Results of phase field simulations for dendritic solidification of a pure material in two and three dimensions are shown and compared with reference work [1]. Discussion on algorithm details and the CPU time will be outlined.
An Adaptive Path Planning Algorithm for Cooperating Unmanned Air Vehicles
Cunningham, C.T.; Roberts, R.S.
2000-09-12
An adaptive path planning algorithm is presented for cooperating Unmanned Air Vehicles (UAVs) that are used to deploy and operate land-based sensor networks. The algorithm employs a global cost function to generate paths for the UAVs, and adapts the paths to exceptions that might occur. Examples are provided of the paths and adaptation.
Adaptive path planning algorithm for cooperating unmanned air vehicles
Cunningham, C T; Roberts, R S
2001-02-08
An adaptive path planning algorithm is presented for cooperating Unmanned Air Vehicles (UAVs) that are used to deploy and operate land-based sensor networks. The algorithm employs a global cost function to generate paths for the UAVs, and adapts the paths to exceptions that might occur. Examples are provided of the paths and adaptation.
Three-dimensional numerical simulations of falling films using an adaptive unstructured mesh
NASA Astrophysics Data System (ADS)
Pain, Chris; Xie, Zhihua; Matar, Omar
2015-11-01
Falling liquid films have rich wave dynamics, often occurring in many industrial applications, such as condensers, evaporators and chemical reactors. A number of numerical studies featuring falling liquid films are available in the literature; the majority of them, however, have focused on two-dimensional falling films. Far fewer studies have considered three-dimensional falling films, and those that have only studied the flow in a periodic domain. The objective of this study is to investigate flow dynamics of developing three-dimensional falling films using the Navier-Stokes equations coupled with interface capturing approach over extended domains. An adaptive, unstructured mesh modelling framework is employed here to study this problem, which can modify and adapt three-dimensional meshes to better represent the underlying physics of multiphase problems and reduce computational effort without sacrificing accuracy. Numerical examples of three-dimensional falling films in a long domain are presented and discussed. EPSRC Programme Grant, MEMPHIS, EP/K0039761/1.
Improved Simulation of Electrodiffusion in the Node of Ranvier by Mesh Adaptation.
Dione, Ibrahima; Deteix, Jean; Briffard, Thomas; Chamberland, Eric; Doyon, Nicolas
2016-01-01
In neural structures with complex geometries, numerical resolution of the Poisson-Nernst-Planck (PNP) equations is necessary to accurately model electrodiffusion. This formalism allows one to describe ionic concentrations and the electric field (even away from the membrane) with arbitrary spatial and temporal resolution which is impossible to achieve with models relying on cable theory. However, solving the PNP equations on complex geometries involves handling intricate numerical difficulties related either to the spatial discretization, temporal discretization or the resolution of the linearized systems, often requiring large computational resources which have limited the use of this approach. In the present paper, we investigate the best ways to use the finite elements method (FEM) to solve the PNP equations on domains with discontinuous properties (such as occur at the membrane-cytoplasm interface). 1) Using a simple 2D geometry to allow comparison with analytical solution, we show that mesh adaptation is a very (if not the most) efficient way to obtain accurate solutions while limiting the computational efforts, 2) We use mesh adaptation in a 3D model of a node of Ranvier to reveal details of the solution which are nearly impossible to resolve with other modelling techniques. For instance, we exhibit a non linear distribution of the electric potential within the membrane due to the non uniform width of the myelin and investigate its impact on the spatial profile of the electric field in the Debye layer. PMID:27548674
Improved Simulation of Electrodiffusion in the Node of Ranvier by Mesh Adaptation
Dione, Ibrahima; Briffard, Thomas; Doyon, Nicolas
2016-01-01
In neural structures with complex geometries, numerical resolution of the Poisson-Nernst-Planck (PNP) equations is necessary to accurately model electrodiffusion. This formalism allows one to describe ionic concentrations and the electric field (even away from the membrane) with arbitrary spatial and temporal resolution which is impossible to achieve with models relying on cable theory. However, solving the PNP equations on complex geometries involves handling intricate numerical difficulties related either to the spatial discretization, temporal discretization or the resolution of the linearized systems, often requiring large computational resources which have limited the use of this approach. In the present paper, we investigate the best ways to use the finite elements method (FEM) to solve the PNP equations on domains with discontinuous properties (such as occur at the membrane-cytoplasm interface). 1) Using a simple 2D geometry to allow comparison with analytical solution, we show that mesh adaptation is a very (if not the most) efficient way to obtain accurate solutions while limiting the computational efforts, 2) We use mesh adaptation in a 3D model of a node of Ranvier to reveal details of the solution which are nearly impossible to resolve with other modelling techniques. For instance, we exhibit a non linear distribution of the electric potential within the membrane due to the non uniform width of the myelin and investigate its impact on the spatial profile of the electric field in the Debye layer. PMID:27548674
Time integration algorithms for the two-dimensional Euler equations on unstructured meshes
NASA Technical Reports Server (NTRS)
Slack, David C.; Whitaker, D. L.; Walters, Robert W.
1994-01-01
Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.
Energy Science and Technology Software Center (ESTSC)
2010-10-05
MeshKit is an open-source library of mesh generation functionality. MeshKit has general mesh manipulation and generation functions such as Copoy, Move, Rotate and Extrude mesh. In addition, new quad mesh and embedded boundary Cartesian mesh algorithm (EB Mesh) are included. Interfaces to several public domain meshing algorithms (TetGen, netgen, triangle, Gmsh, camal) are also offered. This library interacts with mesh data mostly through iMesh including accessing the mesh in parallel. It also can interact withmore » iGeom interface to provide geometry functionality such as importing solid model based geometries. iGeom and IMesh are implemented in the CGM and MOAB packages, respectively. For some non-existing function in iMesh such as tree-construction and ray-tracing, MeshKit also interacts with MOAB functions directly.« less
2010-10-05
MeshKit is an open-source library of mesh generation functionality. MeshKit has general mesh manipulation and generation functions such as Copoy, Move, Rotate and Extrude mesh. In addition, new quad mesh and embedded boundary Cartesian mesh algorithm (EB Mesh) are included. Interfaces to several public domain meshing algorithms (TetGen, netgen, triangle, Gmsh, camal) are also offered. This library interacts with mesh data mostly through iMesh including accessing the mesh in parallel. It also can interact with iGeom interface to provide geometry functionality such as importing solid model based geometries. iGeom and IMesh are implemented in the CGM and MOAB packages, respectively. For some non-existing function in iMesh such as tree-construction and ray-tracing, MeshKit also interacts with MOAB functions directly.
Multi-dimensional upwind fluctuation splitting scheme with mesh adaption for hypersonic viscous flow
NASA Astrophysics Data System (ADS)
Wood, William Alfred, III
production is shown relative to DMFDSFV. Remarkably the fluctuation splitting scheme shows grid converged skin friction coefficients with only five points in the boundary layer for this case. A viscous Mach 17.6 (perfect gas) cylinder case demonstrates solution monotonicity and heat transfer capability with the fluctuation splitting scheme. While fluctuation splitting is recommended over DMFDSFV, the difference in performance between the schemes is not so great as to obsolete DMFDSFV. The second half of the dissertation develops a local, compact, anisotropic unstructured mesh adaption scheme in conjunction with the multi-dimensional upwind solver, exhibiting a characteristic alignment behavior for scalar problems. This alignment behavior stands in contrast to the curvature clustering nature of the local, anisotropic unstructured adaption strategy based upon a posteriori error estimation that is used for comparison. The characteristic alignment is most pronounced for linear advection, with reduced improvement seen for the more complex non-linear advection and advection-diffusion cases. The adaption strategy is extended to the two-dimensional and axisymmetric Navier-Stokes equations of motion through the concept of fluctuation minimization. The system test case for the adaption strategy is a sting mounted capsule at Mach-10 wind tunnel conditions, considered in both two-dimensional and axisymmetric configurations. For this complex flowfield the adaption results are disappointing since feature alignment does not emerge from the local operations. Aggressive adaption is shown to result in a loss of robustness for the solver, particularly in the bow shock/stagnation point interaction region. Reducing the adaption strength maintains solution robustness but fails to produce significant improvement in the surface heat transfer predictions.
Kim, Mi Jeong; Maeng, Sung Joon; Cho, Yong Soo
2015-01-01
In this paper, a distributed synchronization technique based on a bio-inspired algorithm is proposed for an orthogonal frequency division multiple access (OFDMA)-based wireless mesh network (WMN) with a time difference of arrival. The proposed time- and frequency-synchronization technique uses only the signals received from the neighbor nodes, by considering the effect of the propagation delay between the nodes. It achieves a fast synchronization with a relatively low computational complexity because it is operated in a distributed manner, not requiring any feedback channel for the compensation of the propagation delays. In addition, a self-organization scheme that can be effectively used to construct 1-hop neighbor nodes is proposed for an OFDMA-based WMN with a large number of nodes. The performance of the proposed technique is evaluated with regard to the convergence property and synchronization success probability using a computer simulation. PMID:26225974
A mesh partitioning algorithm for preserving spatial locality in arbitrary geometries
Nivarti, Girish V. Salehi, M. Mahdi; Bushe, W. Kendal
2015-01-15
Highlights: •An algorithm for partitioning computational meshes is proposed. •The Morton order space-filling curve is modified to achieve improved locality. •A spatial locality metric is defined to compare results with existing approaches. •Results indicate improved performance of the algorithm in complex geometries. -- Abstract: A space-filling curve (SFC) is a proximity preserving linear mapping of any multi-dimensional space and is widely used as a clustering tool. Equi-sized partitioning of an SFC ignores the loss in clustering quality that occurs due to inaccuracies in the mapping. Often, this results in poor locality within partitions, especially for the conceptually simple, Morton order curves. We present a heuristic that improves partition locality in arbitrary geometries by slicing a Morton order curve at points where spatial locality is sacrificed. In addition, we develop algorithms that evenly distribute points to the extent possible while maintaining spatial locality. A metric is defined to estimate relative inter-partition contact as an indicator of communication in parallel computing architectures. Domain partitioning tests have been conducted on geometries relevant to turbulent reactive flow simulations. The results obtained highlight the performance of our method as an unsupervised and computationally inexpensive domain partitioning tool.
An adaptive replacement algorithm for paged-memory computer systems.
NASA Technical Reports Server (NTRS)
Thorington, J. M., Jr.; Irwin, J. D.
1972-01-01
A general class of adaptive replacement schemes for use in paged memories is developed. One such algorithm, called SIM, is simulated using a probability model that generates memory traces, and the results of the simulation of this adaptive scheme are compared with those obtained using the best nonlookahead algorithms. A technique for implementing this type of adaptive replacement algorithm with state of the art digital hardware is also presented.
Friedman, A.; Miller, W. Jr.
1993-12-31
The program was divided into segments: (Week 1) geometric modeling and mesh generation (Weeks 2 and 3) error estimation and adaptive strategies. Participants in the program came from a wide variety of disciplines dealing with remarkably analogous problems in this area. Ideas were exchanged and interdisciplinary collaboration was initiated in informal contexts as well as in the talks and question periods. In the talks, a number of algorithms were described along with specific applications to problems of great current interest in various scientific and engineering disciplines. In this emerging field, participants developed criteria for evaluation of algorithms and established guidelines for selection of algorithms appropriate to any specific problem. Special features of a problem may include curved surfaces, complicated boundaries, evolving interfaces (such as occur in coating flows), and/or criticality of error estimation.
White Dwarf Mergers on Adaptive Meshes. I. Methodology and Code Verification
NASA Astrophysics Data System (ADS)
Katz, Max P.; Zingale, Michael; Calder, Alan C.; Swesty, F. Douglas; Almgren, Ann S.; Zhang, Weiqun
2016-03-01
The Type Ia supernova (SN Ia) progenitor problem is one of the most perplexing and exciting problems in astrophysics, requiring detailed numerical modeling to complement observations of these explosions. One possible progenitor that has merited recent theoretical attention is the white dwarf (WD) merger scenario, which has the potential to naturally explain many of the observed characteristics of SNe Ia. To date there have been relatively few self-consistent simulations of merging WD systems using mesh-based hydrodynamics. This is the first paper in a series describing simulations of these systems using a hydrodynamics code with adaptive mesh refinement. In this paper we describe our numerical methodology and discuss our implementation in the compressible hydrodynamics code CASTRO, which solves the Euler equations, and the Poisson equation for self-gravity, and couples the gravitational and rotation forces to the hydrodynamics. Standard techniques for coupling gravitation and rotation forces to the hydrodynamics do not adequately conserve the total energy of the system for our problem, but recent advances in the literature allow progress and we discuss our implementation here. We present a set of test problems demonstrating the extent to which our software sufficiently models a system where large amounts of mass are advected on the computational domain over long timescales. Future papers in this series will describe our treatment of the initial conditions of these systems and will examine the early phases of the merger to determine its viability for triggering a thermonuclear detonation.
NASA Technical Reports Server (NTRS)
Ashford, Gregory A.; Powell, Kenneth G.
1995-01-01
A method for generating high quality unstructured triangular grids for high Reynolds number Navier-Stokes calculations about complex geometries is described. Careful attention is paid in the mesh generation process to resolving efficiently the disparate length scales which arise in these flows. First the surface mesh is constructed in a way which ensures that the geometry is faithfully represented. The volume mesh generation then proceeds in two phases thus allowing the viscous and inviscid regions of the flow to be meshed optimally. A solution-adaptive remeshing procedure which allows the mesh to adapt itself to flow features is also described. The procedure for tracking wakes and refinement criteria appropriate for shock detection are described. Although at present it has only been implemented in two dimensions, the grid generation process has been designed with the extension to three dimensions in mind. An implicit, higher-order, upwind method is also presented for computing compressible turbulent flows on these meshes. Two recently developed one-equation turbulence models have been implemented to simulate the effects of the fluid turbulence. Results for flow about a RAE 2822 airfoil and a Douglas three-element airfoil are presented which clearly show the improved resolution obtainable.
NASA Astrophysics Data System (ADS)
Ashford, Gregory A.; Powell, Kenneth G.
1995-10-01
A method for generating high quality unstructured triangular grids for high Reynolds number Navier-Stokes calculations about complex geometries is described. Careful attention is paid in the mesh generation process to resolving efficiently the disparate length scales which arise in these flows. First the surface mesh is constructed in a way which ensures that the geometry is faithfully represented. The volume mesh generation then proceeds in two phases thus allowing the viscous and inviscid regions of the flow to be meshed optimally. A solution-adaptive remeshing procedure which allows the mesh to adapt itself to flow features is also described. The procedure for tracking wakes and refinement criteria appropriate for shock detection are described. Although at present it has only been implemented in two dimensions, the grid generation process has been designed with the extension to three dimensions in mind. An implicit, higher-order, upwind method is also presented for computing compressible turbulent flows on these meshes. Two recently developed one-equation turbulence models have been implemented to simulate the effects of the fluid turbulence. Results for flow about a RAE 2822 airfoil and a Douglas three-element airfoil are presented which clearly show the improved resolution obtainable.
An adaptive algorithm for motion compensated color image coding
NASA Technical Reports Server (NTRS)
Kwatra, Subhash C.; Whyte, Wayne A.; Lin, Chow-Ming
1987-01-01
This paper presents an adaptive algorithm for motion compensated color image coding. The algorithm can be used for video teleconferencing or broadcast signals. Activity segmentation is used to reduce the bit rate and a variable stage search is conducted to save computations. The adaptive algorithm is compared with the nonadaptive algorithm and it is shown that with approximately 60 percent savings in computing the motion vector and 33 percent additional compression, the performance of the adaptive algorithm is similar to the nonadaptive algorithm. The adaptive algorithm results also show improvement of up to 1 bit/pel over interframe DPCM coding with nonuniform quantization. The test pictures used for this study were recorded directly from broadcast video in color.
Rattner, Alexander S.; Guillen, Donna Post; Joshi, Alark; Garimella, Srinivas
2016-03-17
Photo- and physically realistic techniques are often insufficient for visualization of fluid flow simulations, especially for 3D and time-varying studies. Substantial research effort has been dedicated to the development of non-photorealistic and illustration-inspired visualization techniques for compact and intuitive presentation of such complex datasets. However, a great deal of work has been reproduced in this field, as many research groups have developed specialized visualization software. Additionally, interoperability between illustrative visualization software is limited due to diverse processing and rendering architectures employed in different studies. In this investigation, a framework for illustrative visualization is proposed, and implemented in MarmotViz, a ParaViewmore » plug-in, enabling its use on a variety of computing platforms with various data file formats and mesh geometries. Region-of-interest identification and feature-tracking algorithms incorporated into this tool are described. Implementations of multiple illustrative effect algorithms are also presented to demonstrate the use and flexibility of this framework. Here, by providing an integrated framework for illustrative visualization of CFD data, MarmotViz can serve as a valuable asset for the interpretation of simulations of ever-growing scale.« less
Alexander S. Rattner; Donna Post Guillen; Alark Joshi
2012-12-01
Photo- and physically-realistic techniques are often insufficient for visualization of simulation results, especially for 3D and time-varying datasets. Substantial research efforts have been dedicated to the development of non-photorealistic and illustration-inspired visualization techniques for compact and intuitive presentation of such complex datasets. While these efforts have yielded valuable visualization results, a great deal of work has been reproduced in studies as individual research groups often develop purpose-built platforms. Additionally, interoperability between illustrative visualization software is limited due to specialized processing and rendering architectures employed in different studies. In this investigation, a generalized framework for illustrative visualization is proposed, and implemented in marmotViz, a ParaView plugin, enabling its use on variety of computing platforms with various data file formats and mesh geometries. Detailed descriptions of the region-of-interest identification and feature-tracking algorithms incorporated into this tool are provided. Additionally, implementations of multiple illustrative effect algorithms are presented to demonstrate the use and flexibility of this framework. By providing a framework and useful underlying functionality, the marmotViz tool can act as a springboard for future research in the field of illustrative visualization.
Multifluid adaptive-mesh simulation of the solar wind interaction with the local interstellar medium
Kryukov, I. A.; Borovikov, S. N.; Pogorelov, N. V.; Zank, G. P.
2006-09-26
DOE's SciDAC adaptive mesh refinement code Chombo has been modified for solution of compressible MHD flows with the application of high resolution, shock-capturing numerical schemes. The code developed is further extended to involve multiple fluids and applied to the problem of the solar wind interaction with the local interstellar medium. For this purpose, a set of MHD equations is solved together with a few sets of the Euler gas dynamics equations, depending on the number of neutral fluids included in the model. Our first results are presented that were obtained in the framework of an axially symmetric multifluid model which is applicable to magnetic-field-aligned flows. Details are shown of the generation and development of Rayleigh-Taylor and Kelvin-Helmholtz instabilities of the heliopause. A comparison is given of the results obtained with a two- and four-fluid models.
Goal functional evaluations for phase-field fracture using PU-based DWR mesh adaptivity
NASA Astrophysics Data System (ADS)
Wick, Thomas
2016-03-01
In this study, a posteriori error estimation and goal-oriented mesh adaptivity are developed for phase-field fracture propagation. Goal functionals are computed with the dual-weighted residual (DWR) method, which is realized by a recently introduced novel localization technique based on a partition-of-unity (PU). This technique is straightforward to apply since the weak residual is used. The influence of neighboring cells is gathered by the PU. Consequently, neither strong residuals nor jumps over element edges are required. Therefore, this approach facilitates the application of the DWR method to coupled (nonlinear) multiphysics problems such as fracture propagation. These developments then allow for a systematic investigation of the discretization error for certain quantities of interest. Specifically, our focus on the relationship between the phase-field regularization and the spatial discretization parameter in terms of goal functional evaluations is novel.
Detached Eddy Simulation of the UH-60 Rotor Wake Using Adaptive Mesh Refinement
NASA Technical Reports Server (NTRS)
Chaderjian, Neal M.; Ahmad, Jasim U.
2012-01-01
Time-dependent Navier-Stokes flow simulations have been carried out for a UH-60 rotor with simplified hub in forward flight and hover flight conditions. Flexible rotor blades and flight trim conditions are modeled and established by loosely coupling the OVERFLOW Computational Fluid Dynamics (CFD) code with the CAMRAD II helicopter comprehensive code. High order spatial differences, Adaptive Mesh Refinement (AMR), and Detached Eddy Simulation (DES) are used to obtain highly resolved vortex wakes, where the largest turbulent structures are captured. Special attention is directed towards ensuring the dual time accuracy is within the asymptotic range, and verifying the loose coupling convergence process using AMR. The AMR/DES simulation produced vortical worms for forward flight and hover conditions, similar to previous results obtained for the TRAM rotor in hover. AMR proved to be an efficient means to capture a rotor wake without a priori knowledge of the wake shape.
Galaxy Mergers with Adaptive Mesh Refinement: Star Formation and Hot Gas Outflow
Kim, Ji-hoon; Wise, John H.; Abel, Tom; /KIPAC, Menlo Park /Stanford U., Phys. Dept.
2011-06-22
In hierarchical structure formation, merging of galaxies is frequent and known to dramatically affect their properties. To comprehend these interactions high-resolution simulations are indispensable because of the nonlinear coupling between pc and Mpc scales. To this end, we present the first adaptive mesh refinement (AMR) simulation of two merging, low mass, initially gas-rich galaxies (1.8 x 10{sup 10} M{sub {circle_dot}} each), including star formation and feedback. With galaxies resolved by {approx} 2 x 10{sup 7} total computational elements, we achieve unprecedented resolution of the multiphase interstellar medium, finding a widespread starburst in the merging galaxies via shock-induced star formation. The high dynamic range of AMR also allows us to follow the interplay between the galaxies and their embedding medium depicting how galactic outflows and a hot metal-rich halo form. These results demonstrate that AMR provides a powerful tool in understanding interacting galaxies.
A consistent approach to large eddy simulation using adaptive mesh refinement
Cook, A.W.
1999-09-01
The large eddy simulation of turbulent flows is discussed with particular attention paid to the issue of commutation of differentiation and filtering. Multi-level adaptive mesh refinement is proposed as a means of mostly avoiding commutation errors where increased grid resolution is required to capture key flow features. The strategy is to employ multiple uniform grids in a nested hierarchy using a constant-width filter for each grid. It is shown that commutivity of fine and coarse grid filters must be enforced in order to consistently relate variables at different refinement levels. Methods for treating fine grid boundaries and walls are also discussed. It is shown that errors associated with boundary treatments are small and localized.
NASA Astrophysics Data System (ADS)
Zanotti, O.; Dumbser, M.; Fambri, F.
2016-05-01
We describe a new method for the solution of the ideal MHD equations in special relativity which adopts the following strategy: (i) the main scheme is based on Discontinuous Galerkin (DG) methods, allowing for an arbitrary accuracy of order N+1, where N is the degree of the basis polynomials; (ii) in order to cope with oscillations at discontinuities, an ”a-posteriori” sub-cell limiter is activated, which scatters the DG polynomials of the previous time-step onto a set of 2N+1 sub-cells, over which the solution is recomputed by means of a robust finite volume scheme; (iii) a local spacetime Discontinuous-Galerkin predictor is applied both on the main grid of the DG scheme and on the sub-grid of the finite volume scheme; (iv) adaptive mesh refinement (AMR) with local time-stepping is used. We validate the new scheme and comment on its potential applications in high energy astrophysics.
AstroBEAR: Adaptive Mesh Refinement Code for Ideal Hydrodynamics & Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Cunningham, Andrew J.; Frank, Adam; Varniere, Peggy; Mitran, Sorin; Jones, Thomas W.
2011-04-01
AstroBEAR is a modular hydrodynamic & magnetohydrodynamic code environment designed for a variety of astrophysical applications. It uses the BEARCLAW package, a multidimensional, Eulerian computational code used to solve hyperbolic systems of equations. AstroBEAR allows adaptive-mesh-refinment (AMR) simulations in 2, 2.5 (i.e., cylindrical), and 3 dimensions, in either cartesian or curvilinear coordinates. Parallel applications are supported through the MPI architecture. AstroBEAR is written in Fortran 90/95 using standard libraries. AstroBEAR supports hydrodynamic (HD) and magnetohydrodynamic (MHD) applications using a variety of spatial and temporal methods. MHD simulations are kept divergence-free via the constrained transport (CT) methods of Balsara & Spicer. Three different equation of state environments are available: ideal gas, gas with differing isentropic γ, and the analytic Thomas-Fermi formulation of A.R. Bell [2]. Current work is being done to develop a more advanced real gas equation of state.
Dynamic Implicit 3D Adaptive Mesh Refinement for Non-Equilibrium Radiation Diffusion
Philip, Bobby; Wang, Zhen; Berrill, Mark A; Rodriguez Rodriguez, Manuel; Pernice, Michael
2014-01-01
The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial confinement fusion. The associated initial boundary value problems that are encountered exhibit a wide range of scales in space and time and are extremely challenging to solve. To efficiently and accurately simulate these systems we describe our research on combining techniques that will also find use more broadly for long term time integration of nonlinear multiphysics systems: implicit time integration for efficient long term time integration of stiff multiphysics systems, local control theory based step size control to minimize the required global number of time steps while controlling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent linear solver convergence.
3D Adaptive Mesh Refinement Simulations of Pellet Injection in Tokamaks
R. Samtaney; S.C. Jardin; P. Colella; D.F. Martin
2003-10-20
We present results of Adaptive Mesh Refinement (AMR) simulations of the pellet injection process, a proven method of refueling tokamaks. AMR is a computationally efficient way to provide the resolution required to simulate realistic pellet sizes relative to device dimensions. The mathematical model comprises of single-fluid MHD equations with source terms in the continuity equation along with a pellet ablation rate model. The numerical method developed is an explicit unsplit upwinding treatment of the 8-wave formulation, coupled with a MAC projection method to enforce the solenoidal property of the magnetic field. The Chombo framework is used for AMR. The role of the E x B drift in mass redistribution during inside and outside pellet injections is emphasized.
On the Computation of Integral Curves in Adaptive Mesh Refinement Vector Fields
Deines, Eduard; Weber, Gunther H.; Garth, Christoph; Van Straalen, Brian; Borovikov, Sergey; Martin, Daniel F.; Joy, Kenneth I.
2011-06-27
Integral curves, such as streamlines, streaklines, pathlines, and timelines, are an essential tool in the analysis of vector field structures, offering straightforward and intuitive interpretation of visualization results. While such curves have a long-standing tradition in vector field visualization, their application to Adaptive Mesh Refinement (AMR) simulation results poses unique problems. AMR is a highly effective discretization method for a variety of physical simulation problems and has recently been applied to the study of vector fields in flow and magnetohydrodynamic applications. The cell-centered nature of AMR data and discontinuities in the vector field representation arising from AMR level boundaries complicate the application of numerical integration methods to compute integral curves. In this paper, we propose a novel approach to alleviate these problems and show its application to streamline visualization in an AMR model of the magnetic field of the solar system as well as to a simulation of two incompressible viscous vortex rings merging.
Goal functional evaluations for phase-field fracture using PU-based DWR mesh adaptivity
NASA Astrophysics Data System (ADS)
Wick, Thomas
2016-06-01
In this study, a posteriori error estimation and goal-oriented mesh adaptivity are developed for phase-field fracture propagation. Goal functionals are computed with the dual-weighted residual (DWR) method, which is realized by a recently introduced novel localization technique based on a partition-of-unity (PU). This technique is straightforward to apply since the weak residual is used. The influence of neighboring cells is gathered by the PU. Consequently, neither strong residuals nor jumps over element edges are required. Therefore, this approach facilitates the application of the DWR method to coupled (nonlinear) multiphysics problems such as fracture propagation. These developments then allow for a systematic investigation of the discretization error for certain quantities of interest. Specifically, our focus on the relationship between the phase-field regularization and the spatial discretization parameter in terms of goal functional evaluations is novel.
NASA Astrophysics Data System (ADS)
Zhang, Xiaoning; Li, Lemin; Wang, Sheng; Wei, Xuetao
2008-04-01
In this paper, we propose a novel robust routing algorithm based on Valiant load-balancing under the model of polyhedral uncertainty (i.e., hose uncertainty model) for WDM (wavelength division multiplexing) mesh networks. Valiant load-balanced robust routing algorithm constructs the stable virtual topology on which any traffic patterns under the hose uncertainty model can be efficiently routed. Considering there are multi-granularity connection requests in WDM mesh networks, we propose the method called hose-model separation to solve the problem for the proposed algorithm. Our goal is to minimize total network cost when constructing the stable virtual topology that assures robust routing for the hose model in WDM mesh networks. A mathematical formulation (integer linear programming, ILP) about Valiant load-balanced robust routing algorithm is presented. Two fast heuristic approaches are also proposed and evaluated. We compare the network throughput of the virtual topology constructed by the proposed algorithm with that of the traditional traffic grooming algorithm under the same total network cost by computer simulation.
The PLUTO Code for Adaptive Mesh Computations in Astrophysical Fluid Dynamics
NASA Astrophysics Data System (ADS)
Mignone, A.; Zanni, C.; Tzeferacos, P.; van Straalen, B.; Colella, P.; Bodo, G.
2012-01-01
We present a description of the adaptive mesh refinement (AMR) implementation of the PLUTO code for solving the equations of classical and special relativistic magnetohydrodynamics (MHD and RMHD). The current release exploits, in addition to the static grid version of the code, the distributed infrastructure of the CHOMBO library for multidimensional parallel computations over block-structured, adaptively refined grids. We employ a conservative finite-volume approach where primary flow quantities are discretized at the cell center in a dimensionally unsplit fashion using the Corner Transport Upwind method. Time stepping relies on a characteristic tracing step where piecewise parabolic method, weighted essentially non-oscillatory, or slope-limited linear interpolation schemes can be handily adopted. A characteristic decomposition-free version of the scheme is also illustrated. The solenoidal condition of the magnetic field is enforced by augmenting the equations with a generalized Lagrange multiplier providing propagation and damping of divergence errors through a mixed hyperbolic/parabolic explicit cleaning step. Among the novel features, we describe an extension of the scheme to include non-ideal dissipative processes, such as viscosity, resistivity, and anisotropic thermal conduction without operator splitting. Finally, we illustrate an efficient treatment of point-local, potentially stiff source terms over hierarchical nested grids by taking advantage of the adaptivity in time. Several multidimensional benchmarks and applications to problems of astrophysical relevance assess the potentiality of the AMR version of PLUTO in resolving flow features separated by large spatial and temporal disparities.
THE PLUTO CODE FOR ADAPTIVE MESH COMPUTATIONS IN ASTROPHYSICAL FLUID DYNAMICS
Mignone, A.; Tzeferacos, P.; Zanni, C.; Bodo, G.; Van Straalen, B.; Colella, P.
2012-01-01
We present a description of the adaptive mesh refinement (AMR) implementation of the PLUTO code for solving the equations of classical and special relativistic magnetohydrodynamics (MHD and RMHD). The current release exploits, in addition to the static grid version of the code, the distributed infrastructure of the CHOMBO library for multidimensional parallel computations over block-structured, adaptively refined grids. We employ a conservative finite-volume approach where primary flow quantities are discretized at the cell center in a dimensionally unsplit fashion using the Corner Transport Upwind method. Time stepping relies on a characteristic tracing step where piecewise parabolic method, weighted essentially non-oscillatory, or slope-limited linear interpolation schemes can be handily adopted. A characteristic decomposition-free version of the scheme is also illustrated. The solenoidal condition of the magnetic field is enforced by augmenting the equations with a generalized Lagrange multiplier providing propagation and damping of divergence errors through a mixed hyperbolic/parabolic explicit cleaning step. Among the novel features, we describe an extension of the scheme to include non-ideal dissipative processes, such as viscosity, resistivity, and anisotropic thermal conduction without operator splitting. Finally, we illustrate an efficient treatment of point-local, potentially stiff source terms over hierarchical nested grids by taking advantage of the adaptivity in time. Several multidimensional benchmarks and applications to problems of astrophysical relevance assess the potentiality of the AMR version of PLUTO in resolving flow features separated by large spatial and temporal disparities.
A Parallel Ocean Model With Adaptive Mesh Refinement Capability For Global Ocean Prediction
Herrnstein, A
2005-09-08
An ocean model with adaptive mesh refinement (AMR) capability is presented for simulating ocean circulation on decade time scales. The model closely resembles the LLNL ocean general circulation model with some components incorporated from other well known ocean models when appropriate. Spatial components are discretized using finite differences on a staggered grid where tracer and pressure variables are defined at cell centers and velocities at cell vertices (B-grid). Horizontal motion is modeled explicitly with leapfrog and Euler forward-backward time integration, and vertical motion is modeled semi-implicitly. New AMR strategies are presented for horizontal refinement on a B-grid, leapfrog time integration, and time integration of coupled systems with unequal time steps. These AMR capabilities are added to the LLNL software package SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure) and validated with standard benchmark tests. The ocean model is built on top of the amended SAMRAI library. The resulting model has the capability to dynamically increase resolution in localized areas of the domain. Limited basin tests are conducted using various refinement criteria and produce convergence trends in the model solution as refinement is increased. Carbon sequestration simulations are performed on decade time scales in domains the size of the North Atlantic and the global ocean. A suggestion is given for refinement criteria in such simulations. AMR predicts maximum pH changes and increases in CO{sub 2} concentration near the injection sites that are virtually unattainable with a uniform high resolution due to extremely long run times. Fine scale details near the injection sites are achieved by AMR with shorter run times than the finest uniform resolution tested despite the need for enhanced parallel performance. The North Atlantic simulations show a reduction in passive tracer errors when AMR is applied instead of a uniform coarse resolution. No
Multiphase flow modelling of explosive volcanic eruptions using adaptive unstructured meshes
NASA Astrophysics Data System (ADS)
Jacobs, Christian T.; Collins, Gareth S.; Piggott, Matthew D.; Kramer, Stephan C.
2014-05-01
Explosive volcanic eruptions generate highly energetic plumes of hot gas and ash particles that produce diagnostic deposits and pose an extreme environmental hazard. The formation, dispersion and collapse of these volcanic plumes are complex multiscale processes that are extremely challenging to simulate numerically. Accurate description of particle and droplet aggregation, movement and settling requires a model capable of capturing the dynamics on a range of scales (from cm to km) and a model that can correctly describe the important multiphase interactions that take place. However, even the most advanced models of eruption dynamics to date are restricted by the fixed mesh-based approaches that they employ. The research presented herein describes the development of a compressible multiphase flow model within Fluidity, a combined finite element / control volume computational fluid dynamics (CFD) code, for the study of explosive volcanic eruptions. Fluidity adopts a state-of-the-art adaptive unstructured mesh-based approach to discretise the domain and focus numerical resolution only in areas important to the dynamics, while decreasing resolution where it is not needed as a simulation progresses. This allows the accurate but economical representation of the flow dynamics throughout time, and potentially allows large multi-scale problems to become tractable in complex 3D domains. The multiphase flow model is verified with the method of manufactured solutions, and validated by simulating published gas-solid shock tube experiments and comparing the numerical results against pressure gauge data. The application of the model considers an idealised 7 km by 7 km domain in which the violent eruption of hot gas and volcanic ash high into the atmosphere is simulated. Although the simulations do not correspond to a particular eruption case study, the key flow features observed in a typical explosive eruption event are successfully captured. These include a shock wave resulting
FEATURE-BASED MULTIBLOCK FINITE ELEMENT MESH GENERATION
Shivanna, Kiran H.; Tadepalli, Srinivas C.; Grosland, Nicole M.
2010-01-01
Hexahedral finite element mesh development for anatomic structures and biomedical implants can be cumbersome. Moreover, using traditional meshing techniques, detailed features may be inadequately captured. In this paper, we describe methodologies to handle multi-feature datasets (i.e., feature edges and surfaces). Coupling multi-feature information with multiblock meshing techniques has enabled anatomic structures, as well as orthopaedic implants, to be readily meshed. Moreover, the projection process, node and element set creation are automated, thus reducing the user interaction during model development. To improve the mesh quality, Laplacian- and optimization-based mesh improvement algorithms have been adapted to the multi-feature datasets. PMID:21076650
Development of a scalable gas-dynamics solver with adaptive mesh refinement
NASA Astrophysics Data System (ADS)
Korkut, Burak
There are various computational physics areas in which Direct Simulation Monte Carlo (DSMC) and Particle in Cell (PIC) methods are being employed. The accuracy of results from such simulations depend on the fidelity of the physical models being used. The computationally demanding nature of these problems make them ideal candidates to make use of modern supercomputers. The software developed to run such simulations also needs special attention so that the maintainability and extendability is considered with the recent numerical methods and programming paradigms. Suited for gas-dynamics problems, a software called SUGAR (Scalable Unstructured Gas dynamics with Adaptive mesh Refinement) has recently been developed and written in C++ and MPI. Physical and numerical models were added to this framework to simulate ion thruster plumes. SUGAR is used to model the charge-exchange (CEX) reactions occurring between the neutral and ion species as well as the induced electric field effect due to ions. Multiple adaptive mesh refinement (AMR) meshes were used in order to capture different physical length scales present in the flow. A multiple-thruster configuration was run to extend the studies to cases for which there is no axial or radial symmetry present that could only be modeled with a three-dimensional simulation capability. The combined plume structure showed interactions between individual thrusters where AMR capability captured this in an automated way. The back flow for ions was found to occur when CEX and momentum-exchange (MEX) collisions are present and strongly enhanced when the induced electric field is considered. The ion energy distributions in the back flow region were obtained and it was found that the inclusion of the electric field modeling is the most important factor in determining its shape. The plume back flow structure was also examined for a triple-thruster, 3-D geometry case and it was found that the ion velocity in the back flow region appears to be
NASA Astrophysics Data System (ADS)
Zhang, Xiaoning; Li, Lemin; Wang, Sheng
2006-09-01
The paper considers the problem of establishing robust routes for multi-granularity connection requests in traffic-grooming WDM mesh networks and proposes a novel Valiant Load-Balanced robust routing scheme for the hose uncertain model. Our objective is to minimize the total network cost when assuring robust routing for all possible multi-granularity connection requests under the hose model. Since the optimization problem is recently shown to be NP-hard, two heuristic algorithms are proposed and compared. When implementing Valiant Load-Balanced robust routing scheme to WDM mesh networks, a novel traffic-grooming algorithm called MHF (minimal hop first) is proposed. We evaluate MHF by Valiant Load-Balanced robust routing with the traditional traffic-grooming algorithm by computer simulation.
NASA Astrophysics Data System (ADS)
Cui, Laizhong; Jiang, Yong; Wu, Jianping; Xia, Shutao
Most large-scale Peer-to-Peer (P2P) live streaming systems are constructed as a mesh structure, which can provide robustness in the dynamic P2P environment. The pull scheduling algorithm is widely used in this mesh structure, which degrades the performance of the entire system. Recently, network coding was introduced in mesh P2P streaming systems to improve the performance, which makes the push strategy feasible. One of the most famous scheduling algorithms based on network coding is R2, with a random push strategy. Although R2 has achieved some success, the push scheduling strategy still lacks a theoretical model and optimal solution. In this paper, we propose a novel optimal pull-push scheduling algorithm based on network coding, which consists of two stages: the initial pull stage and the push stage. The main contributions of this paper are: 1) we put forward a theoretical analysis model that considers the scarcity and timeliness of segments; 2) we formulate the push scheduling problem to be a global optimization problem and decompose it into local optimization problems on individual peers; 3) we introduce some rules to transform the local optimization problem into a classical min-cost optimization problem for solving it; 4) We combine the pull strategy with the push strategy and systematically realize our scheduling algorithm. Simulation results demonstrate that decode delay, decode ratio and redundant fraction of the P2P streaming system with our algorithm can be significantly improved, without losing throughput and increasing overhead.
Approaches to the automatic generation and control of finite element meshes
NASA Technical Reports Server (NTRS)
Shephard, Mark S.
1987-01-01
The algorithmic approaches being taken to the development of finite element mesh generators capable of automatically discretizing general domains without the need for user intervention are discussed. It is demonstrated that because of the modeling demands placed on a automatic mesh generator, all the approaches taken to date produce unstructured meshes. Consideration is also given to both a priori and a posteriori mesh control devices for automatic mesh generators as well as their integration with geometric modeling and adaptive analysis procedures.
An Adaptive Unified Differential Evolution Algorithm for Global Optimization
Qiang, Ji; Mitchell, Chad
2014-11-03
In this paper, we propose a new adaptive unified differential evolution algorithm for single-objective global optimization. Instead of the multiple mutation strate- gies proposed in conventional differential evolution algorithms, this algorithm employs a single equation unifying multiple strategies into one expression. It has the virtue of mathematical simplicity and also provides users the flexibility for broader exploration of the space of mutation operators. By making all control parameters in the proposed algorithm self-adaptively evolve during the process of optimization, it frees the application users from the burden of choosing appro- priate control parameters and also improves the performance of the algorithm. In numerical tests using thirteen basic unimodal and multimodal functions, the proposed adaptive unified algorithm shows promising performance in compari- son to several conventional differential evolution algorithms.
Performance Characteristics of an Adaptive Mesh RefinementCalculation on Scalar and Vector Platforms
Welcome, Michael; Rendleman, Charles; Oliker, Leonid; Biswas, Rupak
2006-01-31
Adaptive mesh refinement (AMR) is a powerful technique thatreduces the resources necessary to solve otherwise in-tractable problemsin computational science. The AMR strategy solves the problem on arelatively coarse grid, and dynamically refines it in regions requiringhigher resolution. However, AMR codes tend to be far more complicatedthan their uniform grid counterparts due to the software infrastructurenecessary to dynamically manage the hierarchical grid framework. Despitethis complexity, it is generally believed that future multi-scaleapplications will increasingly rely on adaptive methods to study problemsat unprecedented scale and resolution. Recently, a new generation ofparallel-vector architectures have become available that promise toachieve extremely high sustained performance for a wide range ofapplications, and are the foundation of many leadership-class computingsystems worldwide. It is therefore imperative to understand the tradeoffsbetween conventional scalar and parallel-vector platforms for solvingAMR-based calculations. In this paper, we examine the HyperCLaw AMRframework to compare and contrast performance on the Cray X1E, IBM Power3and Power5, and SGI Altix. To the best of our knowledge, this is thefirst work that investigates and characterizes the performance of an AMRcalculation on modern parallel-vector systems.
NASA Astrophysics Data System (ADS)
Hatori, Tomoharu; Ito, Atsushi M.; Nunami, Masanori; Usui, Hideyuki; Miura, Hideaki
2016-08-01
We propose a numerical method to determine the artificial viscosity in magnetohydrodynamics (MHD) simulations with adaptive mesh refinement (AMR) method, where the artificial viscosity is adaptively changed due to the resolution level of the AMR hierarchy. Although the suitable value of the artificial viscosity depends on the governing equations and the model of target problem, it can be determined by von Neumann stability analysis. By means of the new method, "level-by-level artificial viscosity method," MHD simulations of Rayleigh-Taylor instability (RTI) are carried out with the AMR method. The validity of the level-by-level artificial viscosity method is confirmed by the comparison of the linear growth rates of RTI between the AMR simulations and the simple simulations with uniform grid and uniform artificial viscosity whose resolution is the same as that in the highest level of the AMR simulation. Moreover, in the nonlinear phase of RTI, the secondary instability is clearly observed where the hierarchical data structure of AMR calculation is visualized as high resolution region floats up like terraced fields. In the applications of the method to general fluid simulations, the growth of small structures can be sufficiently reproduced, while the divergence of numerical solutions can be suppressed.
Adaptive DNA Computing Algorithm by Using PCR and Restriction Enzyme
NASA Astrophysics Data System (ADS)
Kon, Yuji; Yabe, Kaoru; Rajaee, Nordiana; Ono, Osamu
In this paper, we introduce an adaptive DNA computing algorithm by using polymerase chain reaction (PCR) and restriction enzyme. The adaptive algorithm is designed based on Adleman-Lipton paradigm[3] of DNA computing. In this work, however, unlike the Adleman- Lipton architecture a cutting operation has been introduced to the algorithm and the mechanism in which the molecules used by computation were feedback to the next cycle devised. Moreover, the amplification by PCR is performed in the molecule used by feedback and the difference concentration arisen in the base sequence can be used again. By this operation the molecules which serve as a solution candidate can be reduced down and the optimal solution is carried out in the shortest path problem. The validity of the proposed adaptive algorithm is considered with the logical simulation and finally we go on to propose applying adaptive algorithm to the chemical experiment which used the actual DNA molecules for solving an optimal network problem.
An adaptive algorithm for simulation of stochastic reaction-diffusion processes
Ferm, Lars Hellander, Andreas Loetstedt, Per
2010-01-20
We propose an adaptive hybrid method suitable for stochastic simulation of diffusion dominated reaction-diffusion processes. For such systems, simulation of the diffusion requires the predominant part of the computing time. In order to reduce the computational work, the diffusion in parts of the domain is treated macroscopically, in other parts with the tau-leap method and in the remaining parts with Gillespie's stochastic simulation algorithm (SSA) as implemented in the next subvolume method (NSM). The chemical reactions are handled by SSA everywhere in the computational domain. A trajectory of the process is advanced in time by an operator splitting technique and the timesteps are chosen adaptively. The spatial adaptation is based on estimates of the errors in the tau-leap method and the macroscopic diffusion. The accuracy and efficiency of the method are demonstrated in examples from molecular biology where the domain is discretized by unstructured meshes.
Bauer, Carl A.; Werner, Gregory R.; Cary, John R.
2011-03-01
A new frequency-domain electromagnetics algorithm is developed for simulating curved interfaces between anisotropic dielectrics embedded in a Yee mesh with second-order error in resonant frequencies. The algorithm is systematically derived using the finite integration formulation of Maxwell's equations on the Yee mesh. Second-order convergence of the error in resonant frequencies is achieved by guaranteeing first-order error on dielectric boundaries and second-order error in bulk (possibly anisotropic) regions. Convergence studies, conducted for an analytically solvable problem and for a photonic crystal of ellipsoids with anisotropic dielectric constant, both show second-order convergence of frequency error; the convergence is sufficiently smooth that Richardson extrapolation yields roughly third-order convergence. The convergence of electric fields near the dielectric interface for the analytic problem is also presented.
Computational results for parallel unstructured mesh computations
Jones, M.T.; Plassmann, P.E.
1994-12-31
The majority of finite element models in structural engineering are composed of unstructured meshes. These unstructured meshes are often very large and require significant computational resources; hence they are excellent candidates for massively parallel computation. Parallel solution of the sparse matrices that arise from such meshes has been studied heavily, and many good algorithms have been developed. Unfortunately, many of the other aspects of parallel unstructured mesh computation have gone largely ignored. The authors present a set of algorithms that allow the entire unstructured mesh computation process to execute in parallel -- including adaptive mesh refinement, equation reordering, mesh partitioning, and sparse linear system solution. They briefly describe these algorithms and state results regarding their running-time and performance. They then give results from the 512-processor Intel DELTA for a large-scale structural analysis problem. These results demonstrate that the new algorithms are scalable and efficient. The algorithms are able to achieve up to 2.2 gigaflops for this unstructured mesh problem.
Self-adaptive genetic algorithms with simulated binary crossover.
Deb, K; Beyer, H G
2001-01-01
Self-adaptation is an essential feature of natural evolution. However, in the context of function optimization, self-adaptation features of evolutionary search algorithms have been explored mainly with evolution strategy (ES) and evolutionary programming (EP). In this paper, we demonstrate the self-adaptive feature of real-parameter genetic algorithms (GAs) using a simulated binary crossover (SBX) operator and without any mutation operator. The connection between the working of self-adaptive ESs and real-parameter GAs with the SBX operator is also discussed. Thereafter, the self-adaptive behavior of real-parameter GAs is demonstrated on a number of test problems commonly used in the ES literature. The remarkable similarity in the working principle of real-parameter GAs and self-adaptive ESs shown in this study suggests the need for emphasizing further studies on self-adaptive GAs. PMID:11382356
NASA Astrophysics Data System (ADS)
Moura, R. C.; Silva, A. F. C.; Bigarella, E. D. V.; Fazenda, A. L.; Ortega, M. A.
2016-08-01
This paper proposes two important improvements to shock-capturing strategies using a discontinuous Galerkin scheme, namely, accurate shock identification via finite-time Lyapunov exponent (FTLE) operators and efficient shock treatment through a point-implicit discretization of a PDE-based artificial viscosity technique. The advocated approach is based on the FTLE operator, originally developed in the context of dynamical systems theory to identify certain types of coherent structures in a flow. We propose the application of FTLEs in the detection of shock waves and demonstrate the operator's ability to identify strong and weak shocks equally well. The detection algorithm is coupled with a mesh refinement procedure and applied to transonic and supersonic flows. While the proposed strategy can be used potentially with any numerical method, a high-order discontinuous Galerkin solver is used in this study. In this context, two artificial viscosity approaches are employed to regularize the solution near shocks: an element-wise constant viscosity technique and a PDE-based smooth viscosity model. As the latter approach is more sophisticated and preferable for complex problems, a point-implicit discretization in time is proposed to reduce the extra stiffness introduced by the PDE-based technique, making it more competitive in terms of computational cost.
Advances in Rotor Performance and Turbulent Wake Simulation Using DES and Adaptive Mesh Refinement
NASA Technical Reports Server (NTRS)
Chaderjian, Neal M.
2012-01-01
Time-dependent Navier-Stokes simulations have been carried out for a rigid V22 rotor in hover, and a flexible UH-60A rotor in forward flight. Emphasis is placed on understanding and characterizing the effects of high-order spatial differencing, grid resolution, and Spalart-Allmaras (SA) detached eddy simulation (DES) in predicting the rotor figure of merit (FM) and resolving the turbulent rotor wake. The FM was accurately predicted within experimental error using SA-DES. Moreover, a new adaptive mesh refinement (AMR) procedure revealed a complex and more realistic turbulent rotor wake, including the formation of turbulent structures resembling vortical worms. Time-dependent flow visualization played a crucial role in understanding the physical mechanisms involved in these complex viscous flows. The predicted vortex core growth with wake age was in good agreement with experiment. High-resolution wakes for the UH-60A in forward flight exhibited complex turbulent interactions and turbulent worms, similar to the V22. The normal force and pitching moment coefficients were in good agreement with flight-test data.
Operator splitting and adaptive mesh refinement for the Luo-Rudy I model
NASA Astrophysics Data System (ADS)
Trangenstein, John A.; Kim, Chisup
2004-05-01
We apply second-order operator splitting to the Luo-Rudy I model for electrical wave propagation in the heart. The purpose of the operator splitting is to separate the nonlinear but local reaction computations from the linear but globally coupled diffusion computations. This approach allows us to use local nonlinear iterations for the stiff nonlinear reactions and to solve global linear systems for the implicit treatment of diffusion. For computational efficiency, we use dynamically adaptive mesh refinement (AMR), involving hierarchies of unions of grid patches on distinct levels of refinement. The linear system for the discretization of the diffusion on the composite AMR grid is formulated via standard conforming finite elements on unions grid patches within a level of refinement and aligned mortar elements along interfaces between levels of refinement. The linear systems are solved iteratively by preconditioned conjugate gradients. Our preconditioner uses multiplicative domain decomposition between levels of refinement; the smoother involves algebraic additive domain decomposition between patches within a level of refinement, and Gauss-Seidel iteration within grid patches. Numerical results are presented in 1D and 2D, including spiral waves.
EMMA: an adaptive mesh refinement cosmological simulation code with radiative transfer
NASA Astrophysics Data System (ADS)
Aubert, Dominique; Deparis, Nicolas; Ocvirk, Pierre
2015-11-01
EMMA is a cosmological simulation code aimed at investigating the reionization epoch. It handles simultaneously collisionless and gas dynamics, as well as radiative transfer physics using a moment-based description with the M1 approximation. Field quantities are stored and computed on an adaptive three-dimensional mesh and the spatial resolution can be dynamically modified based on physically motivated criteria. Physical processes can be coupled at all spatial and temporal scales. We also introduce a new and optional approximation to handle radiation: the light is transported at the resolution of the non-refined grid and only once the dynamics has been fully updated, whereas thermo-chemical processes are still tracked on the refined elements. Such an approximation reduces the overheads induced by the treatment of radiation physics. A suite of standard tests are presented and passed by EMMA, providing a validation for its future use in studies of the reionization epoch. The code is parallel and is able to use graphics processing units (GPUs) to accelerate hydrodynamics and radiative transfer calculations. Depending on the optimizations and the compilers used to generate the CPU reference, global GPU acceleration factors between ×3.9 and ×16.9 can be obtained. Vectorization and transfer operations currently prevent better GPU performance and we expect that future optimizations and hardware evolution will lead to greater accelerations.
Dynamic implicit 3D adaptive mesh refinement for non-equilibrium radiation diffusion
B. Philip; Z. Wang; M.A. Berrill; M. Birke; M. Pernice
2014-04-01
The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial confinement fusion. The associated initial boundary value problems that are encountered often exhibit a wide range of scales in space and time and are extremely challenging to solve. To efficiently and accurately simulate these systems we describe our research on combining techniques that will also find use more broadly for long term time integration of nonlinear multi-physics systems: implicit time integration for efficient long term time integration of stiff multi-physics systems, local control theory based step size control to minimize the required global number of time steps while controlling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton–Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver convergence.
NASA Astrophysics Data System (ADS)
Teyssier, Romain; Fromang, Sébastien; Dormy, Emmanuel
2006-10-01
We propose to extend the well-known MUSCL-Hancock scheme for Euler equations to the induction equation modeling the magnetic field evolution in kinematic dynamo problems. The scheme is based on an integral form of the underlying conservation law which, in our formulation, results in a “finite-surface” scheme for the induction equation. This naturally leads to the well-known “constrained transport” method, with additional continuity requirement on the magnetic field representation. The second ingredient in the MUSCL scheme is the predictor step that ensures second order accuracy both in space and time. We explore specific constraints that the mathematical properties of the induction equations place on this predictor step, showing that three possible variants can be considered. We show that the most aggressive formulations (referred to as C-MUSCL and U-MUSCL) reach the same level of accuracy as the other one (referred to as Runge Kutta), at a lower computational cost. More interestingly, these two schemes are compatible with the adaptive mesh refinement (AMR) framework. It has been implemented in the AMR code RAMSES. It offers a novel and efficient implementation of a second order scheme for the induction equation. We have tested it by solving two kinematic dynamo problems in the low diffusion limit. The construction of this scheme for the induction equation constitutes a step towards solving the full MHD set of equations using an extension of our current methodology.
woptic: Optical conductivity with Wannier functions and adaptive k-mesh refinement
NASA Astrophysics Data System (ADS)
Assmann, E.; Wissgott, P.; Kuneš, J.; Toschi, A.; Blaha, P.; Held, K.
2016-05-01
We present an algorithm for the adaptive tetrahedral integration over the Brillouin zone of crystalline materials, and apply it to compute the optical conductivity, dc conductivity, and thermopower. For these quantities, whose contributions are often localized in small portions of the Brillouin zone, adaptive integration is especially relevant. Our implementation, the woptic package, is tied into the WIEN2WANNIER framework and allows including a local many-body self energy, e.g. from dynamical mean-field theory (DMFT). Wannier functions and dipole matrix elements are computed with the DFT package WIEN2k and Wannier90. For illustration, we show DFT results for fcc-Al and DMFT results for the correlated metal SrVO3.
A finite-element mesh generator based on growing neural networks.
Triantafyllidis, D G; Labridis, D P
2002-01-01
A mesh generator for the production of high-quality finite-element meshes is being proposed. The mesh generator uses an artificial neural network, which grows during the training process in order to adapt itself to a prespecified probability distribution. The initial mesh is a constrained Delaunay triangulation of the domain to be triangulated. Two new algorithms to accelerate the location of the best matching unit are introduced. The mesh generator has been found able to produce meshes of high quality in a number of classic cases examined and is highly suited for problems where the mesh density vector can be calculated in advance. PMID:18244543
6th International Meshing Roundtable '97
White, D.
1997-09-01
The goal of the 6th International Meshing Roundtable is to bring together researchers and developers from industry, academia, and government labs in a stimulating, open environment for the exchange of technical information related to the meshing process. In the pas~ the Roundtable has enjoyed significant participation born each of these groups from a wide variety of countries. The Roundtable will consist of technical presentations from contributed papers and abstracts, two invited speakers, and two invited panels of experts discussing topics related to the development and use of automatic mesh generation tools. In addition, this year we will feature a "Bring Your Best Mesh" competition and poster session to encourage discussion and participation from a wide variety of mesh generation tool users. The schedule and evening social events are designed to provide numerous opportunities for informal dialog. A proceedings will be published by Sandia National Laboratories and distributed at the Roundtable. In addition, papers of exceptionally high quaIity will be submitted to a special issue of the International Journal of Computational Geometry and Applications. Papers and one page abstracts were sought that present original results on the meshing process. Potential topics include but are got limited to: Unstructured triangular and tetrahedral mesh generation Unstructured quadrilateral and hexahedral mesh generation Automated blocking and structured mesh generation Mixed element meshing Surface mesh generation Geometry decomposition and clean-up techniques Geometry modification techniques related to meshing Adaptive mesh refinement and mesh quality control Mesh visualization Special purpose meshing algorithms for particular applications Theoretical or novel ideas with practical potential Technical presentations from industrial researchers.
Adaptive path planning: Algorithm and analysis
Chen, Pang C.
1995-03-01
To address the need for a fast path planner, we present a learning algorithm that improves path planning by using past experience to enhance future performance. The algorithm relies on an existing path planner to provide solutions difficult tasks. From these solutions, an evolving sparse work of useful robot configurations is learned to support faster planning. More generally, the algorithm provides a framework in which a slow but effective planner may be improved both cost-wise and capability-wise by a faster but less effective planner coupled with experience. We analyze algorithm by formalizing the concept of improvability and deriving conditions under which a planner can be improved within the framework. The analysis is based on two stochastic models, one pessimistic (on task complexity), the other randomized (on experience utility). Using these models, we derive quantitative bounds to predict the learning behavior. We use these estimation tools to characterize the situations in which the algorithm is useful and to provide bounds on the training time. In particular, we show how to predict the maximum achievable speedup. Additionally, our analysis techniques are elementary and should be useful for studying other types of probabilistic learning as well.
Optimal Pid Controller Design Using Adaptive Vurpso Algorithm
NASA Astrophysics Data System (ADS)
Zirkohi, Majid Moradi
2015-04-01
The purpose of this paper is to improve theVelocity Update Relaxation Particle Swarm Optimization algorithm (VURPSO). The improved algorithm is called Adaptive VURPSO (AVURPSO) algorithm. Then, an optimal design of a Proportional-Integral-Derivative (PID) controller is obtained using the AVURPSO algorithm. An adaptive momentum factor is used to regulate a trade-off between the global and the local exploration abilities in the proposed algorithm. This operation helps the system to reach the optimal solution quickly and saves the computation time. Comparisons on the optimal PID controller design confirm the superiority of AVURPSO algorithm to the optimization algorithms mentioned in this paper namely the VURPSO algorithm, the Ant Colony algorithm, and the conventional approach. Comparisons on the speed of convergence confirm that the proposed algorithm has a faster convergence in a less computation time to yield a global optimum value. The proposed AVURPSO can be used in the diverse areas of optimization problems such as industrial planning, resource allocation, scheduling, decision making, pattern recognition and machine learning. The proposed AVURPSO algorithm is efficiently used to design an optimal PID controller.
NASA Astrophysics Data System (ADS)
Adam, A.; Pavlidis, D.; Percival, J. R.; Salinas, P.; Xie, Z.; Fang, F.; Pain, C. C.; Muggeridge, A. H.; Jackson, M. D.
2016-09-01
A general, higher-order, conservative and bounded interpolation for the dynamic and adaptive meshing of control-volume fields dual to continuous and discontinuous finite element representations is presented. Existing techniques such as node-wise interpolation are not conservative and do not readily generalise to discontinuous fields, whilst conservative methods such as Grandy interpolation are often too diffusive. The new method uses control-volume Galerkin projection to interpolate between control-volume fields. Bounded solutions are ensured by using a post-interpolation diffusive correction. Example applications of the method to interface capturing during advection and also to the modelling of multiphase porous media flow are presented to demonstrate the generality and robustness of the approach.
NASA Astrophysics Data System (ADS)
Skutnik, Steven E.; Davis, David R.
2016-05-01
The use of passive gamma and neutron signatures from fission indicators is a common means of estimating used fuel burnup, enrichment, and cooling time. However, while characteristic fission product signatures such as 134Cs, 137Cs, 154Eu, and others are generally reliable estimators for used fuel burnup within the context where the assembly initial enrichment and the discharge time are known, in the absence of initial enrichment and/or cooling time information (such as when applying NDA measurements in a safeguards/verification context), these fission product indicators no longer yield a unique solution for assembly enrichment, burnup, and cooling time after discharge. Through the use of a new Mesh-Adaptive Direct Search (MADS) algorithm, it is possible to directly probe the shape of this "degeneracy space" characteristic of individual nuclides (and combinations thereof), both as a function of constrained parameters (such as the assembly irradiation history) and unconstrained parameters (e.g., the cooling time before measurement and the measurement precision for particular indicator nuclides). In doing so, this affords the identification of potential means of narrowing the uncertainty space of potential assembly enrichment, burnup, and cooling time combinations, thereby bounding estimates of assembly plutonium content. In particular, combinations of gamma-emitting nuclides with distinct half-lives (e.g., 134Cs with 137Cs and 154Eu) in conjunction with gross neutron counting (via 244Cm) are able to reasonably constrain the degeneracy space of possible solutions to a space small enough to perform useful discrimination and verification of fuel assemblies based on their irradiation history.
An adaptive inverse kinematics algorithm for robot manipulators
NASA Technical Reports Server (NTRS)
Colbaugh, R.; Glass, K.; Seraji, H.
1990-01-01
An adaptive algorithm for solving the inverse kinematics problem for robot manipulators is presented. The algorithm is derived using model reference adaptive control (MRAC) theory and is computationally efficient for online applications. The scheme requires no a priori knowledge of the kinematics of the robot if Cartesian end-effector sensing is available, and it requires knowledge of only the forward kinematics if joint position sensing is used. Computer simulation results are given for the redundant seven-DOF robotics research arm, demonstrating that the proposed algorithm yields accurate joint angle trajectories for a given end-effector position/orientation trajectory.
NASA Astrophysics Data System (ADS)
Zheng, J.; Zhu, J.; Wang, Z.; Fang, F.; Pain, C. C.; Xiang, J.
2015-10-01
An integrated method of advanced anisotropic hr-adaptive mesh and discretization numerical techniques has been, for first time, applied to modelling of multiscale advection-diffusion problems, which is based on a discontinuous Galerkin/control volume discretization on unstructured meshes. Over existing air quality models typically based on static-structured grids using a locally nesting technique, the advantage of the anisotropic hr-adaptive model has the ability to adapt the mesh according to the evolving pollutant distribution and flow features. That is, the mesh resolution can be adjusted dynamically to simulate the pollutant transport process accurately and effectively. To illustrate the capability of the anisotropic adaptive unstructured mesh model, three benchmark numerical experiments have been set up for two-dimensional (2-D) advection phenomena. Comparisons have been made between the results obtained using uniform resolution meshes and anisotropic adaptive resolution meshes. Performance achieved in 3-D simulation of power plant plumes indicates that this new adaptive multiscale model has the potential to provide accurate air quality modelling solutions effectively.
NASA Astrophysics Data System (ADS)
Subber, Waad; Matouš, Karel
2016-02-01
Large-scale practical engineering problems featuring localized phenomena often benefit from local control of mesh and time resolutions to efficiently capture the spatial and temporal scales of interest. To this end, we propose an asynchronous space-time algorithm based on a domain decomposition method for structural dynamics problems on non-matching meshes. The three-field algorithm is based on the dual-primal like domain decomposition approach utilizing the localized Lagrange multipliers along the space and time common-refinement-based interface. The proposed algorithm is parallel in nature and well suited for a heterogeneous computing environment. Moreover, two-levels of parallelism are embedded in this novel scheme. For linear dynamical problems, the algorithm is unconditionally stable, shows an optimal order of convergence with respect to space and time discretizations as well as ensures conservation of mass, momentum and energy across the non-matching grid interfaces. The method of manufactured solutions is used to verify the implementation, and an engineering application is considered, where a sandwich plate is impacted by a projectile.
NASA Astrophysics Data System (ADS)
Ravindran, Prashaanth
The unstable nature of detonation waves is a result of the critical relationship between the hydrodynamic shock and the chemical reactions sustaining the shock. A perturbative analysis of the critical point is quite challenging due to the multiple spatio-temporal scales involved along with the non-linear nature of the shock-reaction mechanism. The author's research attempts to provide detailed resolution of the instabilities at the shock front. Another key aspect of the present research is to develop an understanding of the causality between the non-linear dynamics of the front and the eventual breakdown of the sub-structures. An accurate numerical simulation of detonation waves requires a very efficient solution of the Euler equations in conservation form with detailed, non-equilibrium chemistry. The difference in the flow and reaction length scales results in very stiff source terms, requiring the problem to be solved with adaptive mesh refinement. For this purpose, Berger-Colella's block-structured adaptive mesh refinement (AMR) strategy has been developed and applied to time-explicit finite volume methods. The block-structured technique uses a hierarchy of parent-child sub-grids, integrated recursively over time. One novel approach to partition the problem within a large supercomputer was the use of modified Peano-Hilbert space filling curves. The AMR framework was merged with CLAWPACK, a package providing finite volume numerical methods tailored for wave-propagation problems. The stiffness problem is bypassed by using a 1st order Godunov or a 2nd order Strang splitting technique, where the flow variables and source terms are integrated independently. A linearly explicit fourth-order Runge-Kutta integrator is used for the flow, and an ODE solver was used to overcome the numerical stiffness. Second-order spatial resolution is obtained by using a second-order Roe-HLL scheme with the inclusion of numerical viscosity to stabilize the solution near the discontinuity
Projections of grounding line retreat in West Antarctica carried out with an adaptive mesh model
NASA Astrophysics Data System (ADS)
Cornford, Stephen; Payne, Antony; Martin, Daniel; Le Brocq, Anne
2013-04-01
Present and future sea level rise associated with mass loss from West Antarctica is typically attributed to marine glaciers retreating in response to a warming ocean. Warmer waters melt the floating ice shelves that restrain some, if not all, marine glaciers, and the glaciers themselves respond by speeding up. That leads to thinning and in turn grounding line retreat. Satellite observations indicate that Amundsen Sea Embayment and, in particular, Pine Island Glacier, are undergoing this kind of dynamic change today. Numerical models, however, struggle to reproduce the observed behavior because either high resolution or some other kind special treatment is required at the grounding line. We present 200-year projections of three major glacier systems of West Antarctica: those that drain into the Amundsen Sea , the Filchner-Ronne Ice Shelf and the Ross Ice shelf. We do so using the newly developed BISICLES ice sheet model, which employs adaptive mesh refinement to maintain sub-kilometer resolution close to the grounding line and coarser resolution elsewhere. Ice accumulation and ice shelf melt-rate are derived from a range of models of the Antarctic atmosphere and ocean forced by the SRES A1B and E1 scenarios. We find that a substantial proportion of the grounding line in West Antarctica retreats, however the total sea level rise is less than 50 mm by 2100, and less than 100 mm by 2200. The lion's share of the mass loss is attributed to Pine Island Glacier, while its immediate neighbor Thwaites Glacier does not retreat until the end of the simulations.
NASA Astrophysics Data System (ADS)
Schaal, Kevin; Bauer, Andreas; Chandrashekar, Praveen; Pakmor, Rüdiger; Klingenberg, Christian; Springel, Volker
2015-11-01
Solving the Euler equations of ideal hydrodynamics as accurately and efficiently as possible is a key requirement in many astrophysical simulations. It is therefore important to continuously advance the numerical methods implemented in current astrophysical codes, especially also in light of evolving computer technology, which favours certain computational approaches over others. Here we introduce the new adaptive mesh refinement (AMR) code TENET, which employs a high-order discontinuous Galerkin (DG) scheme for hydrodynamics. The Euler equations in this method are solved in a weak formulation with a polynomial basis by means of explicit Runge-Kutta time integration and Gauss-Legendre quadrature. This approach offers significant advantages over commonly employed second-order finite-volume (FV) solvers. In particular, the higher order capability renders it computationally more efficient, in the sense that the same precision can be obtained at significantly less computational cost. Also, the DG scheme inherently conserves angular momentum in regions where no limiting takes place, and it typically produces much smaller numerical diffusion and advection errors than an FV approach. A further advantage lies in a more natural handling of AMR refinement boundaries, where a fall-back to first order can be avoided. Finally, DG requires no wide stencils at high order, and offers an improved data locality and a focus on local computations, which is favourable for current and upcoming highly parallel supercomputers. We describe the formulation and implementation details of our new code, and demonstrate its performance and accuracy with a set of two- and three-dimensional test problems. The results confirm that DG schemes have a high potential for astrophysical applications.
Feature-Sensitive Tetrahedral Mesh Generation with Guaranteed Quality
Wang, Jun; Yu, Zeyun
2012-01-01
Tetrahedral meshes are being extensively used in finite element methods (FEM). This paper proposes an algorithm to generate feature-sensitive and high-quality tetrahedral meshes from an arbitrary surface mesh model. A top-down octree subdivision is conducted on the surface mesh and a set of tetrahedra are constructed using adaptive body-centered cubic (BCC) lattices. Special treatments are given to the tetrahedra near the surface such that the quality of the resulting tetrahedral mesh is provably guaranteed: the smallest dihedral angle is always greater than 5.71°. The meshes generated by our method are not only adaptive from the interior to the boundary, but also feature-sensitive on the surface with denser elements in high-curvature regions where geometric feature most likely reside. A variety of experimental results are presented to demonstrate the effectiveness and robustness of this algorithm. PMID:22328787
Adaptively resizing populations: Algorithm, analysis, and first results
NASA Technical Reports Server (NTRS)
Smith, Robert E.; Smuda, Ellen
1993-01-01
Deciding on an appropriate population size for a given Genetic Algorithm (GA) application can often be critical to the algorithm's success. Too small, and the GA can fall victim to sampling error, affecting the efficacy of its search. Too large, and the GA wastes computational resources. Although advice exists for sizing GA populations, much of this advice involves theoretical aspects that are not accessible to the novice user. An algorithm for adaptively resizing GA populations is suggested. This algorithm is based on recent theoretical developments that relate population size to schema fitness variance. The suggested algorithm is developed theoretically, and simulated with expected value equations. The algorithm is then tested on a problem where population sizing can mislead the GA. The work presented suggests that the population sizing algorithm may be a viable way to eliminate the population sizing decision from the application of GA's.
A Novel Hybrid Self-Adaptive Bat Algorithm
Fister, Iztok; Brest, Janez
2014-01-01
Nature-inspired algorithms attract many researchers worldwide for solving the hardest optimization problems. One of the newest members of this extensive family is the bat algorithm. To date, many variants of this algorithm have emerged for solving continuous as well as combinatorial problems. One of the more promising variants, a self-adaptive bat algorithm, has recently been proposed that enables a self-adaptation of its control parameters. In this paper, we have hybridized this algorithm using different DE strategies and applied these as a local search heuristics for improving the current best solution directing the swarm of a solution towards the better regions within a search space. The results of exhaustive experiments were promising and have encouraged us to invest more efforts into developing in this direction. PMID:25187904
An adaptive algorithm for low contrast infrared image enhancement
NASA Astrophysics Data System (ADS)
Liu, Sheng-dong; Peng, Cheng-yuan; Wang, Ming-jia; Wu, Zhi-guo; Liu, Jia-qi
2013-08-01
An adaptive infrared image enhancement algorithm for low contrast is proposed in this paper, to deal with the problem that conventional image enhancement algorithm is not able to effective identify the interesting region when dynamic range is large in image. This algorithm begin with the human visual perception characteristics, take account of the global adaptive image enhancement and local feature boost, not only the contrast of image is raised, but also the texture of picture is more distinct. Firstly, the global image dynamic range is adjusted from the overall, the dynamic range of original image and display grayscale form corresponding relationship, the gray scale of bright object is raised and the the gray scale of dark target is reduced at the same time, to improve the overall image contrast. Secondly, the corresponding filtering algorithm is used on the current point and its neighborhood pixels to extract image texture information, to adjust the brightness of the current point in order to enhance the local contrast of the image. The algorithm overcomes the default that the outline is easy to vague in traditional edge detection algorithm, and ensure the distinctness of texture detail in image enhancement. Lastly, we normalize the global luminance adjustment image and the local brightness adjustment image, to ensure a smooth transition of image details. A lot of experiments is made to compare the algorithm proposed in this paper with other convention image enhancement algorithm, and two groups of vague IR image are taken in experiment. Experiments show that: the contrast ratio of the picture is boosted after handled by histogram equalization algorithm, but the detail of the picture is not clear, the detail of the picture can be distinguished after handled by the Retinex algorithm. The image after deal with by self-adaptive enhancement algorithm proposed in this paper becomes clear in details, and the image contrast is markedly improved in compared with Retinex
An adaptive, lossless data compression algorithm and VLSI implementations
NASA Technical Reports Server (NTRS)
Venbrux, Jack; Zweigle, Greg; Gambles, Jody; Wiseman, Don; Miller, Warner H.; Yeh, Pen-Shu
1993-01-01
This paper first provides an overview of an adaptive, lossless, data compression algorithm originally devised by Rice in the early '70s. It then reports the development of a VLSI encoder/decoder chip set developed which implements this algorithm. A recent effort in making a space qualified version of the encoder is described along with several enhancements to the algorithm. The performance of the enhanced algorithm is compared with those from other currently available lossless compression techniques on multiple sets of test data. The results favor our implemented technique in many applications.
NASA Astrophysics Data System (ADS)
Sui, Yi; Spelt, Peter D. M.; Ding, Hang
2010-11-01
Diffuse Interface (DI) methods are employed widely for the numerical simulation of two-phase flows, even with moving contact lines. In a DI method, the interface thickness should be as thin as possible to simulate spreading phenomena under realistic flow conditions, so a fine grid is required, beyond the reach of current methods that employ a uniform grid. Here we have integrated a DI method based on a uniform mesh, to a block-based adaptive mesh refinement method, so that only the regions near the interface are resolved by a fine mesh. The performance of the present method is tested by simulations including drop deformation in shear flow, Rayleigh-Taylor instability and drop spreading on a flat surface, et al. The results show that the present method can give accurate results with much smaller computational cost, compared to the original DI method based on a uniform mesh. Based on the present method, simulation of drop spreading is carried out with Cahn number of 0.001 and the contact line region is well resolved. The flow field near the contact line, the contact line speed as well as the apparent contact angle are investigated in detail and compared with previous analytical work.
KNUPP,PATRICK
2000-12-13
We investigate a well-motivated mesh untangling objective function whose optimization automatically produces non-inverted elements when possible. Examples show the procedure is highly effective on simplicial meshes and on non-simplicial (e.g., hexahedral) meshes constructed via mapping or sweeping algorithms. The current whisker-weaving (WW) algorithm in CUBIT usually produces hexahedral meshes that are unsuitable for analyses due to inverted elements. The majority of these meshes cannot be untangled using the new objective function. The most likely source of the difficulty is poor mesh topology.
Adaptive image contrast enhancement algorithm for point-based rendering
NASA Astrophysics Data System (ADS)
Xu, Shaoping; Liu, Xiaoping P.
2015-03-01
Surgical simulation is a major application in computer graphics and virtual reality, and most of the existing work indicates that interactive real-time cutting simulation of soft tissue is a fundamental but challenging research problem in virtual surgery simulation systems. More specifically, it is difficult to achieve a fast enough graphic update rate (at least 30 Hz) on commodity PC hardware by utilizing traditional triangle-based rendering algorithms. In recent years, point-based rendering (PBR) has been shown to offer the potential to outperform the traditional triangle-based rendering in speed when it is applied to highly complex soft tissue cutting models. Nevertheless, the PBR algorithms are still limited in visual quality due to inherent contrast distortion. We propose an adaptive image contrast enhancement algorithm as a postprocessing module for PBR, providing high visual rendering quality as well as acceptable rendering efficiency. Our approach is based on a perceptible image quality technique with automatic parameter selection, resulting in a visual quality comparable to existing conventional PBR algorithms. Experimental results show that our adaptive image contrast enhancement algorithm produces encouraging results both visually and numerically compared to representative algorithms, and experiments conducted on the latest hardware demonstrate that the proposed PBR framework with the postprocessing module is superior to the conventional PBR algorithm and that the proposed contrast enhancement algorithm can be utilized in (or compatible with) various variants of the conventional PBR algorithm.
An Adaptive Hybrid Algorithm for Global Network Alignment.
Xie, Jiang; Xiang, Chaojuan; Ma, Jin; Tan, Jun; Wen, Tieqiao; Lei, Jinzhi; Nie, Qing
2016-01-01
It is challenging to obtain reliable and optimal mapping between networks for alignment algorithms when both nodal and topological structures are taken into consideration due to the underlying NP-hard problem. Here, we introduce an adaptive hybrid algorithm that combines the classical Hungarian algorithm and the Greedy algorithm (HGA) for the global alignment of biomolecular networks. With this hybrid algorithm, every pair of nodes with one in each network is first aligned based on node information (e.g., their sequence attributes) and then followed by an adaptive and convergent iteration procedure for aligning the topological connections in the networks. For four well-studied protein interaction networks, i.e., C.elegans, yeast, D.melanogaster, and human, applications of HGA lead to improved alignments in acceptable running time. The mapping between yeast and human PINs obtained by the new algorithm has the largest value of common gene ontology (GO) terms compared to those obtained by other existing algorithms, while it still has lower Mean normalized entropy (MNE) and good performances on several other measures. Overall, the adaptive HGA is effective and capable of providing good mappings between aligned networks in which the biological properties of both the nodes and the connections are important. PMID:27295633
Adaptive sensor tasking using genetic algorithms
NASA Astrophysics Data System (ADS)
Shea, Peter J.; Kirk, Joe; Welchons, Dave
2007-04-01
Today's battlefield environment contains a large number of sensors, and sensor types, onboard multiple platforms. The set of sensor types includes SAR, EO/IR, GMTI, AMTI, HSI, MSI, and video, and for each sensor type there may be multiple sensing modalities to select from. In an attempt to maximize sensor performance, today's sensors employ either static tasking approaches or require an operator to manually change sensor tasking operations. In a highly dynamic environment this leads to a situation whereby the sensors become less effective as the sensing environments deviates from the assumed conditions. Through a Phase I SBIR effort we developed a system architecture and a common tasking approach for solving the sensor tasking problem for a multiple sensor mix. As part of our sensor tasking effort we developed a genetic algorithm based task scheduling approach and demonstrated the ability to automatically task and schedule sensors in an end-to-end closed loop simulation. Our approach allows for multiple sensors as well as system and sensor constraints. This provides a solid foundation for our future efforts including incorporation of other sensor types. This paper will describe our approach for scheduling using genetic algorithms to solve the sensor tasking problem in the presence of resource constraints and required task linkage. We will conclude with a discussion of results for a sample problem and of the path forward.
Locally-adaptive and memetic evolutionary pattern search algorithms.
Hart, William E
2003-01-01
Recent convergence analyses of evolutionary pattern search algorithms (EPSAs) have shown that these methods have a weak stationary point convergence theory for a broad class of unconstrained and linearly constrained problems. This paper describes how the convergence theory for EPSAs can be adapted to allow each individual in a population to have its own mutation step length (similar to the design of evolutionary programing and evolution strategies algorithms). These are called locally-adaptive EPSAs (LA-EPSAs) since each individual's mutation step length is independently adapted in different local neighborhoods. The paper also describes a variety of standard formulations of evolutionary algorithms that can be used for LA-EPSAs. Further, it is shown how this convergence theory can be applied to memetic EPSAs, which use local search to refine points within each iteration. PMID:12804096
NASA Astrophysics Data System (ADS)
Pantano, Carlos
2005-11-01
We describe a hybrid finite difference method for large-eddy simulation (LES) of compressible flows with a low-numerical dissipation scheme and structured adaptive mesh refinement (SAMR). Numerical experiments and validation calculations are presented including a turbulent jet and the strongly shock-driven mixing of a Richtmyer-Meshkov instability. The approach is a conservative flux-based SAMR formulation and as such, it utilizes refinement to computational advantage. The numerical method for the resolved scale terms encompasses the cases of scheme alternation and internal mesh interfaces resulting from SAMR. An explicit centered scheme that is consistent with a skew-symmetric finite difference formulation is used in turbulent flow regions while a weighted essentially non-oscillatory (WENO) scheme is employed to capture shocks. The subgrid stresses and transports are calculated by means of the streched-vortex model, Misra & Pullin (1997)
NASA Astrophysics Data System (ADS)
Pantano, C.; Deiterding, R.; Hill, D. J.; Pullin, D. I.
2007-01-01
We present a methodology for the large-eddy simulation of compressible flows with a low-numerical dissipation scheme and structured adaptive mesh refinement (SAMR). A description of a conservative, flux-based hybrid numerical method that uses both centered finite-difference and a weighted essentially non-oscillatory (WENO) scheme is given, encompassing the cases of scheme alternation and internal mesh interfaces resulting from SAMR. In this method, the centered scheme is used in turbulent flow regions while WENO is employed to capture shocks. One-, two- and three-dimensional numerical experiments and example simulations are presented including homogeneous shock-free turbulence, a turbulent jet and the strongly shock-driven mixing of a Richtmyer-Meshkov instability.
A local anisotropic adaptive algorithm for the solution of low-Mach transient combustion problems
NASA Astrophysics Data System (ADS)
Carpio, Jaime; Prieto, Juan Luis; Vera, Marcos
2016-02-01
A novel numerical algorithm for the simulation of transient combustion problems at low Mach and moderately high Reynolds numbers is presented. These problems are often characterized by the existence of a large disparity of length and time scales, resulting in the development of directional flow features, such as slender jets, boundary layers, mixing layers, or flame fronts. This makes local anisotropic adaptive techniques quite advantageous computationally. In this work we propose a local anisotropic refinement algorithm using, for the spatial discretization, unstructured triangular elements in a finite element framework. For the time integration, the problem is formulated in the context of semi-Lagrangian schemes, introducing the semi-Lagrange-Galerkin (SLG) technique as a better alternative to the classical semi-Lagrangian (SL) interpolation. The good performance of the numerical algorithm is illustrated by solving a canonical laminar combustion problem: the flame/vortex interaction. First, a premixed methane-air flame/vortex interaction with simplified transport and chemistry description (Test I) is considered. Results are found to be in excellent agreement with those in the literature, proving the superior performance of the SLG scheme when compared with the classical SL technique, and the advantage of using anisotropic adaptation instead of uniform meshes or isotropic mesh refinement. As a more realistic example, we then conduct simulations of non-premixed hydrogen-air flame/vortex interactions (Test II) using a more complex combustion model which involves state-of-the-art transport and chemical kinetics. In addition to the analysis of the numerical features, this second example allows us to perform a satisfactory comparison with experimental visualizations taken from the literature.
Adaptive learning algorithms for vibration energy harvesting
NASA Astrophysics Data System (ADS)
Ward, John K.; Behrens, Sam
2008-06-01
By scavenging energy from their local environment, portable electronic devices such as MEMS devices, mobile phones, radios and wireless sensors can achieve greater run times with potentially lower weight. Vibration energy harvesting is one such approach where energy from parasitic vibrations can be converted into electrical energy through the use of piezoelectric and electromagnetic transducers. Parasitic vibrations come from a range of sources such as human movement, wind, seismic forces and traffic. Existing approaches to vibration energy harvesting typically utilize a rectifier circuit, which is tuned to the resonant frequency of the harvesting structure and the dominant frequency of vibration. We have developed a novel approach to vibration energy harvesting, including adaptation to non-periodic vibrations so as to extract the maximum amount of vibration energy available. Experimental results of an experimental apparatus using an off-the-shelf transducer (i.e. speaker coil) show mechanical vibration to electrical energy conversion efficiencies of 27-34%.
Adaptive Multigrid Algorithm for the Lattice Wilson-Dirac Operator
Babich, R.; Brower, R. C.; Rebbi, C.; Brannick, J.; Clark, M. A.; Manteuffel, T. A.; McCormick, S. F.; Osborn, J. C.
2010-11-12
We present an adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD. The key components leading to the success of our proposed algorithm are the use of an adaptive projection onto coarse grids that preserves the near null space of the system matrix together with a simplified form of the correction based on the so-called {gamma}{sub 5}-Hermitian symmetry of the Dirac operator. We demonstrate that the algorithm nearly eliminates critical slowing down in the chiral limit and that it has weak dependence on the lattice volume.
Adaptive multigrid algorithm for the lattice Wilson-Dirac operator.
Babich, R; Brannick, J; Brower, R C; Clark, M A; Manteuffel, T A; McCormick, S F; Osborn, J C; Rebbi, C
2010-11-12
We present an adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD. The key components leading to the success of our proposed algorithm are the use of an adaptive projection onto coarse grids that preserves the near null space of the system matrix together with a simplified form of the correction based on the so-called γ5-Hermitian symmetry of the Dirac operator. We demonstrate that the algorithm nearly eliminates critical slowing down in the chiral limit and that it has weak dependence on the lattice volume. PMID:21231217
Adaptive NUC algorithm for uncooled IRFPA based on neural networks
NASA Astrophysics Data System (ADS)
Liu, Ziji; Jiang, Yadong; Lv, Jian; Zhu, Hongbin
2010-10-01
With developments in uncooled infrared plane array (UFPA) technology, many new advanced uncooled infrared sensors are used in defensive weapons, scientific research, industry and commercial applications. A major difference in imaging techniques between infrared IRFPA imaging system and a visible CCD camera is that, IRFPA need nonuniformity correction and dead pixel compensation, we usually called it infrared image pre-processing. Two-point or multi-point correction algorithms based on calibration commonly used may correct the non-uniformity of IRFPAs, but they are limited by pixel linearity and instability. Therefore, adaptive non-uniformity correction techniques are developed. Two of these adaptive non-uniformity correction algorithms are mostly discussed, one is based on temporal high-pass filter, and another is based on neural network. In this paper, a new NUC algorithm based on improved neural networks is introduced, and involves the compare result between improved neural networks and other adaptive correction techniques. A lot of different will discussed in different angle, like correction effects, calculation efficiency, hardware implementation and so on. According to the result and discussion, it could be concluding that the adaptive algorithm offers improved performance compared to traditional calibration mode techniques. This new algorithm not only provides better sensitivity, but also increases the system dynamic range. As the sensor application expended, it will be very useful in future infrared imaging systems.
Extended TA Algorithm for Adapting a Situation Ontology
NASA Astrophysics Data System (ADS)
Zweigle, Oliver; Häussermann, Kai; Käppeler, Uwe-Philipp; Levi, Paul
In this work we introduce an improved version of a learning algorithm for the automatic adaption of a situation ontology (TAA) [1] which extends the basic principle of the learning algorithm. The approach bases on the assumption of uncertain data and includes elements from the domain of Bayesian Networks and Machine Learning. It is embedded into the cluster of excellence Nexus at the University of Stuttgart which has the aim to build a distributed context aware system for sharing context data.
An adaptive algorithm for modifying hyperellipsoidal decision surfaces
Kelly, P.M.; Hush, D.R.; White, J.M.
1992-05-01
The LVQ algorithm is a common method which allows a set of reference vectors for a distance classifier to adapt to a given training set. We have developed a similar learning algorithm, LVQ-MM, which manipulates hyperellipsoidal cluster boundaries as opposed to reference vectors. Regions of the input feature space are first enclosed by ellipsoidal decision boundaries, and then these boundaries are iteratively modified to reduce classification error. Results obtained by classifying the Iris data set are provided.
An adaptive algorithm for modifying hyperellipsoidal decision surfaces
Kelly, P.M.; Hush, D.R. . Dept. of Electrical and Computer Engineering); White, J.M. )
1992-01-01
The LVQ algorithm is a common method which allows a set of reference vectors for a distance classifier to adapt to a given training set. We have developed a similar learning algorithm, LVQ-MM, which manipulates hyperellipsoidal cluster boundaries as opposed to reference vectors. Regions of the input feature space are first enclosed by ellipsoidal decision boundaries, and then these boundaries are iteratively modified to reduce classification error. Results obtained by classifying the Iris data set are provided.
Adaptive Mesh Refinement Cosmological Simulations of Cosmic Rays in Galaxy Clusters
NASA Astrophysics Data System (ADS)
Skillman, Samuel William
2013-12-01
Galaxy clusters are unique astrophysical laboratories that contain many thermal and non-thermal phenomena. In particular, they are hosts to cosmic shocks, which propagate through the intracluster medium as a by-product of structure formation. It is believed that at these shock fronts, magnetic field inhomogeneities in a compressing flow may lead to the acceleration of cosmic ray electrons and ions. These relativistic particles decay and radiate through a variety of mechanisms, and have observational signatures in radio, hard X-ray, and Gamma-ray wavelengths. We begin this dissertation by developing a method to find shocks in cosmological adaptive mesh refinement simulations of structure formation. After describing the evolution of shock properties through cosmic time, we make estimates for the amount of kinetic energy processed and the total number of cosmic ray protons that could be accelerated at these shocks. We then use this method of shock finding and a model for the acceleration of and radio synchrotron emission from cosmic ray electrons to estimate the radio emission properties in large scale structures. By examining the time-evolution of the radio emission with respect to the X-ray emission during a galaxy cluster merger, we find that the relative timing of the enhancements in each are important consequences of the shock dynamics. By calculating the radio emission expected from a given mass galaxy cluster, we make estimates for future large-area radio surveys. Next, we use a state-of-the-art magnetohydrodynamic simulation to follow the electron acceleration in a massive merging galaxy cluster. We use the magnetic field information to calculate not only the total radio emission, but also create radio polarization maps that are compared to recent observations. We find that we can naturally reproduce Mpc-scale radio emission that resemble many of the known double radio relic systems. Finally, motivated by our previous studies, we develop and introduce a
Lipnikov, Konstantin; Agouzal, Abdellatif; Vassilevski, Yuri
2009-01-01
We present a new technology for generating meshes minimizing the interpolation and discretization errors or their gradients. The key element of this methodology is construction of a space metric from edge-based error estimates. For a mesh with N{sub h} triangles, the error is proportional to N{sub h}{sup -1} and the gradient of error is proportional to N{sub h}{sup -1/2} which are optimal asymptotics. The methodology is verified with numerical experiments.
Data-adaptive algorithms for calling alleles in repeat polymorphisms.
Stoughton, R; Bumgarner, R; Frederick, W J; McIndoe, R A
1997-01-01
Data-adaptive algorithms are presented for separating overlapping signatures of heterozygotic allele pairs in electrophoresis data. Application is demonstrated for human microsatellite CA-repeat polymorphisms in LiCor 4000 and ABI 373 data. The algorithms allow overlapping alleles to be called correctly in almost every case where a trained observer could do so, and provide a fast automated objective alternative to human reading of the gels. The algorithm also supplies an indication of confidence level which can be used to flag marginal cases for verification by eye, or as input to later stages of statistical analysis. PMID:9059812
McGhee, J.M.; Roberts, R.M.; Morel, J.E.
1997-06-01
A spherical harmonics research code (DANTE) has been developed which is compatible with parallel computer architectures. DANTE provides 3-D, multi-material, deterministic, transport capabilities using an arbitrary finite element mesh. The linearized Boltzmann transport equation is solved in a second order self-adjoint form utilizing a Galerkin finite element spatial differencing scheme. The core solver utilizes a preconditioned conjugate gradient algorithm. Other distinguishing features of the code include options for discrete-ordinates and simplified spherical harmonics angular differencing, an exact Marshak boundary treatment for arbitrarily oriented boundary faces, in-line matrix construction techniques to minimize memory consumption, and an effective diffusion based preconditioner for scattering dominated problems. Algorithm efficiency is demonstrated for a massively parallel SIMD architecture (CM-5), and compatibility with MPP multiprocessor platforms or workstation clusters is anticipated.
Adaptive clustering algorithm for community detection in complex networks.
Ye, Zhenqing; Hu, Songnian; Yu, Jun
2008-10-01
Community structure is common in various real-world networks; methods or algorithms for detecting such communities in complex networks have attracted great attention in recent years. We introduced a different adaptive clustering algorithm capable of extracting modules from complex networks with considerable accuracy and robustness. In this approach, each node in a network acts as an autonomous agent demonstrating flocking behavior where vertices always travel toward their preferable neighboring groups. An optimal modular structure can emerge from a collection of these active nodes during a self-organization process where vertices constantly regroup. In addition, we show that our algorithm appears advantageous over other competing methods (e.g., the Newman-fast algorithm) through intensive evaluation. The applications in three real-world networks demonstrate the superiority of our algorithm to find communities that are parallel with the appropriate organization in reality. PMID:18999501
The Kernel Adaptive Autoregressive-Moving-Average Algorithm.
Li, Kan; Príncipe, José C
2016-02-01
In this paper, we present a novel kernel adaptive recurrent filtering algorithm based on the autoregressive-moving-average (ARMA) model, which is trained with recurrent stochastic gradient descent in the reproducing kernel Hilbert spaces. This kernelized recurrent system, the kernel adaptive ARMA (KAARMA) algorithm, brings together the theories of adaptive signal processing and recurrent neural networks (RNNs), extending the current theory of kernel adaptive filtering (KAF) using the representer theorem to include feedback. Compared with classical feedforward KAF methods, the KAARMA algorithm provides general nonlinear solutions for complex dynamical systems in a state-space representation, with a deferred teacher signal, by propagating forward the hidden states. We demonstrate its capabilities to provide exact solutions with compact structures by solving a set of benchmark nondeterministic polynomial-complete problems involving grammatical inference. Simulation results show that the KAARMA algorithm outperforms equivalent input-space recurrent architectures using first- and second-order RNNs, demonstrating its potential as an effective learning solution for the identification and synthesis of deterministic finite automata. PMID:25935049
An Adaptive Tradeoff Algorithm for Multi-issue SLA Negotiation
NASA Astrophysics Data System (ADS)
Son, Seokho; Sim, Kwang Mong
Since participants in a Cloud may be independent bodies, mechanisms are necessary for resolving different preferences in leasing Cloud services. Whereas there are currently mechanisms that support service-level agreement negotiation, there is little or no negotiation support for concurrent price and timeslot for Cloud service reservations. For the concurrent price and timeslot negotiation, a tradeoff algorithm to generate and evaluate a proposal which consists of price and timeslot proposal is necessary. The contribution of this work is thus to design an adaptive tradeoff algorithm for multi-issue negotiation mechanism. The tradeoff algorithm referred to as "adaptive burst mode" is especially designed to increase negotiation speed and total utility and to reduce computational load by adaptively generating concurrent set of proposals. The empirical results obtained from simulations carried out using a testbed suggest that due to the concurrent price and timeslot negotiation mechanism with adaptive tradeoff algorithm: 1) both agents achieve the best performance in terms of negotiation speed and utility; 2) the number of evaluations of each proposal is comparatively lower than previous scheme (burst-N).
NASA Astrophysics Data System (ADS)
Weller, Hilary; Browne, Philip; Budd, Chris; Cullen, Mike
2016-03-01
An equation of Monge-Ampère type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport generates meshes that keep the same connectivity as the original mesh, making them suitable for r-adaptive simulations, in which the equations of motion can be solved in a moving frame of reference in order to avoid mapping the solution between old and new meshes and to avoid load balancing problems on parallel computers. The semi-implicit solution of the Monge-Ampère type equation involves a new linearisation of the Hessian term, and exponential maps are used to map from old to new meshes on the sphere. The determinant of the Hessian is evaluated as the change in volume between old and new mesh cells, rather than using numerical approximations to the gradients. OT meshes are generated to compare with centroidal Voronoi tessellations on the sphere and are found to have advantages and disadvantages; OT equidistribution is more accurate, the number of iterations to convergence is independent of the mesh size, face skewness is reduced and the connectivity does not change. However anisotropy is higher and the OT meshes are non-orthogonal. It is shown that optimal transport on the sphere leads to meshes that do not tangle. However, tangling can be introduced by numerical errors in calculating the gradient of the mesh potential. Methods for alleviating this problem are explored. Finally, OT meshes are generated using observed precipitation as a monitor function, in order to demonstrate the potential power of the technique.
An Adaptive Immune Genetic Algorithm for Edge Detection
NASA Astrophysics Data System (ADS)
Li, Ying; Bai, Bendu; Zhang, Yanning
An adaptive immune genetic algorithm (AIGA) based on cost minimization technique method for edge detection is proposed. The proposed AIGA recommends the use of adaptive probabilities of crossover, mutation and immune operation, and a geometric annealing schedule in immune operator to realize the twin goals of maintaining diversity in the population and sustaining the fast convergence rate in solving the complex problems such as edge detection. Furthermore, AIGA can effectively exploit some prior knowledge and information of the local edge structure in the edge image to make vaccines, which results in much better local search ability of AIGA than that of the canonical genetic algorithm. Experimental results on gray-scale images show the proposed algorithm perform well in terms of quality of the final edge image, rate of convergence and robustness to noise.
Flight data processing with the F-8 adaptive algorithm
NASA Technical Reports Server (NTRS)
Hartmann, G.; Stein, G.; Petersen, K.
1977-01-01
An explicit adaptive control algorithm based on maximum likelihood estimation of parameters has been designed for NASA's DFBW F-8 aircraft. To avoid iterative calculations, the algorithm uses parallel channels of Kalman filters operating at fixed locations in parameter space. This algorithm has been implemented in NASA/DFRC's Remotely Augmented Vehicle (RAV) facility. Real-time sensor outputs (rate gyro, accelerometer and surface position) are telemetered to a ground computer which sends new gain values to an on-board system. Ground test data and flight records were used to establish design values of noise statistics and to verify the ground-based adaptive software. The software and its performance evaluation based on flight data are described
A new adaptive GMRES algorithm for achieving high accuracy
Sosonkina, M.; Watson, L.T.; Kapania, R.K.; Walker, H.F.
1996-12-31
GMRES(k) is widely used for solving nonsymmetric linear systems. However, it is inadequate either when it converges only for k close to the problem size or when numerical error in the modified Gram-Schmidt process used in the GMRES orthogonalization phase dramatically affects the algorithm performance. An adaptive version of GMRES (k) which tunes the restart value k based on criteria estimating the GMRES convergence rate for the given problem is proposed here. The essence of the adaptive GMRES strategy is to adapt the parameter k to the problem, similar in spirit to how a variable order ODE algorithm tunes the order k. With FORTRAN 90, which provides pointers and dynamic memory management, dealing with the variable storage requirements implied by varying k is not too difficult. The parameter k can be both increased and decreased-an increase-only strategy is described next followed by pseudocode.
Adaptive process control using fuzzy logic and genetic algorithms
NASA Technical Reports Server (NTRS)
Karr, C. L.
1993-01-01
Researchers at the U.S. Bureau of Mines have developed adaptive process control systems in which genetic algorithms (GA's) are used to augment fuzzy logic controllers (FLC's). GA's are search algorithms that rapidly locate near-optimum solutions to a wide spectrum of problems by modeling the search procedures of natural genetics. FLC's are rule based systems that efficiently manipulate a problem environment by modeling the 'rule-of-thumb' strategy used in human decision making. Together, GA's and FLC's possess the capabilities necessary to produce powerful, efficient, and robust adaptive control systems. To perform efficiently, such control systems require a control element to manipulate the problem environment, and a learning element to adjust to the changes in the problem environment. Details of an overall adaptive control system are discussed. A specific laboratory acid-base pH system is used to demonstrate the ideas presented.
Adaptive Process Control with Fuzzy Logic and Genetic Algorithms
NASA Technical Reports Server (NTRS)
Karr, C. L.
1993-01-01
Researchers at the U.S. Bureau of Mines have developed adaptive process control systems in which genetic algorithms (GA's) are used to augment fuzzy logic controllers (FLC's). GA's are search algorithms that rapidly locate near-optimum solutions to a wide spectrum of problems by modeling the search procedures of natural genetics. FLC's are rule based systems that efficiently manipulate a problem environment by modeling the 'rule-of-thumb' strategy used in human decision-making. Together, GA's and FLC's possess the capabilities necessary to produce powerful, efficient, and robust adaptive control systems. To perform efficiently, such control systems require a control element to manipulate the problem environment, an analysis element to recognize changes in the problem environment, and a learning element to adjust to the changes in the problem environment. Details of an overall adaptive control system are discussed. A specific laboratory acid-base pH system is used to demonstrate the ideas presented.
An interactive adaptive remeshing algorithm for the two-dimensional Euler equations
NASA Technical Reports Server (NTRS)
Slack, David C.; Walters, Robert W.; Lohner, R.
1990-01-01
An interactive adaptive remeshing algorithm utilizing a frontal grid generator and a variety of time integration schemes for the two-dimensional Euler equations on unstructured meshes is presented. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. The time integration methods available include: an explicit four stage Runge-Kutta and a fully implicit LU decomposition. A cell-centered finite volume upwind scheme utilizing Roe's approximate Riemann solver is developed. To obtain higher order accurate results a monotone linear reconstruction procedure proposed by Barth is utilized. Results for flow over a transonic circular arc and flow through a supersonic nozzle are examined.
NASA Astrophysics Data System (ADS)
Wilson, C. R.; Kramer, S. C.; Collins, G. S.
2010-12-01
Linear wave models cannot reproduce the highly nonlinear generation mechanisms required to accurately predict the consequences of landslide-generated tsunamis. Models based on the nonlinear Navier-Stokes equations can simulate complex landslide-water interactions at realistic scales; however, the computing power required for such a simulation can be prohibitively high for large domains with realistic bathymetries. The variable resolution available with the use of unstructured adaptive meshes allows larger domains to be modeled at the same resolution for a lower computational cost than on structured meshes; they are also better at representing complex geometries and bathymetries. However, unstructured meshes introduce extra numerical challenges requiring the use of novel interface preservation techniques coupled with velocity-pressure discretisations that ensure the conservation and boundedness of all materials in the simulation. In this study we describe some of the challenges encountered extending the finite element, finite volume multiple-material fluid dynamics model Fluidity to large-scale landslide-generated tsunami simulations. In particular, we focus on the ability of the model to preserve the balance between the buoyancy and pressure gradient forces. Failure to discretely satisfy this relationship is shown to result in spurious waves that contaminate any physical tsunami signal. However, ensuring that balance is preserved in a computationally efficient manner imposes extra constraints on the dynamic mesh optimisation process. Incorporating these restrictions allows us to validate our model against multi-scale experimental simulations of landslide generated tsunami (see figure). Experimental (top, taken from Di Risio et. al. 2009, doi:10.1029/2008JC004858) and equivalent numerical simulation (bottom) of a subaerial landslide impacting into water. In the experiment the 80cm long landslide produces waves of amplitude 1-2cm around a 9m diameter island in a 50x
Adaptive Flocking of Robot Swarms: Algorithms and Properties
NASA Astrophysics Data System (ADS)
Lee, Geunho; Chong, Nak Young
This paper presents a distributed approach for adaptive flocking of swarms of mobile robots that enables to navigate autonomously in complex environments populated with obstacles. Based on the observation of the swimming behavior of a school of fish, we propose an integrated algorithm that allows a swarm of robots to navigate in a coordinated manner, split into multiple swarms, or merge with other swarms according to the environment conditions. We prove the convergence of the proposed algorithm using Lyapunov stability theory. We also verify the effectiveness of the algorithm through extensive simulations, where a swarm of robots repeats the process of splitting and merging while passing around multiple stationary and moving obstacles. The simulation results show that the proposed algorithm is scalable, and robust to variations in the sensing capability of individual robots.
Mesh Quality Improvement Toolkit
Energy Science and Technology Software Center (ESTSC)
2002-11-15
MESQUITE is a linkable software library to be used by simulation and mesh generation tools to improve the quality of meshes. Mesh quality is improved by node movement and/or local topological modifications. Various aspects of mesh quality such as smoothness, element shape, size, and orientation are controlled by choosing the appropriate mesh qualtiy metric, and objective function tempate, and a numerical optimization solver to optimize the quality of meshes, MESQUITE uses the TSTT mesh interfacemore » specification to provide an interoperable toolkit that can be used by applications which adopt the standard. A flexible code design makes it easy for meshing researchers to add additional mesh quality metrics, templates, and solvers to develop new quality improvement algorithms by making use of the MESQUITE infrastructure.« less
Christon, M.; Hardin, D.; Compton, J.; Zosel, M.
1994-08-29
Building complex meshes for large-scale numerical simulations presents immense difficulties in exploiting high-performance computers. Industry and research leaders will describe the current state of the art for generating meshes for such large scientific problems. This will be followed by a panel and general audience discussion of the algorithmic and architectural issues surrounding the generation of meshes with10{sup 7} to 10{sup 9} grid points. (Note: The terms ``mesh`` and ``grid`` are used interchangeably in the literature.)
NASA Astrophysics Data System (ADS)
Ghattas, O.; Burstedde, C.; Stadler, G.; Wilcox, L. C.; Tu, T.; Issac, T.; Gurnis, M.; Alisic, L.; Tan, E.; Zhong, S.
2009-12-01
Many problems in solid earth geophysics are characterized by dynamics occurring on a wide range of length and time scales, placing the solution of the governing partial differential equations (PDEs) for such problems among the grand challenges of computational geophysics. One approach to overcoming the tyranny of scales is adaptive mesh refinement (AMR), which locally and dynamically adapts the mesh to resolve spatio-temporal scales and features of interest. For example, we are interested in modeling global mantle convection with nonlinear rheology and kilometer-scale resolution at faulted plate boundaries. Another problem of interest is modeling the dynamics of polar ice sheets with fine resolution in the vicinity of stick-slip transitions. Geophysical inverse problems characterized by a wide range of medium properties can also benefit from AMR as the earth model is updated. While AMR promises to help overcome the challenges inherent in modeling multiscale problems, the benefits are difficult to achieve in practice, particularly on petascale computers that are essential for frontier problems. Due to the complex dynamic data structures and communication patterns, and frequent data exchange and redistribution, scaling dynamic AMR to tens of thousands of processors has long been considered a challenge. Another difficulty is extending parallel AMR techniques to high-order-accurate, complex-geometry-conforming finite element methods that are favored for many classes of solid earth geophysical problems. Here, we present the ALPS (Adaptive Large-scale Parallel Simulations) framework for parallel adaptive solution of PDEs. ALPS includes the octor and p4est libraries for parallel dynamic mesh adaptivity on single-octree-based and forest-of-octree-based geometries, respectively, and the mangll library for arbitrary-order hexahedral continuous and discontinuous finite/spectral element discretizations on general multi-octree geometries. ALPS has been shown to scale well
An adaptive grid algorithm for one-dimensional nonlinear equations
NASA Technical Reports Server (NTRS)
Gutierrez, William E.; Hills, Richard G.
1990-01-01
Richards' equation, which models the flow of liquid through unsaturated porous media, is highly nonlinear and difficult to solve. Step gradients in the field variables require the use of fine grids and small time step sizes. The numerical instabilities caused by the nonlinearities often require the use of iterative methods such as Picard or Newton interation. These difficulties result in large CPU requirements in solving Richards equation. With this in mind, adaptive and multigrid methods are investigated for use with nonlinear equations such as Richards' equation. Attention is focused on one-dimensional transient problems. To investigate the use of multigrid and adaptive grid methods, a series of problems are studied. First, a multigrid program is developed and used to solve an ordinary differential equation, demonstrating the efficiency with which low and high frequency errors are smoothed out. The multigrid algorithm and an adaptive grid algorithm is used to solve one-dimensional transient partial differential equations, such as the diffusive and convective-diffusion equations. The performance of these programs are compared to that of the Gauss-Seidel and tridiagonal methods. The adaptive and multigrid schemes outperformed the Gauss-Seidel algorithm, but were not as fast as the tridiagonal method. The adaptive grid scheme solved the problems slightly faster than the multigrid method. To solve nonlinear problems, Picard iterations are introduced into the adaptive grid and tridiagonal methods. Burgers' equation is used as a test problem for the two algorithms. Both methods obtain solutions of comparable accuracy for similar time increments. For the Burgers' equation, the adaptive grid method finds the solution approximately three times faster than the tridiagonal method. Finally, both schemes are used to solve the water content formulation of the Richards' equation. For this problem, the adaptive grid method obtains a more accurate solution in fewer work units and
NASA Technical Reports Server (NTRS)
Barth, Timothy J.; Kutler, Paul (Technical Monitor)
1998-01-01
Several stabilized demoralization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin demoralization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS, and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobean linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Discrete maximum principle theory will be presented for general finite volume approximations on unstructured meshes. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc, will. be addressed as needed.
Adaptive sensor array algorithm for structural health monitoring of helmet
NASA Astrophysics Data System (ADS)
Zou, Xiaotian; Tian, Ye; Wu, Nan; Sun, Kai; Wang, Xingwei
2011-04-01
The adaptive neural network is a standard technique used in nonlinear system estimation and learning applications for dynamic models. In this paper, we introduced an adaptive sensor fusion algorithm for a helmet structure health monitoring system. The helmet structure health monitoring system is used to study the effects of ballistic/blast events on the helmet and human skull. Installed inside the helmet system, there is an optical fiber pressure sensors array. After implementing the adaptive estimation algorithm into helmet system, a dynamic model for the sensor array has been developed. The dynamic response characteristics of the sensor network are estimated from the pressure data by applying an adaptive control algorithm using artificial neural network. With the estimated parameters and position data from the dynamic model, the pressure distribution of the whole helmet can be calculated following the Bazier Surface interpolation method. The distribution pattern inside the helmet will be very helpful for improving helmet design to provide better protection to soldiers from head injuries.
A GPU accelerated moving mesh correspondence algorithm with applications to RV segmentation.
Punithakumar, Kumaradevan; Noga, Michelle; Boulanger, Pierre
2015-08-01
This study proposes a parallel nonrigid registration algorithm to obtain point correspondence between a sequence of images. Several recent studies have shown that computation of point correspondence is an excellent way to delineate organs from a sequence of images, for example, delineation of cardiac right ventricle (RV) from a series of magnetic resonance (MR) images. However, nonrigid registration algorithms involve optimization of similarity functions, and are therefore, computationally expensive. We propose Graphics Processing Unit (GPU) computing to accelerate the algorithm. The proposed approach consists of two parallelization components: 1) parallel Compute Unified Device Architecture (CUDA) version of the non-rigid registration algorithm; and 2) application of an image concatenation approach to further parallelize the algorithm. The proposed approach was evaluated over a data set of 16 subjects and took an average of 4.36 seconds to segment a sequence of 19 MR images, a significant performance improvement over serial image registration approach. PMID:26737222
Estimating meme fitness in adaptive memetic algorithms for combinatorial problems.
Smith, J E
2012-01-01
Among the most promising and active research areas in heuristic optimisation is the field of adaptive memetic algorithms (AMAs). These gain much of their reported robustness by adapting the probability with which each of a set of local improvement operators is applied, according to an estimate of their current value to the search process. This paper addresses the issue of how the current value should be estimated. Assuming the estimate occurs over several applications of a meme, we consider whether the extreme or mean improvements should be used, and whether this aggregation should be global, or local to some part of the solution space. To investigate these issues, we use the well-established COMA framework that coevolves the specification of a population of memes (representing different local search algorithms) alongside a population of candidate solutions to the problem at hand. Two very different memetic algorithms are considered: the first using adaptive operator pursuit to adjust the probabilities of applying a fixed set of memes, and a second which applies genetic operators to dynamically adapt and create memes and their functional definitions. For the latter, especially on combinatorial problems, credit assignment mechanisms based on historical records, or on notions of landscape locality, will have limited application, and it is necessary to estimate the value of a meme via some form of sampling. The results on a set of binary encoded combinatorial problems show that both methods are very effective, and that for some problems it is necessary to use thousands of variables in order to tease apart the differences between different reward schemes. However, for both memetic algorithms, a significant pattern emerges that reward based on mean improvement is better than that based on extreme improvement. This contradicts recent findings from adapting the parameters of operators involved in global evolutionary search. The results also show that local reward schemes
NASA Astrophysics Data System (ADS)
Cheng, Sheng-Yi; Liu, Wen-Jin; Chen, Shan-Qiu; Dong, Li-Zhi; Yang, Ping; Xu, Bing
2015-08-01
Among all kinds of wavefront control algorithms in adaptive optics systems, the direct gradient wavefront control algorithm is the most widespread and common method. This control algorithm obtains the actuator voltages directly from wavefront slopes through pre-measuring the relational matrix between deformable mirror actuators and Hartmann wavefront sensor with perfect real-time characteristic and stability. However, with increasing the number of sub-apertures in wavefront sensor and deformable mirror actuators of adaptive optics systems, the matrix operation in direct gradient algorithm takes too much time, which becomes a major factor influencing control effect of adaptive optics systems. In this paper we apply an iterative wavefront control algorithm to high-resolution adaptive optics systems, in which the voltages of each actuator are obtained through iteration arithmetic, which gains great advantage in calculation and storage. For AO system with thousands of actuators, the computational complexity estimate is about O(n2) ˜ O(n3) in direct gradient wavefront control algorithm, while the computational complexity estimate in iterative wavefront control algorithm is about O(n) ˜ (O(n)3/2), in which n is the number of actuators of AO system. And the more the numbers of sub-apertures and deformable mirror actuators, the more significant advantage the iterative wavefront control algorithm exhibits. Project supported by the National Key Scientific and Research Equipment Development Project of China (Grant No. ZDYZ2013-2), the National Natural Science Foundation of China (Grant No. 11173008), and the Sichuan Provincial Outstanding Youth Academic Technology Leaders Program, China (Grant No. 2012JQ0012).
Efficient implementation of the adaptive scale pixel decomposition algorithm
NASA Astrophysics Data System (ADS)
Zhang, L.; Bhatnagar, S.; Rau, U.; Zhang, M.
2016-08-01
Context. Most popular algorithms in use to remove the effects of a telescope's point spread function (PSF) in radio astronomy are variants of the CLEAN algorithm. Most of these algorithms model the sky brightness using the delta-function basis, which results in undesired artefacts when used to image extended emission. The adaptive scale pixel decomposition (Asp-Clean) algorithm models the sky brightness on a scale-sensitive basis and thus gives a significantly better imaging performance when imaging fields that contain both resolved and unresolved emission. Aims: However, the runtime cost of Asp-Clean is higher than that of scale-insensitive algorithms. In this paper, we identify the most expensive step in the original Asp-Clean algorithm and present an efficient implementation of it, which significantly reduces the computational cost while keeping the imaging performance comparable to the original algorithm. The PSF sidelobe levels of modern wide-band telescopes are significantly reduced, allowing us to make approximations to reduce the computational cost, which in turn allows for the deconvolution of larger images on reasonable timescales. Methods: As in the original algorithm, scales in the image are estimated through function fitting. Here we introduce an analytical method to model extended emission, and a modified method for estimating the initial values used for the fitting procedure, which ultimately leads to a lower computational cost. Results: The new implementation was tested with simulated EVLA data and the imaging performance compared well with the original Asp-Clean algorithm. Tests show that the current algorithm can recover features at different scales with lower computational cost.
Fast frequency acquisition via adaptive least squares algorithm
NASA Technical Reports Server (NTRS)
Kumar, R.
1986-01-01
A new least squares algorithm is proposed and investigated for fast frequency and phase acquisition of sinusoids in the presence of noise. This algorithm is a special case of more general, adaptive parameter-estimation techniques. The advantages of the algorithms are their conceptual simplicity, flexibility and applicability to general situations. For example, the frequency to be acquired can be time varying, and the noise can be nonGaussian, nonstationary and colored. As the proposed algorithm can be made recursive in the number of observations, it is not necessary to have a priori knowledge of the received signal-to-noise ratio or to specify the measurement time. This would be required for batch processing techniques, such as the fast Fourier transform (FFT). The proposed algorithm improves the frequency estimate on a recursive basis as more and more observations are obtained. When the algorithm is applied in real time, it has the extra advantage that the observations need not be stored. The algorithm also yields a real time confidence measure as to the accuracy of the estimator.
PHURBAS: AN ADAPTIVE, LAGRANGIAN, MESHLESS, MAGNETOHYDRODYNAMICS CODE. I. ALGORITHM
Maron, Jason L.; McNally, Colin P.; Mac Low, Mordecai-Mark E-mail: cmcnally@amnh.org
2012-05-01
We present an algorithm for simulating the equations of ideal magnetohydrodynamics and other systems of differential equations on an unstructured set of points represented by sample particles. Local, third-order, least-squares, polynomial interpolations (Moving Least Squares interpolations) are calculated from the field values of neighboring particles to obtain field values and spatial derivatives at the particle position. Field values and particle positions are advanced in time with a second-order predictor-corrector scheme. The particles move with the fluid, so the time step is not limited by the Eulerian Courant-Friedrichs-Lewy condition. Full spatial adaptivity is implemented to ensure the particles fill the computational volume, which gives the algorithm substantial flexibility and power. A target resolution is specified for each point in space, with particles being added and deleted as needed to meet this target. Particle addition and deletion is based on a local void and clump detection algorithm. Dynamic artificial viscosity fields provide stability to the integration. The resulting algorithm provides a robust solution for modeling flows that require Lagrangian or adaptive discretizations to resolve. This paper derives and documents the Phurbas algorithm as implemented in Phurbas version 1.1. A following paper presents the implementation and test problem results.
Landsat ecosystem disturbance adaptive processing system (LEDAPS) algorithm description
Schmidt, Gail; Jenkerson, Calli; Masek, Jeffrey; Vermote, Eric; Gao, Feng
2013-01-01
The Landsat Ecosystem Disturbance Adaptive Processing System (LEDAPS) software was originally developed by the National Aeronautics and Space Administration–Goddard Space Flight Center and the University of Maryland to produce top-of-atmosphere reflectance from LandsatThematic Mapper and Enhanced Thematic Mapper Plus Level 1 digital numbers and to apply atmospheric corrections to generate a surface-reflectance product.The U.S. Geological Survey (USGS) has adopted the LEDAPS algorithm for producing the Landsat Surface Reflectance Climate Data Record.This report discusses the LEDAPS algorithm, which was implemented by the USGS.
A new approach to automatic quadrilateral mesh generation
Zhou, J.M.; Shao, K.R.; Zhou, K.D.; Li, L.R. )
1993-03-01
This paper presents a new methodology for automatic quadrilateral mesh generation. It is based on a novel application of the Delaunay triangulation algorithm, by which quadrilateral meshes can be generated as easily as triangular meshes for complex domains. The relative element size method (RESM) has been used for effective a priori and a posterior control of the number and distribution of elements. A new adaptive quadrilateral mesh refinement technique, which allows specified solution accuracy to be achieved with one, at most two refinement cycles, is also proposed. Its robustness is demonstrated by examples.
Solution algorithms for the two-dimensional Euler equations on unstructured meshes
NASA Technical Reports Server (NTRS)
Whitaker, D. L.; Slack, David C.; Walters, Robert W.
1990-01-01
The objective of the study was to analyze implicit techniques employed in structured grid algorithms for solving two-dimensional Euler equations and extend them to unstructured solvers in order to accelerate convergence rates. A comparison is made between nine different algorithms for both first-order and second-order accurate solutions. Higher-order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The discussion is illustrated by results for flow over a transonic circular arc.
Adaptive experiments with a multivariate Elo-type algorithm.
Doebler, Philipp; Alavash, Mohsen; Giessing, Carsten
2015-06-01
The present article introduces the multivariate Elo-type algorithm (META), which is inspired by the Elo rating system, a tool for the measurement of the performance of chess players. The META is intended for adaptive experiments with correlated traits. The relationship of the META to other existing procedures is explained, and useful variants and modifications are discussed. The META was investigated within three simulation studies. The gain in efficiency of the univariate Elo-type algorithm was compared to standard univariate procedures; the impact of using correlational information in the META was quantified; and the adaptability to learning and fatigue was investigated. Our results show that the META is a powerful tool to efficiently control task performance in a short time period and to assess correlated traits. The R code of the simulations, the implementation of the META in MATLAB, and an example of how to use the META in the context of neuroscience are provided in supplemental materials. PMID:24878597
Kelley, Mireille E; Miller, Logan E; Urban, Jillian E; Stitzel, Joel D
2015-01-01
The brain-skull interface plays an important role in the strain and pressure response of the brain due to impact. In this study, a finite element (FE) model was developed from a brain atlas, representing an adult brain, by converting each 1mm isotropic voxel into a single element of the same size using a custom code developed in MATLAB. This model includes the brain (combined cerebrum and cerebellum), cerebrospinal fluid (CSF), ventricles, and a rigid skull. A voxel-based approach to develop a FE model causes the outer surface of each part to be stair-stepped, which may affect the stress and strain measurements at interfaces between parts. To improve the interaction between the skull, CSF, and brain surfaces, a previously developed mesh smoothing algorithm based on a Laplacian non-shrinking smoothing algorithm was applied to the FE model. This algorithm not only applies smoothing to the surface of the model, but also to the interfaces between the brain, CSF, and skull, while preserving volume and element quality. Warpage, jacobian, aspect ratio, and skew were evaluated and reveal that >99% of the elements retain good element quality. Future work includes implementation of contact definitions to accurately represent the brain-skull interface and to ultimately better understand and predict head injury. PMID:25996716
Evaluation of discretization procedures for transition elements in adaptive mesh refinement
NASA Technical Reports Server (NTRS)
Park, K. C.; Levit, Itzak; Stanley, Gary M.
1991-01-01
Three transition interpolation schemes for use in h-or r-refinement have been analyzed in terms of accuracy, implementation ease and extendability. They include blending-function interpolation, displacement averaging, and strain matching at discrete points along the transition edge lines. The results suggest that the choice of matching depends strongly on the element formulations, (viz. displacement or assumed strain, etc.) and mesh refinement criteria employed, and to a lesser extent the choice of computer architecture (serial vs. parallel) and the equation solution procedures. A recommended pairing of some of the elements with the choice factors is suggested.
An adaptive-mesh finite-difference solution method for the Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Luchini, Paolo
1987-02-01
An adjustable variable-spacing grid is presented which permits the addition or deletion of single points during iterative solutions of the Navier-Stokes equations by finite difference methods. The grid is designed for application to two-dimensional steady-flow problems which can be described by partial differential equations whose second derivatives are constrained to the Laplacian operator. An explicit Navier-Stokes equations solution technique defined for use with the grid incorporates a hybrid form of the convective terms. Three methods are developed for automatic modifications of the mesh during calculations.
On some limitations of adaptive feedback measurement algorithm
NASA Astrophysics Data System (ADS)
Opalski, Leszek J.
2015-09-01
The brilliant idea of Adaptive Feedback Control Systems (AFCS) makes possible creation of highly efficient adaptive systems for estimation, identification and filtering of signals and physical processes. The research problem considered in this paper is: how performance of AFCS changes if some of the assumptions used to formulate iterative estimation algorithm are not fulfilled exactly. To limit the scope of research a particular implementation of the AFCS concept was considered, i.e. an adaptive feedback measurement system (AFMS). The iterative measurement algorithm used was derived under some idealized conditions, notably with perfect knowledge of the system model and Gaussian communication channels. The selected non-idealities of interest are non-zero mean value of noise processes and non-ideal calibration of transmission gain in the forward channel - because they are related to intrinsic non-idealities of analog building blocks, used for the AFMS implementation. The presented original analysis of the iterative measurement algorithm provides quantitative information on speed of convergence and limit behavior. The analysis should be useful for AFCS implementors in the measurement area - since the results are presented in terms of accuracy and precision of iterative measurement process.
A kernel adaptive algorithm for quaternion-valued inputs.
Paul, Thomas K; Ogunfunmi, Tokunbo
2015-10-01
The use of quaternion data can provide benefit in applications like robotics and image recognition, and particularly for performing transforms in 3-D space. Here, we describe a kernel adaptive algorithm for quaternions. A least mean square (LMS)-based method was used, resulting in the derivation of the quaternion kernel LMS (Quat-KLMS) algorithm. Deriving this algorithm required describing the idea of a quaternion reproducing kernel Hilbert space (RKHS), as well as kernel functions suitable with quaternions. A modified HR calculus for Hilbert spaces was used to find the gradient of cost functions defined on a quaternion RKHS. In addition, the use of widely linear (or augmented) filtering is proposed to improve performance. The benefit of the Quat-KLMS and widely linear forms in learning nonlinear transformations of quaternion data are illustrated with simulations. PMID:25594982
Adaptive Load-Balancing Algorithms Using Symmetric Broadcast Networks
NASA Technical Reports Server (NTRS)
Das, Sajal K.; Biswas, Rupak; Chancellor, Marisa K. (Technical Monitor)
1997-01-01
In a distributed-computing environment, it is important to ensure that the processor workloads are adequately balanced. Among numerous load-balancing algorithms, a unique approach due to Dam and Prasad defines a symmetric broadcast network (SBN) that provides a robust communication pattern among the processors in a topology-independent manner. In this paper, we propose and analyze three novel SBN-based load-balancing algorithms, and implement them on an SP2. A thorough experimental study with Poisson-distributed synthetic loads demonstrates that these algorithms are very effective in balancing system load while minimizing processor idle time. They also compare favorably with several other existing load-balancing techniques. Additional experiments performed with real data demonstrate that the SBN approach is effective in adaptive computational science and engineering applications where dynamic load balancing is extremely crucial.
A local adaptive discretization algorithm for Smoothed Particle Hydrodynamics
NASA Astrophysics Data System (ADS)
Spreng, Fabian; Schnabel, Dirk; Mueller, Alexandra; Eberhard, Peter
2014-06-01
In this paper, an extension to the Smoothed Particle Hydrodynamics (SPH) method is proposed that allows for an adaptation of the discretization level of a simulated continuum at runtime. By combining a local adaptive refinement technique with a newly developed coarsening algorithm, one is able to improve the accuracy of the simulation results while reducing the required computational cost at the same time. For this purpose, the number of particles is, on the one hand, adaptively increased in critical areas of a simulation model. Typically, these are areas that show a relatively low particle density and high gradients in stress or temperature. On the other hand, the number of SPH particles is decreased for domains with a high particle density and low gradients. Besides a brief introduction to the basic principle of the SPH discretization method, the extensions to the original formulation providing such a local adaptive refinement and coarsening of the modeled structure are presented in this paper. After having introduced its theoretical background, the applicability of the enhanced formulation, as well as the benefit gained from the adaptive model discretization, is demonstrated in the context of four different simulation scenarios focusing on solid continua. While presenting the results found for these examples, several properties of the proposed adaptive technique are discussed, e.g. the conservation of momentum as well as the existing correlation between the chosen refinement and coarsening patterns and the observed quality of the results.
Adaptive Firefly Algorithm: Parameter Analysis and its Application
Shen, Hong-Bin
2014-01-01
As a nature-inspired search algorithm, firefly algorithm (FA) has several control parameters, which may have great effects on its performance. In this study, we investigate the parameter selection and adaptation strategies in a modified firefly algorithm — adaptive firefly algorithm (AdaFa). There are three strategies in AdaFa including (1) a distance-based light absorption coefficient; (2) a gray coefficient enhancing fireflies to share difference information from attractive ones efficiently; and (3) five different dynamic strategies for the randomization parameter. Promising selections of parameters in the strategies are analyzed to guarantee the efficient performance of AdaFa. AdaFa is validated over widely used benchmark functions, and the numerical experiments and statistical tests yield useful conclusions on the strategies and the parameter selections affecting the performance of AdaFa. When applied to the real-world problem — protein tertiary structure prediction, the results demonstrated improved variants can rebuild the tertiary structure with the average root mean square deviation less than 0.4Å and 1.5Å from the native constrains with noise free and 10% Gaussian white noise. PMID:25397812
Discrete-time minimal control synthesis adaptive algorithm
NASA Astrophysics Data System (ADS)
di Bernardo, M.; di Gennaro, F.; Olm, J. M.; Santini, S.
2010-12-01
This article proposes a discrete-time Minimal Control Synthesis (MCS) algorithm for a class of single-input single-output discrete-time systems written in controllable canonical form. As it happens with the continuous-time MCS strategy, the algorithm arises from the family of hyperstability-based discrete-time model reference adaptive controllers introduced in (Landau, Y. (1979), Adaptive Control: The Model Reference Approach, New York: Marcel Dekker, Inc.) and is able to ensure tracking of the states of a given reference model with minimal knowledge about the plant. The control design shows robustness to parameter uncertainties, slow parameter variation and matched disturbances. Furthermore, it is proved that the proposed discrete-time MCS algorithm can be used to control discretised continuous-time plants with the same performance features. Contrary to previous discrete-time implementations of the continuous-time MCS algorithm, here a formal proof of asymptotic stability is given for generic n-dimensional plants in controllable canonical form. The theoretical approach is validated by means of simulation results.
Adaptive firefly algorithm: parameter analysis and its application.
Cheung, Ngaam J; Ding, Xue-Ming; Shen, Hong-Bin
2014-01-01
As a nature-inspired search algorithm, firefly algorithm (FA) has several control parameters, which may have great effects on its performance. In this study, we investigate the parameter selection and adaptation strategies in a modified firefly algorithm - adaptive firefly algorithm (AdaFa). There are three strategies in AdaFa including (1) a distance-based light absorption coefficient; (2) a gray coefficient enhancing fireflies to share difference information from attractive ones efficiently; and (3) five different dynamic strategies for the randomization parameter. Promising selections of parameters in the strategies are analyzed to guarantee the efficient performance of AdaFa. AdaFa is validated over widely used benchmark functions, and the numerical experiments and statistical tests yield useful conclusions on the strategies and the parameter selections affecting the performance of AdaFa. When applied to the real-world problem - protein tertiary structure prediction, the results demonstrated improved variants can rebuild the tertiary structure with the average root mean square deviation less than 0.4Å and 1.5Å from the native constrains with noise free and 10% Gaussian white noise. PMID:25397812
Generalized pattern search algorithms with adaptive precision function evaluations
Polak, Elijah; Wetter, Michael
2003-05-14
In the literature on generalized pattern search algorithms, convergence to a stationary point of a once continuously differentiable cost function is established under the assumption that the cost function can be evaluated exactly. However, there is a large class of engineering problems where the numerical evaluation of the cost function involves the solution of systems of differential algebraic equations. Since the termination criteria of the numerical solvers often depend on the design parameters, computer code for solving these systems usually defines a numerical approximation to the cost function that is discontinuous with respect to the design parameters. Standard generalized pattern search algorithms have been applied heuristically to such problems, but no convergence properties have been stated. In this paper we extend a class of generalized pattern search algorithms to a form that uses adaptive precision approximations to the cost function. These numerical approximations need not define a continuous function. Our algorithms can be used for solving linearly constrained problems with cost functions that are at least locally Lipschitz continuous. Assuming that the cost function is smooth, we prove that our algorithms converge to a stationary point. Under the weaker assumption that the cost function is only locally Lipschitz continuous, we show that our algorithms converge to points at which the Clarke generalized directional derivatives are nonnegative in predefined directions. An important feature of our adaptive precision scheme is the use of coarse approximations in the early iterations, with the approximation precision controlled by a test. Such an approach leads to substantial time savings in minimizing computationally expensive functions.
NASA Astrophysics Data System (ADS)
Kimura, Satoshi; Candy, Adam S.; Holland, Paul R.; Piggott, Matthew D.; Jenkins, Adrian
2013-07-01
Several different classes of ocean model are capable of representing floating glacial ice shelves. We describe the incorporation of ice shelves into Fluidity-ICOM, a nonhydrostatic finite-element ocean model with the capacity to utilize meshes that are unstructured and adaptive in three dimensions. This geometric flexibility offers several advantages over previous approaches. The model represents melting and freezing on all ice-shelf surfaces including vertical faces, treats the ice shelf topography as continuous rather than stepped, and does not require any smoothing of the ice topography or any of the additional parameterisations of the ocean mixed layer used in isopycnal or z-coordinate models. The model can also represent a water column that decreases to zero thickness at the 'grounding line', where the floating ice shelf is joined to its tributary ice streams. The model is applied to idealised ice-shelf geometries in order to demonstrate these capabilities. In these simple experiments, arbitrarily coarsening the mesh outside the ice-shelf cavity has little effect on the ice-shelf melt rate, while the mesh resolution within the cavity is found to be highly influential. Smoothing the vertical ice front results in faster flow along the smoothed ice front, allowing greater exchange with the ocean than in simulations with a realistic ice front. A vanishing water-column thickness at the grounding line has little effect in the simulations studied. We also investigate the response of ice shelf basal melting to variations in deep water temperature in the presence of salt stratification.
NASA Technical Reports Server (NTRS)
Barth, Timothy; Chancellor, Marisa K. (Technical Monitor)
1997-01-01
Several stabilized discretization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin discretization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobian linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. These variants have been implemented in the "ELF" library for which example calculations will be shown. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Some prevalent limiting strategies will be reviewed. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc. will be addressed as needed.
NASA Astrophysics Data System (ADS)
Angelidis, Dionysios; Sotiropoulos, Fotis
2015-11-01
The geometrical details of wind turbines determine the structure of the turbulence in the near and far wake and should be taken in account when performing high fidelity calculations. Multi-resolution simulations coupled with an immersed boundary method constitutes a powerful framework for high-fidelity calculations past wind farms located over complex terrains. We develop a 3D Immersed-Boundary Adaptive Mesh Refinement flow solver (IB-AMR) which enables turbine-resolving LES of wind turbines. The idea of using a hybrid staggered/non-staggered grid layout adopted in the Curvilinear Immersed Boundary Method (CURVIB) has been successfully incorporated on unstructured meshes and the fractional step method has been employed. The overall performance and robustness of the second order accurate, parallel, unstructured solver is evaluated by comparing the numerical simulations against conforming grid calculations and experimental measurements of laminar and turbulent flows over complex geometries. We also present turbine-resolving multi-scale LES considering all the details affecting the induced flow field; including the geometry of the tower, the nacelle and especially the rotor blades of a wind tunnel scale turbine. This material is based upon work supported by the Department of Energy under Award Number DE-EE0005482 and the Sandia National Laboratories.
NASA Technical Reports Server (NTRS)
Rogers, David
1991-01-01
G/SPLINES are a hybrid of Friedman's Multivariable Adaptive Regression Splines (MARS) algorithm with Holland's Genetic Algorithm. In this hybrid, the incremental search is replaced by a genetic search. The G/SPLINE algorithm exhibits performance comparable to that of the MARS algorithm, requires fewer least squares computations, and allows significantly larger problems to be considered.
Lopez-Camara, D.; Lazzati, Davide; Morsony, Brian J.; Begelman, Mitchell C.
2013-04-10
We present the results of special relativistic, adaptive mesh refinement, 3D simulations of gamma-ray burst jets expanding inside a realistic stellar progenitor. Our simulations confirm that relativistic jets can propagate and break out of the progenitor star while remaining relativistic. This result is independent of the resolution, even though the amount of turbulence and variability observed in the simulations is greater at higher resolutions. We find that the propagation of the jet head inside the progenitor star is slightly faster in 3D simulations compared to 2D ones at the same resolution. This behavior seems to be due to the fact that the jet head in 3D simulations can wobble around the jet axis, finding the spot of least resistance to proceed. Most of the average jet properties, such as density, pressure, and Lorentz factor, are only marginally affected by the dimensionality of the simulations and therefore results from 2D simulations can be considered reliable.
NASA Astrophysics Data System (ADS)
Schmalzl, J.
2003-04-01
Convective flows govern much of the dynamics of the Earth. Examples of such flows are convection in the Earth's mantle, convection in magma chambers and much of the dynamics of the world oceans. Nowadays these time-dependent flows are often studied by means of three dimensional (3D) numerical models which solve the equations for the transport of heat and momentum alternatingly. These flows are often driven by a temperature difference. But for many flows there is also an active or passive chemical component that has to be considered. One characteristics of these flows is that the chemical diffusivity is very small. Implementing such a chemical field with a very low diffusivity into a numerical model using a field approach is difficult due to numerical diffusion introduced by the Eulerian schemes. Using Lagrangian tracers is also difficult in 3D flow since a massive amount of tracers is needed. We therefore have implemented a tracer-mesh method which tracks only the position of the interface between the two different components. Compared to a 2D tracer-line the insertion of new 3D surface-elements in highly deformed regions is however more complex. This is due to the topology of the mesh which changes because of the adaptive refinement. Luckily the refinement of polygonal meshes is a very active field of research in computer graphics and has been termed "Subdivision Surfaces". There is a wealth of different subdivision schemes with different properties. We applied the Butterfly scheme and the Loop scheme for the refinement of tracer meshes. When a density difference is connected to a chemical component it often acts as a restoring force. In many cases, the governing flow is spatially heterogenous and the spatial location of the heterogeneities is varying in time (e.g. the location of an upwelling plume). The restoring force of the density contrast may result in a situation where a highly deformed, and therefore highly refined region, returns to a simple geometry. In
NASA Astrophysics Data System (ADS)
Schmalzl, J.; Loddoch, A.
2003-12-01
Convective flows govern much of the dynamics of the Earth. Examples of such flows are convection in the Earth's mantle, convection in magma chambers and much of the dynamics of the world oceans. Nowadays these time-dependent flows are often studied by means of three dimensional (3D) numerical models which solve the equations for the transport of heat and momentum alternatingly. These flows are often driven by a temperature difference. But for many flows there is also an active or passive chemical component that has to be considered. One characteristics of these flows is that the chemical diffusivity is very small. Implementing such a chemical field with a very low diffusivity into a numerical model using a field approach is difficult due to numerical diffusion introduced by the Eulerian schemes. Using Lagrangian tracers is also difficult in 3D flow since a massive amount of tracers is needed. We therefore have implemented a tracer-mesh method which tracks only the position of the interface between the two different components. Compared to a 2D tracer-line the insertion of new 3D surface-elements in highly deformed regions is however more complex. This is due to the topology of the mesh which changes because of the adaptive refinement. Luckily the refinement of polygonal meshes is a very active field of research in computer graphics and has been termed "Subdivision Surfaces". There is a wealth of different subdivision schemes with different properties. We applied the Butterfly scheme and the Loop scheme for the refinement of tracer meshes. When a density difference is connected to a chemical component it often acts as a restoring force. In many cases, the governing flow is spatially heterogenous and the spatial location of the heterogeneities is varying in time (e.g. the location of an upwelling plume). The restoring force of the density contrast may result in a situation where a highly deformed, and therefore highly refined region, returns to a simple geometry. In
NASA Technical Reports Server (NTRS)
Chen, Shu-Po
1999-01-01
This paper presents software for solving the non-conforming fluid structure interfaces in aeroelastic simulation. It reviews the algorithm of interpolation and integration, highlights the flexibility and the user-friendly feature that allows the user to select the existing structure and fluid package, like NASTRAN and CLF3D, to perform the simulation. The presented software is validated by computing the High Speed Civil Transport model.
Analysis of adaptive algorithms for an integrated communication network
NASA Technical Reports Server (NTRS)
Reed, Daniel A.; Barr, Matthew; Chong-Kwon, Kim
1985-01-01
Techniques were examined that trade communication bandwidth for decreased transmission delays. When the network is lightly used, these schemes attempt to use additional network resources to decrease communication delays. As the network utilization rises, the schemes degrade gracefully, still providing service but with minimal use of the network. Because the schemes use a combination of circuit and packet switching, they should respond to variations in the types and amounts of network traffic. Also, a combination of circuit and packet switching to support the widely varying traffic demands imposed on an integrated network was investigated. The packet switched component is best suited to bursty traffic where some delays in delivery are acceptable. The circuit switched component is reserved for traffic that must meet real time constraints. Selected packet routing algorithms that might be used in an integrated network were simulated. An integrated traffic places widely varying workload demands on a network. Adaptive algorithms were identified, ones that respond to both the transient and evolutionary changes that arise in integrated networks. A new algorithm was developed, hybrid weighted routing, that adapts to workload changes.
NASA Astrophysics Data System (ADS)
Guo, Zhikui; Chen, Chao; Tao, Chunhui
2016-04-01
Since 2007, there are four China Da yang cruises (CDCs), which have been carried out to investigate polymetallic sulfides in the southwest Indian ridge (SWIR) and have acquired both gravity data and bathymetry data on the corresponding survey lines(Tao et al., 2014). Sandwell et al. (2014) published a new global marine gravity model including the free air gravity data and its first order vertical gradient (Vzz). Gravity data and its gradient can be used to extract unknown density structure information(e.g. crust thickness) under surface of the earth, but they contain all the mass effect under the observation point. Therefore, how to get accurate gravity and its gradient effect of the existing density structure (e.g. terrain) has been a key issue. Using the bathymetry data or ETOPO1 (http://www.ngdc.noaa.gov/mgg/global/global.html) model at a full resolution to calculate the terrain effect could spend too much computation time. We expect to develop an effective method that takes less time but can still yield the desired accuracy. In this study, a constant-density polyhedral model is used to calculate the gravity field and its vertical gradient, which is based on the work of Tsoulis (2012). According to gravity field attenuation with distance and variance of bathymetry, we present an adaptive mesh refinement and coarsening strategies to merge both global topography data and multi-beam bathymetry data. The local coarsening or size of mesh depends on user-defined accuracy and terrain variation (Davis et al., 2011). To depict terrain better, triangular surface element and rectangular surface element are used in fine and coarse mesh respectively. This strategy can also be applied to spherical coordinate in large region and global scale. Finally, we applied this method to calculate Bouguer gravity anomaly (BGA), mantle Bouguer anomaly(MBA) and their vertical gradient in SWIR. Further, we compared the result with previous results in the literature. Both synthetic model
Progress report on the wisker weaving all-hexahedral meshing algorithm
Tautges, T.J.; Mitchell, S.A.
1996-02-01
In this paper, a review of the Spatial Twist Contiuum and the basic whisker weaving algorithm are given. Progress in the detection and resolution of several types of degeneracies formed by whisker weaving are discussed. These examples include so-called knife doublets, triple doublets, through-cells and through-chords. Knife doublets and triple doublets are resolved by preventing their formation a-priori, which forces whisker weaving to remove the element(s) causing the degeneracy. Through-chords and through-cells are left in the weave and resolved after the weave has been closed. The paper concludes with three examples of geometries ``closed`` by whisker weaving.
Statistical behaviour of adaptive multilevel splitting algorithms in simple models
Rolland, Joran Simonnet, Eric
2015-02-15
Adaptive multilevel splitting algorithms have been introduced rather recently for estimating tail distributions in a fast and efficient way. In particular, they can be used for computing the so-called reactive trajectories corresponding to direct transitions from one metastable state to another. The algorithm is based on successive selection–mutation steps performed on the system in a controlled way. It has two intrinsic parameters, the number of particles/trajectories and the reaction coordinate used for discriminating good or bad trajectories. We investigate first the convergence in law of the algorithm as a function of the timestep for several simple stochastic models. Second, we consider the average duration of reactive trajectories for which no theoretical predictions exist. The most important aspect of this work concerns some systems with two degrees of freedom. They are studied in detail as a function of the reaction coordinate in the asymptotic regime where the number of trajectories goes to infinity. We show that during phase transitions, the statistics of the algorithm deviate significatively from known theoretical results when using non-optimal reaction coordinates. In this case, the variance of the algorithm is peaking at the transition and the convergence of the algorithm can be much slower than the usual expected central limit behaviour. The duration of trajectories is affected as well. Moreover, reactive trajectories do not correspond to the most probable ones. Such behaviour disappears when using the optimal reaction coordinate called committor as predicted by the theory. We finally investigate a three-state Markov chain which reproduces this phenomenon and show logarithmic convergence of the trajectory durations.
Adaptivity and smart algorithms for fluid-structure interaction
NASA Technical Reports Server (NTRS)
Oden, J. Tinsley
1990-01-01
This paper reviews new approaches in CFD which have the potential for significantly increasing current capabilities of modeling complex flow phenomena and of treating difficult problems in fluid-structure interaction. These approaches are based on the notions of adaptive methods and smart algorithms, which use instantaneous measures of the quality and other features of the numerical flowfields as a basis for making changes in the structure of the computational grid and of algorithms designed to function on the grid. The application of these new techniques to several problem classes are addressed, including problems with moving boundaries, fluid-structure interaction in high-speed turbine flows, flow in domains with receding boundaries, and related problems.
Characterization of atmospheric contaminant sources using adaptive evolutionary algorithms
NASA Astrophysics Data System (ADS)
Cervone, Guido; Franzese, Pasquale; Grajdeanu, Adrian
2010-10-01
The characteristics of an unknown source of emissions in the atmosphere are identified using an Adaptive Evolutionary Strategy (AES) methodology based on ground concentration measurements and a Gaussian plume model. The AES methodology selects an initial set of source characteristics including position, size, mass emission rate, and wind direction, from which a forward dispersion simulation is performed. The error between the simulated concentrations from the tentative source and the observed ground measurements is calculated. Then the AES algorithm prescribes the next tentative set of source characteristics. The iteration proceeds towards minimum error, corresponding to convergence towards the real source. The proposed methodology was used to identify the source characteristics of 12 releases from the Prairie Grass field experiment of dispersion, two for each atmospheric stability class, ranging from very unstable to stable atmosphere. The AES algorithm was found to have advantages over a simple canonical ES and a Monte Carlo (MC) method which were used as benchmarks.
Feasibility of electrical impedance tomography in haemorrhagic stroke treatment using adaptive mesh
NASA Astrophysics Data System (ADS)
Nasehi Tehrani, J.; Anderson, C.; Jin, C.; van Schaik, A.; Holder, D.; McEwan, A.
2010-04-01
EIT has been proposed for acute stroke differentiation, specifically to determine the type of stroke, either ischaemia (clot) or haemorrhage (bleed) to allow the rapid use of clot-busting drugs in the former (Romsauerova et al 2006) . This addresses an important medical need, although there is little treatment offered in the case of haemorrhage. Also the demands on EIT are high with usually no availability to take a 'before' measurement, ruling out time difference imaging. Recently a new treatment option for haemorrhage has been proposed and is being studied in international randomised controlled trial: the early reduction of elevated blood pressure to attenuate the haematoma. This has been shown via CT to reduce bleeds by up to 1mL by Anderson et al 2008. The use of EIT as a continuous measure is desirable here to monitor the effect of blood pressure reduction. A 1mL increase of haemorrhagic lesion located near scalp on the right side of head caused a boundary voltage change of less than 0.05% at 50 kHz. This could be visually observed in a time difference 3D reconstruction with no change in electrode positions, mesh, background conductivity or drift when baseline noise was less than 0.005% but not when noise was increased to 0.01%. This useful result informs us that the EIT system must have noise of less than 0.005% at 50 kHz including instrumentation, physiological and other biases.
Application of Quaternions for Mesh
NASA Technical Reports Server (NTRS)
Samareh, Jamshid A.
2002-01-01
A new three dimensional mesh deformation algorithm, based on quaternion algebra, is introduced. A brief overview of quaternion algebra is provided, along with some preliminary results for two-dimensional structured and unstructured viscous mesh deformation.
Vertical Scan (V-SCAN) for 3-D Grid Adaptive Mesh Refinement for an atmospheric Model Dynamical Core
NASA Astrophysics Data System (ADS)
Andronova, N. G.; Vandenberg, D.; Oehmke, R.; Stout, Q. F.; Penner, J. E.
2009-12-01
One of the major building blocks of a rigorous representation of cloud evolution in global atmospheric models is a parallel adaptive grid MPI-based communication library (an Adaptive Blocks for Locally Cartesian Topologies library -- ABLCarT), which manages the block-structured data layout, handles ghost cell updates among neighboring blocks and splits a block as refinements occur. The library has several modules that provide a layer of abstraction for adaptive refinement: blocks, which contain individual cells of user data; shells - the global geometry for the problem, including a sphere, reduced sphere, and now a 3D sphere; a load balancer for placement of blocks onto processors; and a communication support layer which encapsulates all data movement. A major performance concern with adaptive mesh refinement is how to represent calculations that have need to be sequenced in a particular order in a direction, such as calculating integrals along a specific path (e.g. atmospheric pressure or geopotential in the vertical dimension). This concern is compounded if the blocks have varying levels of refinement, or are scattered across different processors, as can be the case in parallel computing. In this paper we describe an implementation in ABLCarT of a vertical scan operation, which allows computing along vertical paths in the correct order across blocks transparent to their resolution and processor location. We test this functionality on a 2D and a 3D advection problem, which tests the performance of the model’s dynamics (transport) and physics (sources and sinks) for different model resolutions needed for inclusion of cloud formation.
A mesh partitioning algorithm for preserving spatial locality in arbitrary geometries
NASA Astrophysics Data System (ADS)
Nivarti, Girish V.; Salehi, M. Mahdi; Bushe, W. Kendal
2015-01-01
A space-filling curve (SFC) is a proximity preserving linear mapping of any multi-dimensional space and is widely used as a clustering tool. Equi-sized partitioning of an SFC ignores the loss in clustering quality that occurs due to inaccuracies in the mapping. Often, this results in poor locality within partitions, especially for the conceptually simple, Morton order curves. We present a heuristic that improves partition locality in arbitrary geometries by slicing a Morton order curve at points where spatial locality is sacrificed. In addition, we develop algorithms that evenly distribute points to the extent possible while maintaining spatial locality. A metric is defined to estimate relative inter-partition contact as an indicator of communication in parallel computing architectures. Domain partitioning tests have been conducted on geometries relevant to turbulent reactive flow simulations. The results obtained highlight the performance of our method as an unsupervised and computationally inexpensive domain partitioning tool.
Medical case-based retrieval: integrating query MeSH terms for query-adaptive multi-modal fusion
NASA Astrophysics Data System (ADS)
Seco de Herrera, Alba G.; Foncubierta-Rodríguez, Antonio; Müller, Henning
2015-03-01
Advances in medical knowledge give clinicians more objective information for a diagnosis. Therefore, there is an increasing need for bibliographic search engines that can provide services helping to facilitate faster information search. The ImageCLEFmed benchmark proposes a medical case-based retrieval task. This task aims at retrieving articles from the biomedical literature that are relevant for differential diagnosis of query cases including a textual description and several images. In the context of this campaign many approaches have been investigated showing that the fusion of visual and text information can improve the precision of the retrieval. However, fusion does not always lead to better results. In this paper, a new query-adaptive fusion criterion to decide when to use multi-modal (text and visual) or only text approaches is presented. The proposed method integrates text information contained in MeSH (Medical Subject Headings) terms extracted and visual features of the images to find synonym relations between them. Given a text query, the query-adaptive fusion criterion decides when it is suitable to also use visual information for the retrieval. Results show that this approach can decide if a text or multi{modal approach should be used with 77.15% of accuracy.
NASA Astrophysics Data System (ADS)
Huang, Rongzong; Wu, Huiying
2016-06-01
A total enthalpy-based lattice Boltzmann (LB) method with adaptive mesh refinement (AMR) is developed in this paper to efficiently simulate solid-liquid phase change problem where variables vary significantly near the phase interface and thus finer grid is required. For the total enthalpy-based LB method, the velocity field is solved by an incompressible LB model with multiple-relaxation-time (MRT) collision scheme, and the temperature field is solved by a total enthalpy-based MRT LB model with the phase interface effects considered and the deviation term eliminated. With a kinetic assumption that the density distribution function for solid phase is at equilibrium state, a volumetric LB scheme is proposed to accurately realize the nonslip velocity condition on the diffusive phase interface and in the solid phase. As compared with the previous schemes, this scheme can avoid nonphysical flow in the solid phase. As for the AMR approach, it is developed based on multiblock grids. An indicator function is introduced to control the adaptive generation of multiblock grids, which can guarantee the existence of overlap area between adjacent blocks for information exchange. Since MRT collision schemes are used, the information exchange is directly carried out in the moment space. Numerical tests are firstly performed to validate the strict satisfaction of the nonslip velocity condition, and then melting problems in a square cavity with different Prandtl numbers and Rayleigh numbers are simulated, which demonstrate that the present method can handle solid-liquid phase change problem with high efficiency and accuracy.
Path Planning Algorithms for the Adaptive Sensor Fleet
NASA Technical Reports Server (NTRS)
Stoneking, Eric; Hosler, Jeff
2005-01-01
The Adaptive Sensor Fleet (ASF) is a general purpose fleet management and planning system being developed by NASA in coordination with NOAA. The current mission of ASF is to provide the capability for autonomous cooperative survey and sampling of dynamic oceanographic phenomena such as current systems and algae blooms. Each ASF vessel is a software model that represents a real world platform that carries a variety of sensors. The OASIS platform will provide the first physical vessel, outfitted with the systems and payloads necessary to execute the oceanographic observations described in this paper. The ASF architecture is being designed for extensibility to accommodate heterogenous fleet elements, and is not limited to using the OASIS platform to acquire data. This paper describes the path planning algorithms developed for the acquisition phase of a typical ASF task. Given a polygonal target region to be surveyed, the region is subdivided according to the number of vessels in the fleet. The subdivision algorithm seeks a solution in which all subregions have equal area and minimum mean radius. Once the subregions are defined, a dynamic programming method is used to find a minimum-time path for each vessel from its initial position to its assigned region. This path plan includes the effects of water currents as well as avoidance of known obstacles. A fleet-level planning algorithm then shuffles the individual vessel assignments to find the overall solution which puts all vessels in their assigned regions in the minimum time. This shuffle algorithm may be described as a process of elimination on the sorted list of permutations of a cost matrix. All these path planning algorithms are facilitated by discretizing the region of interest onto a hexagonal tiling.
Constrained-Transport Magnetohydrodynamics with Adaptive-Mesh-Refinement in CHARM
Miniatii, Francesco; Martin, Daniel
2011-05-24
We present the implementation of a three-dimensional, second order accurate Godunov-type algorithm for magneto-hydrodynamic (MHD), in the adaptivemesh-refinement (AMR) cosmological code CHARM. The algorithm is based on the full 12-solve spatially unsplit Corner-Transport-Upwind (CTU) scheme. Thefluid quantities are cell-centered and are updated using the Piecewise-Parabolic- Method (PPM), while the magnetic field variables are face-centered and areevolved through application of the Stokes theorem on cell edges via a Constrained- Transport (CT) method. The so-called ?multidimensional MHD source terms?required in the predictor step for high-order accuracy are applied in a simplified form which reduces their complexity in three dimensions without loss of accuracyor robustness. The algorithm is implemented on an AMR framework which requires specific synchronization steps across refinement levels. These includeface-centered restriction and prolongation operations and a reflux-curl operation, which maintains a solenoidal magnetic field across refinement boundaries. Thecode is tested against a large suite of test problems, including convergence tests in smooth flows, shock-tube tests, classical two- and three-dimensional MHD tests,a three-dimensional shock-cloud interaction problem and the formation of a cluster of galaxies in a fully cosmological context. The magnetic field divergence isshown to remain negligible throughout. Subject headings: cosmology: theory - methods: numerical
Computation of Transient Nonlinear Ship Waves Using AN Adaptive Algorithm
NASA Astrophysics Data System (ADS)
Çelebi, M. S.
2000-04-01
An indirect boundary integral method is used to solve transient nonlinear ship wave problems. A resulting mixed boundary value problem is solved at each time-step using a mixed Eulerian- Lagrangian time integration technique. Two dynamic node allocation techniques, which basically distribute nodes on an ever changing body surface, are presented. Both two-sided hyperbolic tangent and variational grid generation algorithms are developed and compared on station curves. A ship hull form is generated in parametric space using a B-spline surface representation. Two-sided hyperbolic tangent and variational adaptive curve grid-generation methods are then applied on the hull station curves to generate effective node placement. The numerical algorithm, in the first method, used two stretching parameters. In the second method, a conservative form of the parametric variational Euler-Lagrange equations is used the perform an adaptive gridding on each station. The resulting unsymmetrical influence coefficient matrix is solved using both a restarted version of GMRES based on the modified Gram-Schmidt procedure and a line Jacobi method based on LU decomposition. The convergence rates of both matrix iteration techniques are improved with specially devised preconditioners. Numerical examples of node placements on typical hull cross-sections using both techniques are discussed and fully nonlinear ship wave patterns and wave resistance computations are presented.
Wavefront sensors and algorithms for adaptive optical systems
NASA Astrophysics Data System (ADS)
Lukin, V. P.; Botygina, N. N.; Emaleev, O. N.; Konyaev, P. A.
2010-07-01
The results of recent works related to techniques and algorithms for wave-front (WF) measurement using Shack-Hartmann sensors show their high efficiency in solution of very different problems of applied optics. The goal of this paper was to develop a sensitive Shack-Hartmann sensor with high precision WF measurement capability on the base of modern technology of optical elements making and new efficient methods and computational algorithms of WF reconstruction. The Shack-Hartmann sensors sensitive to small WF aberrations are used for adaptive optical systems, compensating the wave distortions caused by atmospheric turbulence. A high precision Shack-Hartmann WF sensor has been developed on the basis of a low-aperture off-axis diffraction lens array. The device is capable of measuring WF slopes at array sub-apertures of size 640×640 μm with an error not exceeding 4.80 arcsec (0.15 pixel), which corresponds to the standard deviation equal to 0.017λ at the reconstructed WF with wavelength λ . Also the modification of this sensor for adaptive system of solar telescope using extended scenes as tracking objects, such as sunspot, pores, solar granulation and limb, is presented. The software package developed for the proposed WF sensors includes three algorithms of local WF slopes estimation (modified centroids, normalized cross-correlation and fast Fourierdemodulation), as well as three methods of WF reconstruction (modal Zernike polynomials expansion, deformable mirror response functions expansion and phase unwrapping), that can be selected during operation with accordance to the application.
A general boundary capability embedded in an orthogonal mesh
Hewett, D.W.; Yu-Jiuan Chen
1995-07-01
The authors describe how they hold onto orthogonal mesh discretization when dealing with curved boundaries. Special difference operators were constructed to approximate numerical zones split by the domain boundary; the operators are particularly simple for this rectangular mesh. The authors demonstrated that this simple numerical approach, termed Dynamic Alternating Direction Implicit, turned out to be considerably more efficient than more complex grid-adaptive algorithms that were tried previously.
A novel adaptive multi-resolution combined watermarking algorithm
NASA Astrophysics Data System (ADS)
Feng, Gui; Lin, QiWei
2008-04-01
The rapid development of IT and WWW technique, causing person frequently confronts with various kinds of authorized identification problem, especially the copyright problem of digital products. The digital watermarking technique was emerged as one kind of solutions. The balance between robustness and imperceptibility is always the object sought by related researchers. In order to settle the problem of robustness and imperceptibility, a novel adaptive multi-resolution combined digital image watermarking algorithm was proposed in this paper. In the proposed algorithm, we first decompose the watermark into several sub-bands, and according to its significance to embed the sub-band to different DWT coefficient of the carrier image. While embedding, the HVS was considered. So under the precondition of keeping the quality of image, the larger capacity of watermark can be embedding. The experimental results have shown that the proposed algorithm has better performance in the aspects of robustness and security. And with the same visual quality, the technique has larger capacity. So the unification of robustness and imperceptibility was achieved.
NASA Astrophysics Data System (ADS)
Schneider, Martin; Kellermann, Walter
2016-01-01
Acoustic echo cancellation (AEC) is a well-known application of adaptive filters in communication acoustics. To implement AEC for multichannel reproduction systems, powerful adaptation algorithms like the generalized frequency-domain adaptive filtering (GFDAF) algorithm are required for satisfactory convergence behavior. In this paper, the GFDAF algorithm is rigorously derived as an approximation of the block recursive least-squares (RLS) algorithm. Thereby, the original formulation of the GFDAF algorithm is generalized while avoiding an error that has been in the original derivation. The presented algorithm formulation is applied to pruned transform-domain loudspeaker-enclosure-microphone models in a mathematically consistent manner. Such pruned models have recently been proposed to cope with the tremendous computational demands of massive multichannel AEC. Beyond its generalization, a regularization of the GFDAF is shown to have a close relation to the well-known block least-mean-squares algorithm.
A Competency-Based Guided-Learning Algorithm Applied on Adaptively Guiding E-Learning
ERIC Educational Resources Information Center
Hsu, Wei-Chih; Li, Cheng-Hsiu
2015-01-01
This paper presents a new algorithm called competency-based guided-learning algorithm (CBGLA), which can be applied on adaptively guiding e-learning. Computational process analysis and mathematical derivation of competency-based learning (CBL) were used to develop the CBGLA. The proposed algorithm could generate an effective adaptively guiding…
Adaptive centroid-finding algorithm for freeform surface measurements.
Guo, Wenjiang; Zhao, Liping; Tong, Chin Shi; I-Ming, Chen; Joshi, Sunil Chandrakant
2013-04-01
Wavefront sensing systems measure the slope or curvature of a surface by calculating the centroid displacement of two focal spot images. Accurately finding the centroid of each focal spot determines the measurement results. This paper studied several widely used centroid-finding techniques and observed that thresholding is the most critical factor affecting the centroid-finding accuracy. Since the focal spot image of a freeform surface usually suffers from various types of image degradation, it is difficult and sometimes impossible to set a best threshold value for the whole image. We propose an adaptive centroid-finding algorithm to tackle this problem and have experimentally proven its effectiveness in measuring freeform surfaces. PMID:23545985
An adaptive genetic algorithm for crystal structure prediction
Wu, Shunqing; Ji, Min; Wang, Cai-Zhuang; Nguyen, Manh Cuong; Zhao, Xin; Umemoto, K.; Wentzcovitch, R. M.; Ho, Kai-Ming
2013-12-18
We present a genetic algorithm (GA) for structural search that combines the speed of structure exploration by classical potentials with the accuracy of density functional theory (DFT) calculations in an adaptive and iterative way. This strategy increases the efficiency of the DFT-based GA by several orders of magnitude. This gain allows a considerable increase in the size and complexity of systems that can be studied by first principles. The performance of the method is illustrated by successful structure identifications of complex binary and ternary intermetallic compounds with 36 and 54 atoms per cell, respectively. The discovery of a multi-TPa Mg-silicate phase with unit cell containing up to 56 atoms is also reported. Such a phase is likely to be an essential component of terrestrial exoplanetary mantles.
Algorithms and data structures for adaptive multigrid elliptic solvers
NASA Technical Reports Server (NTRS)
Vanrosendale, J.
1983-01-01
Adaptive refinement and the complicated data structures required to support it are discussed. These data structures must be carefully tuned, especially in three dimensions where the time and storage requirements of algorithms are crucial. Another major issue is grid generation. The options available seem to be curvilinear fitted grids, constructed on iterative graphics systems, and unfitted Cartesian grids, which can be constructed automatically. On several grounds, including storage requirements, the second option seems preferrable for the well behaved scalar elliptic problems considered here. A variety of techniques for treatment of boundary conditions on such grids are reviewed. A new approach, which may overcome some of the difficulties encountered with previous approaches, is also presented.
Self-adaptive closed constrained solution algorithms for nonlinear conduction
NASA Technical Reports Server (NTRS)
Padovan, J.; Tovichakchaikul, S.
1982-01-01
Self-adaptive solution algorithms are developed for nonlinear heat conduction problems encountered in analyzing materials for use in high temperature or cryogenic conditions. The nonlinear effects are noted to occur due to convection and radiation effects, as well as temperature-dependent properties of the materials. Incremental successive substitution (ISS) and Newton-Raphson (NR) procedures are treated as extrapolation schemes which have solution projections bounded by a hyperline with an externally applied thermal load vector arising from internal heat generation and boundary conditions. Closed constraints are formulated which improve the efficiency and stability of the procedures by employing closed ellipsoidal surfaces to control the size of successive iterations. Governing equations are defined for nonlinear finite element models, and comparisons are made of results using the the new method and the ISS and NR schemes for epoxy, PVC, and CuGe.
NASA Astrophysics Data System (ADS)
Power, C.; Read, J. I.; Hobbs, A.
2014-06-01
We simulate cosmological galaxy cluster formation using three different approaches to solving the equations of non-radiative hydrodynamics - classic smoothed particle hydrodynamics (SPH), novel SPH with a higher order dissipation switch (SPHS), and an adaptive mesh refinement (AMR) method. Comparing spherically averaged entropy profiles, we find that SPHS and AMR approaches result in a well-defined entropy core that converges rapidly with increasing mass and force resolution. In contrast, the central entropy profile in the SPH approach is sensitive to the cluster's assembly history and shows poor numerical convergence. We trace this disagreement to the known artificial surface tension in SPH that appears at phase boundaries. Varying systematically numerical dissipation in SPHS, we study the contributions of numerical and physical dissipation to the entropy core and argue that numerical dissipation is required to ensure single-valued fluid quantities in converging flows. However, provided it occurs only at the resolution limit and does not propagate errors to larger scales, its effect is benign - there is no requirement to build `sub-grid' models of unresolved turbulence for galaxy cluster simulations. We conclude that entropy cores in non-radiative galaxy cluster simulations are physical, resulting from entropy generation in shocked gas during cluster assembly.
NASA Astrophysics Data System (ADS)
Rasia, Elena; Lau, Erwin T.; Borgani, Stefano; Nagai, Daisuke; Dolag, Klaus; Avestruz, Camille; Granato, Gian Luigi; Mazzotta, Pasquale; Murante, Giuseppe; Nelson, Kaylea; Ragone-Figueroa, Cinthia
2014-08-01
Analyses of cosmological hydrodynamic simulations of galaxy clusters suggest that X-ray masses can be underestimated by 10%-30%. The largest bias originates from both violation of hydrostatic equilibrium (HE) and an additional temperature bias caused by inhomogeneities in the X-ray-emitting intracluster medium (ICM). To elucidate this large dispersion among theoretical predictions, we evaluate the degree of temperature structures in cluster sets simulated either with smoothed-particle hydrodynamics (SPH) or adaptive-mesh refinement (AMR) codes. We find that the SPH simulations produce larger temperature variations connected to the persistence of both substructures and their stripped cold gas. This difference is more evident in nonradiative simulations, whereas it is reduced in the presence of radiative cooling. We also find that the temperature variation in radiative cluster simulations is generally in agreement with that observed in the central regions of clusters. Around R 500 the temperature inhomogeneities of the SPH simulations can generate twice the typical HE mass bias of the AMR sample. We emphasize that a detailed understanding of the physical processes responsible for the complex thermal structure in ICM requires improved resolution and high-sensitivity observations in order to extend the analysis to higher temperature systems and larger cluster-centric radii.
Zhang, S.; Yuen, D.A.; Zhu, A.; Song, S.; George, D.L.
2011-01-01
We parallelized the GeoClaw code on one-level grid using OpenMP in March, 2011 to meet the urgent need of simulating tsunami waves at near-shore from Tohoku 2011 and achieved over 75% of the potential speed-up on an eight core Dell Precision T7500 workstation [1]. After submitting that work to SC11 - the International Conference for High Performance Computing, we obtained an unreleased OpenMP version of GeoClaw from David George, who developed the GeoClaw code as part of his PH.D thesis. In this paper, we will show the complementary characteristics of the two approaches used in parallelizing GeoClaw and the speed-up obtained by combining the advantage of each of the two individual approaches with adaptive mesh refinement (AMR), demonstrating the capabilities of running GeoClaw efficiently on many-core systems. We will also show a novel simulation of the Tohoku 2011 Tsunami waves inundating the Sendai airport and Fukushima Nuclear Power Plants, over which the finest grid distance of 20 meters is achieved through a 4-level AMR. This simulation yields quite good predictions about the wave-heights and travel time of the tsunami waves. ?? 2011 IEEE.
Rasia, Elena; Lau, Erwin T.; Nagai, Daisuke; Avestruz, Camille; Borgani, Stefano; Dolag, Klaus; Granato, Gian Luigi; Murante, Giuseppe; Ragone-Figueroa, Cinthia; Mazzotta, Pasquale; Nelson, Kaylea
2014-08-20
Analyses of cosmological hydrodynamic simulations of galaxy clusters suggest that X-ray masses can be underestimated by 10%-30%. The largest bias originates from both violation of hydrostatic equilibrium (HE) and an additional temperature bias caused by inhomogeneities in the X-ray-emitting intracluster medium (ICM). To elucidate this large dispersion among theoretical predictions, we evaluate the degree of temperature structures in cluster sets simulated either with smoothed-particle hydrodynamics (SPH) or adaptive-mesh refinement (AMR) codes. We find that the SPH simulations produce larger temperature variations connected to the persistence of both substructures and their stripped cold gas. This difference is more evident in nonradiative simulations, whereas it is reduced in the presence of radiative cooling. We also find that the temperature variation in radiative cluster simulations is generally in agreement with that observed in the central regions of clusters. Around R {sub 500} the temperature inhomogeneities of the SPH simulations can generate twice the typical HE mass bias of the AMR sample. We emphasize that a detailed understanding of the physical processes responsible for the complex thermal structure in ICM requires improved resolution and high-sensitivity observations in order to extend the analysis to higher temperature systems and larger cluster-centric radii.
Ly{alpha} RADIATIVE TRANSFER IN COSMOLOGICAL SIMULATIONS USING ADAPTIVE MESH REFINEMENT
Laursen, Peter; Razoumov, Alexei O.; Sommer-Larsen, Jesper E-mail: razoumov@ap.smu.ca
2009-05-01
A numerical code for solving various Ly{alpha} radiative transfer (RT) problems is presented. The code is suitable for an arbitrary, three-dimensional distribution of Ly{alpha} emissivity, gas temperature, density, and velocity field. Capable of handling Ly{alpha} RT in an adaptively refined grid-based structure, it enables detailed investigation of the effects of clumpiness of the interstellar (or intergalactic) medium. The code is tested against various geometrically and physically idealized configurations for which analytical solutions exist, and subsequently applied to three different simulated high-resolution 'Lyman-break galaxies', extracted from high-resolution cosmological simulations at redshift z = 3.6. Proper treatment of the Ly{alpha} scattering reveals a diversity of surface brightness (SB) and line profiles. Specifically, for a given galaxy the maximum observed SB can vary by an order of magnitude, and the total flux by a factor of 3-6, depending on the viewing angle. This may provide an explanation for differences in observed properties of high-redshift galaxies, and in particular a possible physical link between Lyman-break galaxies and regular Ly{alpha} emitters.
NASA Technical Reports Server (NTRS)
Thompson, C. P.; Leaf, G. K.; Vanrosendale, J.
1991-01-01
An algorithm is described for the solution of the laminar, incompressible Navier-Stokes equations. The basic algorithm is a multigrid based on a robust, box-based smoothing step. Its most important feature is the incorporation of automatic, dynamic mesh refinement. This algorithm supports generalized simple domains. The program is based on a standard staggered-grid formulation of the Navier-Stokes equations for robustness and efficiency. Special grid transfer operators were introduced at grid interfaces in the multigrid algorithm to ensure discrete mass conservation. Results are presented for three models: the driven-cavity, a backward-facing step, and a sudden expansion/contraction.
Documentation for MeshKit - Reactor Geometry (&mesh) Generator
Jain, Rajeev; Mahadevan, Vijay
2015-09-30
This report gives documentation for using MeshKit’s Reactor Geometry (and mesh) Generator (RGG) GUI and also briefly documents other algorithms and tools available in MeshKit. RGG is a program designed to aid in modeling and meshing of complex/large hexagonal and rectilinear reactor cores. RGG uses Argonne’s SIGMA interfaces, Qt and VTK to produce an intuitive user interface. By integrating a 3D view of the reactor with the meshing tools and combining them into one user interface, RGG streamlines the task of preparing a simulation mesh and enables real-time feedback that reduces accidental scripting mistakes that could waste hours of meshing. RGG interfaces with MeshKit tools to consolidate the meshing process, meaning that going from model to mesh is as easy as a button click. This report is designed to explain RGG v 2.0 interface and provide users with the knowledge and skills to pilot RGG successfully. Brief documentation of MeshKit source code, tools and other algorithms available are also presented for developers to extend and add new algorithms to MeshKit. RGG tools work in serial and parallel and have been used to model complex reactor core models consisting of conical pins, load pads, several thousands of axially varying material properties of instrumentation pins and other interstices meshes.
Design of infrasound-detection system via adaptive LMSTDE algorithm
NASA Technical Reports Server (NTRS)
Khalaf, C. S.; Stoughton, J. W.
1984-01-01
A proposed solution to an aviation safety problem is based on passive detection of turbulent weather phenomena through their infrasonic emission. This thesis describes a system design that is adequate for detection and bearing evaluation of infrasounds. An array of four sensors, with the appropriate hardware, is used for the detection part. Bearing evaluation is based on estimates of time delays between sensor outputs. The generalized cross correlation (GCC), as the conventional time-delay estimation (TDE) method, is first reviewed. An adaptive TDE approach, using the least mean square (LMS) algorithm, is then discussed. A comparison between the two techniques is made and the advantages of the adaptive approach are listed. The behavior of the GCC, as a Roth processor, is examined for the anticipated signals. It is shown that the Roth processor has the desired effect of sharpening the peak of the correlation function. It is also shown that the LMSTDE technique is an equivalent implementation of the Roth processor in the time domain. A LMSTDE lead-lag model, with a variable stability coefficient and a convergence criterion, is designed.
A wavelet packet adaptive filtering algorithm for enhancing manatee vocalizations.
Gur, M Berke; Niezrecki, Christopher
2011-04-01
Approximately a quarter of all West Indian manatee (Trichechus manatus latirostris) mortalities are attributed to collisions with watercraft. A boater warning system based on the passive acoustic detection of manatee vocalizations is one possible solution to reduce manatee-watercraft collisions. The success of such a warning system depends on effective enhancement of the vocalization signals in the presence of high levels of background noise, in particular, noise emitted from watercraft. Recent research has indicated that wavelet domain pre-processing of the noisy vocalizations is capable of significantly improving the detection ranges of passive acoustic vocalization detectors. In this paper, an adaptive denoising procedure, implemented on the wavelet packet transform coefficients obtained from the noisy vocalization signals, is investigated. The proposed denoising algorithm is shown to improve the manatee detection ranges by a factor ranging from two (minimum) to sixteen (maximum) compared to high-pass filtering alone, when evaluated using real manatee vocalization and background noise signals of varying signal-to-noise ratios (SNR). Furthermore, the proposed method is also shown to outperform a previously suggested feedback adaptive line enhancer (FALE) filter on average 3.4 dB in terms of noise suppression and 0.6 dB in terms of waveform preservation. PMID:21476661
NASA Astrophysics Data System (ADS)
Pantano, C.; Deiterding, R.; Hill, D. J.; Pullin, D. I.
2006-09-01
This paper describes a hybrid finite-difference method for the large-eddy simulation of compressible flows with low-numerical dissipation and structured adaptive mesh refinement (SAMR). A conservative flux-based approach is described with an explicit centered scheme used in turbulent flow regions while a weighted essentially non-oscillatory (WENO) scheme is employed to capture shocks. Three-dimensional numerical simulations of a Richtmyer-Meshkov instability are presented.
Moving Overlapping Grids with Adaptive Mesh Refinement for High-Speed Reactive and Non-reactive Flow
Henshaw, W D; Schwendeman, D W
2005-08-30
We consider the solution of the reactive and non-reactive Euler equations on two-dimensional domains that evolve in time. The domains are discretized using moving overlapping grids. In a typical grid construction, boundary-fitted grids are used to represent moving boundaries, and these grids overlap with stationary background Cartesian grids. Block-structured adaptive mesh refinement (AMR) is used to resolve fine-scale features in the flow such as shocks and detonations. Refinement grids are added to base-level grids according to an estimate of the error, and these refinement grids move with their corresponding base-level grids. The numerical approximation of the governing equations takes place in the parameter space of each component grid which is defined by a mapping from (fixed) parameter space to (moving) physical space. The mapped equations are solved numerically using a second-order extension of Godunov's method. The stiff source term in the reactive case is handled using a Runge-Kutta error-control scheme. We consider cases when the boundaries move according to a prescribed function of time and when the boundaries of embedded bodies move according to the surface stress exerted by the fluid. In the latter case, the Newton-Euler equations describe the motion of the center of mass of the each body and the rotation about it, and these equations are integrated numerically using a second-order predictor-corrector scheme. Numerical boundary conditions at slip walls are described, and numerical results are presented for both reactive and non-reactive flows in order to demonstrate the use and accuracy of the numerical approach.
Wordelman, C.J.; Ravaioli, U.
2000-02-01
A particle-particle-particle-mesh (P{sup 3}M) algorithm is integrated with the ensemble Monte Carlo (EMC) method for the treatment of carrier-impurity (c-i) and carrier-carrier (c-c) effects in semiconductor device simulation. Ionized impurities and charge carriers are treated granularly as opposed to the normal continuum methods and c-i and c-c interactions are calculated in three dimensions. The combined P{sup 3}M-EMC method follows the approach of Hockney, but is modified to treat nonuniform rectilinear meshes with arbitrary boundary conditions. Bulk mobility results are obtained for a three-dimensional (3-D) resistor and are compared with previously reported experimental and numerical results.
Evaluating Knowledge Structure-Based Adaptive Testing Algorithms and System Development
ERIC Educational Resources Information Center
Wu, Huey-Min; Kuo, Bor-Chen; Yang, Jinn-Min
2012-01-01
In recent years, many computerized test systems have been developed for diagnosing students' learning profiles. Nevertheless, it remains a challenging issue to find an adaptive testing algorithm to both shorten testing time and precisely diagnose the knowledge status of students. In order to find a suitable algorithm, four adaptive testing…
Adaptable Particle-in-Cell Algorithms for Graphical Processing Units
NASA Astrophysics Data System (ADS)
Decyk, Viktor; Singh, Tajendra
2010-11-01
Emerging computer architectures consist of an increasing number of shared memory computing cores in a chip, often with vector (SIMD) co-processors. Future exascale high performance systems will consist of a hierarchy of such nodes, which will require different algorithms at different levels. Since no one knows exactly how the future will evolve, we have begun development of an adaptable Particle-in-Cell (PIC) code, whose parameters can match different hardware configurations. The data structures reflect three levels of parallelism, contiguous vectors and non-contiguous blocks of vectors, which can share memory, and groups of blocks which do not. Particles are kept ordered at each time step, and the size of a sorting cell is an adjustable parameter. We have implemented a simple 2D electrostatic skeleton code whose inner loop (containing 6 subroutines) runs entirely on the NVIDIA Tesla C1060. We obtained speedups of about 16-25 compared to a 2.66 GHz Intel i7 (Nehalem), depending on the plasma temperature, with an asymptotic limit of 40 for a frozen plasma. We expect speedups of about 70 for an 2D electromagnetic code and about 100 for a 3D electromagnetic code, which have higher computational intensities (more flops/memory access).
Sheng, Zheng; Wang, Jun; Zhou, Shudao; Zhou, Bihua
2014-03-01
This paper introduces a novel hybrid optimization algorithm to establish the parameters of chaotic systems. In order to deal with the weaknesses of the traditional cuckoo search algorithm, the proposed adaptive cuckoo search with simulated annealing algorithm is presented, which incorporates the adaptive parameters adjusting operation and the simulated annealing operation in the cuckoo search algorithm. Normally, the parameters of the cuckoo search algorithm are kept constant that may result in decreasing the efficiency of the algorithm. For the purpose of balancing and enhancing the accuracy and convergence rate of the cuckoo search algorithm, the adaptive operation is presented to tune the parameters properly. Besides, the local search capability of cuckoo search algorithm is relatively weak that may decrease the quality of optimization. So the simulated annealing operation is merged into the cuckoo search algorithm to enhance the local search ability and improve the accuracy and reliability of the results. The functionality of the proposed hybrid algorithm is investigated through the Lorenz chaotic system under the noiseless and noise condition, respectively. The numerical results demonstrate that the method can estimate parameters efficiently and accurately in the noiseless and noise condition. Finally, the results are compared with the traditional cuckoo search algorithm, genetic algorithm, and particle swarm optimization algorithm. Simulation results demonstrate the effectiveness and superior performance of the proposed algorithm. PMID:24697395
Sheng, Zheng; Wang, Jun; Zhou, Bihua; Zhou, Shudao
2014-03-15
This paper introduces a novel hybrid optimization algorithm to establish the parameters of chaotic systems. In order to deal with the weaknesses of the traditional cuckoo search algorithm, the proposed adaptive cuckoo search with simulated annealing algorithm is presented, which incorporates the adaptive parameters adjusting operation and the simulated annealing operation in the cuckoo search algorithm. Normally, the parameters of the cuckoo search algorithm are kept constant that may result in decreasing the efficiency of the algorithm. For the purpose of balancing and enhancing the accuracy and convergence rate of the cuckoo search algorithm, the adaptive operation is presented to tune the parameters properly. Besides, the local search capability of cuckoo search algorithm is relatively weak that may decrease the quality of optimization. So the simulated annealing operation is merged into the cuckoo search algorithm to enhance the local search ability and improve the accuracy and reliability of the results. The functionality of the proposed hybrid algorithm is investigated through the Lorenz chaotic system under the noiseless and noise condition, respectively. The numerical results demonstrate that the method can estimate parameters efficiently and accurately in the noiseless and noise condition. Finally, the results are compared with the traditional cuckoo search algorithm, genetic algorithm, and particle swarm optimization algorithm. Simulation results demonstrate the effectiveness and superior performance of the proposed algorithm.
NASA Astrophysics Data System (ADS)
Sheng, Zheng; Wang, Jun; Zhou, Shudao; Zhou, Bihua
2014-03-01
This paper introduces a novel hybrid optimization algorithm to establish the parameters of chaotic systems. In order to deal with the weaknesses of the traditional cuckoo search algorithm, the proposed adaptive cuckoo search with simulated annealing algorithm is presented, which incorporates the adaptive parameters adjusting operation and the simulated annealing operation in the cuckoo search algorithm. Normally, the parameters of the cuckoo search algorithm are kept constant that may result in decreasing the efficiency of the algorithm. For the purpose of balancing and enhancing the accuracy and convergence rate of the cuckoo search algorithm, the adaptive operation is presented to tune the parameters properly. Besides, the local search capability of cuckoo search algorithm is relatively weak that may decrease the quality of optimization. So the simulated annealing operation is merged into the cuckoo search algorithm to enhance the local search ability and improve the accuracy and reliability of the results. The functionality of the proposed hybrid algorithm is investigated through the Lorenz chaotic system under the noiseless and noise condition, respectively. The numerical results demonstrate that the method can estimate parameters efficiently and accurately in the noiseless and noise condition. Finally, the results are compared with the traditional cuckoo search algorithm, genetic algorithm, and particle swarm optimization algorithm. Simulation results demonstrate the effectiveness and superior performance of the proposed algorithm.
Belyakov, A.A.; Mal`tsev, A.A.; Medvedev, S.Yu.
1995-04-01
A modified least squares algorithm, preventing the overflow of the discharge grid of weight coefficients of an adaptive transverse filter and guaranteeing stable system operation, is suggested for the tuning of an adaptive system of an actively quenched sound field. Experimental results are provided for an adaptive filter with a modified algorithm in a system of several harmonic components of an actively quenched sound field.
An Adaptive RFID Anti-Collision Algorithm Based on Dynamic Framed ALOHA
NASA Astrophysics Data System (ADS)
Lee, Chang Woo; Cho, Hyeonwoo; Kim, Sang Woo
The collision of ID signals from a large number of colocated passive RFID tags is a serious problem; to realize a practical RFID systems we need an effective anti-collision algorithm. This letter presents an adaptive algorithm to minimize the total time slots and the number of rounds required for identifying the tags within the RFID reader's interrogation zone. The proposed algorithm is based on the framed ALOHA protocol, and the frame size is adaptively updated each round. Simulation results show that our proposed algorithm is more efficient than the conventional algorithms based on the framed ALOHA.
NASA Technical Reports Server (NTRS)
Wood, William A., III
2002-01-01
A multi-dimensional upwind fluctuation splitting scheme is developed and implemented for two-dimensional and axisymmetric formulations of the Navier-Stokes equations on unstructured meshes. Key features of the scheme are the compact stencil, full upwinding, and non-linear discretization which allow for second-order accuracy with enforced positivity. Throughout, the fluctuation splitting scheme is compared to a current state-of-the-art finite volume approach, a second-order, dual mesh upwind flux difference splitting scheme (DMFDSFV), and is shown to produce more accurate results using fewer computer resources for a wide range of test cases. A Blasius flat plate viscous validation case reveals a more accurate upsilon-velocity profile for fluctuation splitting, and the reduced artificial dissipation production is shown relative to DMFDSFV. Remarkably, the fluctuation splitting scheme shows grid converged skin friction coefficients with only five points in the boundary layer for this case. The second half of the report develops a local, compact, anisotropic unstructured mesh adaptation scheme in conjunction with the multi-dimensional upwind solver, exhibiting a characteristic alignment behavior for scalar problems. The adaptation strategy is extended to the two-dimensional and axisymmetric Navier-Stokes equations of motion through the concept of fluctuation minimization.
TAP - Tools for Adaptive Partitioning v. 0.99 Beta
Energy Science and Technology Software Center (ESTSC)
2008-11-19
TAP is a set of tools which are essential for conducting research on adaptive partitioners. The basic premise is that a single partitioner may not be a good choice for adaptive mesh simulations; rather one must match a partitioner (obtained from a partitioning package like Zoltan, ParMetis etc) with the mesh being partitioned. TAP provides the tools that can judge the suitability of a partitioning algorithm to a given mesh.
An Adaptable Power System with Software Control Algorithm
NASA Technical Reports Server (NTRS)
Castell, Karen; Bay, Mike; Hernandez-Pellerano, Amri; Ha, Kong
1998-01-01
A low cost, flexible and modular spacecraft power system design was developed in response to a call for an architecture that could accommodate multiple missions in the small to medium load range. Three upcoming satellites will use this design, with one launch date in 1999 and two in the year 2000. The design consists of modular hardware that can be scaled up or down, without additional cost, to suit missions in the 200 to 600 Watt orbital average load range. The design will be applied to satellite orbits that are circular, polar elliptical and a libration point orbit. Mission unique adaptations are accomplished in software and firmware. In designing this advanced, adaptable power system, the major goals were reduction in weight volume and cost. This power system design represents reductions in weight of 78 percent, volume of 86 percent and cost of 65 percent from previous comparable systems. The efforts to miniaturize the electronics without sacrificing performance has created streamlined power electronics with control functions residing in the system microprocessor. The power system design can handle any battery size up to 50 Amp-hour and any battery technology. The three current implementations will use both nickel cadmium and nickel hydrogen batteries ranging in size from 21 to 50 Amp-hours. Multiple batteries can be used by adding another battery module. Any solar cell technology can be used and various array layouts can be incorporated with no change in Power System Electronics (PSE) hardware. Other features of the design are the standardized interfaces between cards and subsystems and immunity to radiation effects up to 30 krad Total Ionizing Dose (TID) and 35 Mev/cm(exp 2)-kg for Single Event Effects (SEE). The control algorithm for the power system resides in a radiation-hardened microprocessor. A table driven software design allows for flexibility in mission specific requirements. By storing critical power system constants in memory, modifying the system
Koch, M.
1995-12-31
A new mesh-adaptive 1D collocation technique has been developed to efficiently solve transient advection-dominated transport problems in porous media that are governed by a hyperbolic/parabolic (singularly perturbed) PDE. After spatial discretization a singularly perturbed ODE is obtained which is solved by a modification of the COLNEW ODE-collocation code. The latter also contains an adaptive mesh procedure that has been enhanced here to resolve linear and nonlinear transport flow problems with steep fronts where regular FD and FE methods often fail. An implicit first-order backward Euler and a third-order Taylor-Donea technique are employed for the time integration. Numerical simulations on a variety of high Peclet-number transport phenomena as they occur in realistic porous media flow situations are presented. Examples include classical linear advection-diffusion, nonlinear adsorption, two-phase Buckley-Leverett flow without and with capillary forces (Rapoport-Leas equation) and Burgers` equation for inviscid fluid flow. In most of these examples sharp fronts and/or shocks develop which are resolved in an oscillation-free manner by the present adaptive collocation method. The backward Euler method has some amount of numerical dissipation is observed when the time-steps are too large. The third-order Taylor-Donea technique is less dissipative but is more prone to numerical oscillations. The simulations show that for the efficient solution of nonlinear singularly perturbed PDE`s governing flow transport a careful balance must be struck between the optimal mesh adaptation, the nonlinear iteration method and the time-stepping procedure. More theoretical research is needed with this regard.
NASA Astrophysics Data System (ADS)
Gill, Stuart P. D.; Knebe, Alexander; Gibson, Brad K.; Flynn, Chris; Ibata, Rodrigo A.; Lewis, Geraint F.
2003-04-01
An adaptive multi grid approach to simulating the formation of structure from collisionless dark matter is described. MLAPM (Multi-Level Adaptive Particle Mesh) is one of the most efficient serial codes available on the cosmological "market" today. As part of Swinburne University's role in the development of the Square Kilometer Array, we are implementing hydrodynamics, feedback, and radiative transfer within the MLAPM adaptive mesh, in order to simulate baryonic processes relevant to the interstellar and intergalactic media at high redshift. We will outline our progress to date in applying the existing MLAPM to a study of the decay of satellite galaxies within massive host potentials.
NASA Astrophysics Data System (ADS)
Innocenti, Maria Elena; Beck, Arnaud; Markidis, Stefano; Lapenta, Giovanni
2013-10-01
Particle in Cell (PIC) simulations of plasmas are not bound anymore by the stability constraints of explicit algorithms. Semi implicit and fully implicit methods allow to use larger grid spacings and time steps. Adaptive Mesh Refinement (AMR) techniques permit to locally change the simulation resolution. The code proposed in Innocenti et al., 2013 and Beck et al., 2013 is however the first to combine the advantages of both. The use of the Implicit Moment Method allows to taylor the resolution used in each level to the physical scales of interest and to use high Refinement Factors (RF) between the levels. The Multi Level Multi Domain (MLMD) structure, where all levels are simulated as complete domains, conjugates algorithmic and practical advantages. The different levels evolve according to the local dynamics and achieve optimal level interlocking. Also, the capabilities of the Object Oriented programming model are fully exploited. The MLMD algorithm is demonstrated with magnetic reconnection and collisionless shocks simulations with very high RFs between the levels. Notable computational gains are achieved with respect to simulations performed on the entire domain with the higher resolution. Beck A. et al. (2013). submitted. Innocenti M. E. et al. (2013). JCP, 238(0):115-140.
New Approach for IIR Adaptive Lattice Filter Structure Using Simultaneous Perturbation Algorithm
NASA Astrophysics Data System (ADS)
Martinez, Jorge Ivan Medina; Nakano, Kazushi; Higuchi, Kohji
Adaptive infinite impulse response (IIR), or recursive, filters are less attractive mainly because of the stability and the difficulties associated with their adaptive algorithms. Therefore, in this paper the adaptive IIR lattice filters are studied in order to devise algorithms that preserve the stability of the corresponding direct-form schemes. We analyze the local properties of stationary points, a transformation achieving this goal is suggested, which gives algorithms that can be efficiently implemented. Application to the Steiglitz-McBride (SM) and Simple Hyperstable Adaptive Recursive Filter (SHARF) algorithms is presented. Also a modified version of Simultaneous Perturbation Stochastic Approximation (SPSA) is presented in order to get the coefficients in a lattice form more efficiently and with a lower computational cost and complexity. The results are compared with previous lattice versions of these algorithms. These previous lattice versions may fail to preserve the stability of stationary points.
Estimating Position of Mobile Robots From Omnidirectional Vision Using an Adaptive Algorithm.
Li, Luyang; Liu, Yun-Hui; Wang, Kai; Fang, Mu
2015-08-01
This paper presents a novel and simple adaptive algorithm for estimating the position of a mobile robot with high accuracy in an unknown and unstructured environment by fusing images of an omnidirectional vision system with measurements of odometry and inertial sensors. Based on a new derivation where the omnidirectional projection can be linearly parameterized by the positions of the robot and natural feature points, we propose a novel adaptive algorithm, which is similar to the Slotine-Li algorithm in model-based adaptive control, to estimate the robot's position by using the tracked feature points in image sequence, the robot's velocity, and orientation angles measured by odometry and inertial sensors. It is proved that the adaptive algorithm leads to global exponential convergence of the position estimation errors to zero. Simulations and real-world experiments are performed to demonstrate the performance of the proposed algorithm. PMID:25265622
The design and application of upwind schemes on unstructured meshes
NASA Technical Reports Server (NTRS)
Barth, Timothy J.; Jespersen, Dennis C.
1989-01-01
Solution and mesh generation algorithms for solving the Euler equations on unstructured meshes consisting of triangle and quadrilateral control volumes are presented. Cell-centered and mesh-vertex upwind finite-volume schemes are developed which utilize multi-dimensional monotone linear reconstruction procedures. These algorithms differ from existing algorithms (even on structured meshes). Numerical results in two dimensions are presented.
Self-Avoiding Walks over Adaptive Triangular Grids
NASA Technical Reports Server (NTRS)
Heber, Gerd; Biswas, Rupak; Gao, Guang R.; Saini, Subhash (Technical Monitor)
1998-01-01
In this paper, we present a new approach to constructing a "self-avoiding" walk through a triangular mesh. Unlike the popular approach of visiting mesh elements using space-filling curves which is based on a geometric embedding, our approach is combinatorial in the sense that it uses the mesh connectivity only. We present an algorithm for constructing a self-avoiding walk which can be applied to any unstructured triangular mesh. The complexity of the algorithm is O(n x log(n)), where n is the number of triangles in the mesh. We show that for hierarchical adaptive meshes, the algorithm can be easily parallelized by taking advantage of the regularity of the refinement rules. The proposed approach should be very useful in the run-time partitioning and load balancing of adaptive unstructured grids.
An Adaptive Digital Image Watermarking Algorithm Based on Morphological Haar Wavelet Transform
NASA Astrophysics Data System (ADS)
Huang, Xiaosheng; Zhao, Sujuan
At present, much more of the wavelet-based digital watermarking algorithms are based on linear wavelet transform and fewer on non-linear wavelet transform. In this paper, we propose an adaptive digital image watermarking algorithm based on non-linear wavelet transform--Morphological Haar Wavelet Transform. In the algorithm, the original image and the watermark image are decomposed with multi-scale morphological wavelet transform respectively. Then the watermark information is adaptively embedded into the original image in different resolutions, combining the features of Human Visual System (HVS). The experimental results show that our method is more robust and effective than the ordinary wavelet transform algorithms.
Comparative study of adaptive-noise-cancellation algorithms for intrusion detection systems
Claassen, J.P.; Patterson, M.M.
1981-01-01
Some intrusion detection systems are susceptible to nonstationary noise resulting in frequent nuisance alarms and poor detection when the noise is present. Adaptive inverse filtering for single channel systems and adaptive noise cancellation for two channel systems have both demonstrated good potential in removing correlated noise components prior detection. For such noise susceptible systems the suitability of a noise reduction algorithm must be established in a trade-off study weighing algorithm complexity against performance. The performance characteristics of several distinct classes of algorithms are established through comparative computer studies using real signals. The relative merits of the different algorithms are discussed in the light of the nature of intruder and noise signals.
Binocular self-calibration performed via adaptive genetic algorithm based on laser line imaging
NASA Astrophysics Data System (ADS)
Apolinar Muñoz Rodríguez, J.; Mejía Alanís, Francisco Carlos
2016-07-01
An accurate technique to perform binocular self-calibration by means of an adaptive genetic algorithm based on a laser line is presented. In this calibration, the genetic algorithm computes the vision parameters through simulated binary crossover (SBX). To carry it out, the genetic algorithm constructs an objective function from the binocular geometry of the laser line projection. Then, the SBX minimizes the objective function via chromosomes recombination. In this algorithm, the adaptive procedure determines the search space via line position to obtain the minimum convergence. Thus, the chromosomes of vision parameters provide the minimization. The approach of the proposed adaptive genetic algorithm is to calibrate and recalibrate the binocular setup without references and physical measurements. This procedure leads to improve the traditional genetic algorithms, which calibrate the vision parameters by means of references and an unknown search space. It is because the proposed adaptive algorithm avoids errors produced by the missing of references. Additionally, the three-dimensional vision is carried out based on the laser line position and vision parameters. The contribution of the proposed algorithm is corroborated by an evaluation of accuracy of binocular calibration, which is performed via traditional genetic algorithms.
A novel algorithm for real-time adaptive signal detection and identification
Sleefe, G.E.; Ladd, M.D.; Gallegos, D.E.; Sicking, C.W.; Erteza, I.A.
1998-04-01
This paper describes a novel digital signal processing algorithm for adaptively detecting and identifying signals buried in noise. The algorithm continually computes and updates the long-term statistics and spectral characteristics of the background noise. Using this noise model, a set of adaptive thresholds and matched digital filters are implemented to enhance and detect signals that are buried in the noise. The algorithm furthermore automatically suppresses coherent noise sources and adapts to time-varying signal conditions. Signal detection is performed in both the time-domain and the frequency-domain, thereby permitting the detection of both broad-band transients and narrow-band signals. The detection algorithm also provides for the computation of important signal features such as amplitude, timing, and phase information. Signal identification is achieved through a combination of frequency-domain template matching and spectral peak picking. The algorithm described herein is well suited for real-time implementation on digital signal processing hardware. This paper presents the theory of the adaptive algorithm, provides an algorithmic block diagram, and demonstrate its implementation and performance with real-world data. The computational efficiency of the algorithm is demonstrated through benchmarks on specific DSP hardware. The applications for this algorithm, which range from vibration analysis to real-time image processing, are also discussed.
Quality Tetrahedral Mesh Smoothing via Boundary-Optimized Delaunay Triangulation
Gao, Zhanheng; Yu, Zeyun; Holst, Michael
2012-01-01
Despite its great success in improving the quality of a tetrahedral mesh, the original optimal Delaunay triangulation (ODT) is designed to move only inner vertices and thus cannot handle input meshes containing “bad” triangles on boundaries. In the current work, we present an integrated approach called boundary-optimized Delaunay triangulation (B-ODT) to smooth (improve) a tetrahedral mesh. In our method, both inner and boundary vertices are repositioned by analytically minimizing the error between a paraboloid function and its piecewise linear interpolation over the neighborhood of each vertex. In addition to the guaranteed volume-preserving property, the proposed algorithm can be readily adapted to preserve sharp features in the original mesh. A number of experiments are included to demonstrate the performance of our method. PMID:23144522
Quality Tetrahedral Mesh Smoothing via Boundary-Optimized Delaunay Triangulation.
Gao, Zhanheng; Yu, Zeyun; Holst, Michael
2012-12-01
Despite its great success in improving the quality of a tetrahedral mesh, the original optimal Delaunay triangulation (ODT) is designed to move only inner vertices and thus cannot handle input meshes containing "bad" triangles on boundaries. In the current work, we present an integrated approach called boundary-optimized Delaunay triangulation (B-ODT) to smooth (improve) a tetrahedral mesh. In our method, both inner and boundary vertices are repositioned by analytically minimizing the error between a paraboloid function and its piecewise linear interpolation over the neighborhood of each vertex. In addition to the guaranteed volume-preserving property, the proposed algorithm can be readily adapted to preserve sharp features in the original mesh. A number of experiments are included to demonstrate the performance of our method. PMID:23144522
Application of Quaternions for Mesh Deformation
NASA Technical Reports Server (NTRS)
Samareh, Jamshid A.
2002-01-01
A new three-dimensional mesh deformation algorithm, based on quaternion algebra, is introduced. A brief overview of quaternion algebra is provided, along with some preliminary results for two-dimensional structured and unstructured viscous mesh deformation.
Adaptive Load-Balancing Algorithms using Symmetric Broadcast Networks
NASA Technical Reports Server (NTRS)
Das, Sajal K.; Harvey, Daniel J.; Biswas, Rupak; Biegel, Bryan A. (Technical Monitor)
2002-01-01
In a distributed computing environment, it is important to ensure that the processor workloads are adequately balanced, Among numerous load-balancing algorithms, a unique approach due to Das and Prasad defines a symmetric broadcast network (SBN) that provides a robust communication pattern among the processors in a topology-independent manner. In this paper, we propose and analyze three efficient SBN-based dynamic load-balancing algorithms, and implement them on an SGI Origin2000. A thorough experimental study with Poisson distributed synthetic loads demonstrates that our algorithms are effective in balancing system load. By optimizing completion time and idle time, the proposed algorithms are shown to compare favorably with several existing approaches.
Design and analysis of closed-loop decoder adaptation algorithms for brain-machine interfaces.
Dangi, Siddharth; Orsborn, Amy L; Moorman, Helene G; Carmena, Jose M
2013-07-01
Closed-loop decoder adaptation (CLDA) is an emerging paradigm for achieving rapid performance improvements in online brain-machine interface (BMI) operation. Designing an effective CLDA algorithm requires making multiple important decisions, including choosing the timescale of adaptation, selecting which decoder parameters to adapt, crafting the corresponding update rules, and designing CLDA parameters. These design choices, combined with the specific settings of CLDA parameters, will directly affect the algorithm's ability to make decoder parameters converge to values that optimize performance. In this article, we present a general framework for the design and analysis of CLDA algorithms and support our results with experimental data of two monkeys performing a BMI task. First, we analyze and compare existing CLDA algorithms to highlight the importance of four critical design elements: the adaptation timescale, selective parameter adaptation, smooth decoder updates, and intuitive CLDA parameters. Second, we introduce mathematical convergence analysis using measures such as mean-squared error and KL divergence as a useful paradigm for evaluating the convergence properties of a prototype CLDA algorithm before experimental testing. By applying these measures to an existing CLDA algorithm, we demonstrate that our convergence analysis is an effective analytical tool that can ultimately inform and improve the design of CLDA algorithms. PMID:23607558
Self-Avoiding Walks Over Adaptive Triangular Grids
NASA Technical Reports Server (NTRS)
Heber, Gerd; Biswas, Rupak; Gao, Guang R.; Saini, Subhash (Technical Monitor)
1999-01-01
Space-filling curves is a popular approach based on a geometric embedding for linearizing computational meshes. We present a new O(n log n) combinatorial algorithm for constructing a self avoiding walk through a two dimensional mesh containing n triangles. We show that for hierarchical adaptive meshes, the algorithm can be locally adapted and easily parallelized by taking advantage of the regularity of the refinement rules. The proposed approach should be very useful in the runtime partitioning and load balancing of adaptive unstructured grids.
Tangle-Free Mesh Motion for Ablation Simulations
NASA Technical Reports Server (NTRS)
Droba, Justin
2016-01-01
Problems involving mesh motion-which should not be mistakenly associated with moving mesh methods, a class of adaptive mesh redistribution techniques-are of critical importance in numerical simulations of the thermal response of melting and ablative materials. Ablation is the process by which material vaporizes or otherwise erodes due to strong heating. Accurate modeling of such materials is of the utmost importance in design of passive thermal protection systems ("heatshields") for spacecraft, the layer of the vehicle that ensures survival of crew and craft during re-entry. In an explicit mesh motion approach, a complete thermal solve is first performed. Afterwards, the thermal response is used to determine surface recession rates. These values are then used to generate boundary conditions for an a posteriori correction designed to update the location of the mesh nodes. Most often, linear elastic or biharmonic equations are used to model this material response, traditionally in a finite element framework so that complex geometries can be simulated. A simple scheme for moving the boundary nodes involves receding along the surface normals. However, for all but the simplest problem geometries, evolution in time following such a scheme will eventually bring the mesh to intersect and "tangle" with itself, inducing failure. This presentation demonstrates a comprehensive and sophisticated scheme that analyzes the local geometry of each node with help from user-provided clues to eliminate the tangle and enable simulations on a wide-class of difficult problem geometries. The method developed is demonstrated for linear elastic equations but is general enough that it may be adapted to other modeling equations. The presentation will explicate the inner workings of the tangle-free mesh motion algorithm for both two and three-dimensional meshes. It will show abstract examples of the method's success, including a verification problem that demonstrates its accuracy and
NASA Astrophysics Data System (ADS)
Leihong, Zhang; Dong, Liang; Bei, Li; Yi, Kang; Zilan, Pan; Dawei, Zhang; Xiuhua, Ma
2016-04-01
In order to improve the reconstruction accuracy and reduce the workload, the algorithm of compressive sensing based on the iterative threshold is combined with the method of adaptive selection of the training sample, and a new algorithm of adaptive compressive sensing is put forward. The three kinds of training sample are used to reconstruct the spectral reflectance of the testing sample based on the compressive sensing algorithm and adaptive compressive sensing algorithm, and the color difference and error are compared. The experiment results show that spectral reconstruction precision based on the adaptive compressive sensing algorithm is better than that based on the algorithm of compressive sensing.
Greenough, Jeffrey A.; de Supinski, Bronis R.; Yates, Robert K.; Rendleman, Charles A.; Skinner, David; Beckner, Vince; Lijewski, Mike; Bell, John; Sexton, James C.
2005-04-25
We describe the performance of the block-structured Adaptive Mesh Refinement (AMR) code Raptor on the 32k node IBM BlueGene/L computer. This machine represents a significant step forward towards petascale computing. As such, it presents Raptor with many challenges for utilizing the hardware efficiently. In terms of performance, Raptor shows excellent weak and strong scaling when running in single level mode (no adaptivity). Hardware performance monitors show Raptor achieves an aggregate performance of 3:0 Tflops in the main integration kernel on the 32k system. Results from preliminary AMR runs on a prototype astrophysical problem demonstrate the efficiency of the current software when running at large scale. The BG/L system is enabling a physics problem to be considered that represents a factor of 64 increase in overall size compared to the largest ones of this type computed to date. Finally, we provide a description of the development work currently underway to address our inefficiencies.
A hybrid adaptive routing algorithm for event-driven wireless sensor networks.
Figueiredo, Carlos M S; Nakamura, Eduardo F; Loureiro, Antonio A F
2009-01-01
Routing is a basic function in wireless sensor networks (WSNs). For these networks, routing algorithms depend on the characteristics of the applications and, consequently, there is no self-contained algorithm suitable for every case. In some scenarios, the network behavior (traffic load) may vary a lot, such as an event-driven application, favoring different algorithms at different instants. This work presents a hybrid and adaptive algorithm for routing in WSNs, called Multi-MAF, that adapts its behavior autonomously in response to the variation of network conditions. In particular, the proposed algorithm applies both reactive and proactive strategies for routing infrastructure creation, and uses an event-detection estimation model to change between the strategies and save energy. To show the advantages of the proposed approach, it is evaluated through simulations. Comparisons with independent reactive and proactive algorithms show improvements on energy consumption. PMID:22423207
Zhang, Zhihua; Sheng, Zheng; Shi, Hanqing; Fan, Zhiqiang
2016-01-01
Using the RFC technique to estimate refractivity parameters is a complex nonlinear optimization problem. In this paper, an improved cuckoo search (CS) algorithm is proposed to deal with this problem. To enhance the performance of the CS algorithm, a parameter dynamic adaptive operation and crossover operation were integrated into the standard CS (DACS-CO). Rechenberg's 1/5 criteria combined with learning factor were used to control the parameter dynamic adaptive adjusting process. The crossover operation of genetic algorithm was utilized to guarantee the population diversity. The new hybrid algorithm has better local search ability and contributes to superior performance. To verify the ability of the DACS-CO algorithm to estimate atmospheric refractivity parameters, the simulation data and real radar clutter data are both implemented. The numerical experiments demonstrate that the DACS-CO algorithm can provide an effective method for near-real-time estimation of the atmospheric refractivity profile from radar clutter. PMID:27212938
Zhang, Zhihua; Sheng, Zheng; Shi, Hanqing; Fan, Zhiqiang
2016-01-01
Using the RFC technique to estimate refractivity parameters is a complex nonlinear optimization problem. In this paper, an improved cuckoo search (CS) algorithm is proposed to deal with this problem. To enhance the performance of the CS algorithm, a parameter dynamic adaptive operation and crossover operation were integrated into the standard CS (DACS-CO). Rechenberg's 1/5 criteria combined with learning factor were used to control the parameter dynamic adaptive adjusting process. The crossover operation of genetic algorithm was utilized to guarantee the population diversity. The new hybrid algorithm has better local search ability and contributes to superior performance. To verify the ability of the DACS-CO algorithm to estimate atmospheric refractivity parameters, the simulation data and real radar clutter data are both implemented. The numerical experiments demonstrate that the DACS-CO algorithm can provide an effective method for near-real-time estimation of the atmospheric refractivity profile from radar clutter. PMID:27212938
SIMULATION OF DISPERSION OF A POWER PLANT PLUME USING AN ADAPTIVE GRID ALGORITHM
A new dynamic adaptive grid algorithm has been developed for use in air quality modeling. This algorithm uses a higher order numerical scheme?the piecewise parabolic method (PPM)?for computing advective solution fields; a weight function capable of promoting grid node clustering ...