AnisWave2D: User's Guide to the 2d Anisotropic Finite-DifferenceCode
Toomey, Aoife
2005-01-06
This document describes a parallel finite-difference code for modeling wave propagation in 2D, fully anisotropic materials. The code utilizes a mesh refinement scheme to improve computational efficiency. Mesh refinement allows the grid spacing to be tailored to the velocity model, so that fine grid spacing can be used in low velocity zones where the seismic wavelength is short, and coarse grid spacing can be used in zones with higher material velocities. Over-sampling of the seismic wavefield in high velocity zones is therefore avoided. The code has been implemented to run in parallel over multiple processors and allows large-scale models and models with large velocity contrasts to be simulated with ease.
Finite Temperature Response of a 2D Dipolar Bose Gas at Different Dipolar Tilt Angles
NASA Astrophysics Data System (ADS)
Shen, Pengtao; Quader, Khandker
We calculate finite temperature (T) response of a 2D Bose gas, subject to dipolar interaction, within the random phase approximation (RPA). We evaluate the appropriate 2D finite-T pair bubble diagram needed in RPA, and explore ranges of density and temperature for various dipolar tilt angles. We find the system to exhibit a collapse transition and a finite momentum instability, signaling a density wave or striped phase. We construct phase diagrams depicting these instabilities and resulting phases, including a normal Bose gas phase. We also consider the finite-T response of a quasi-2D dipolar Bose gas. We discuss how our results may apply to ultracold dense Bose gas of polar molecules, such as 41K87Rb, that has been realized experimentally. Acknowledge partial support from Institute for Complex Adaptive Matter (ICAM).
2D time-domain finite-difference modeling for viscoelastic seismic wave propagation
NASA Astrophysics Data System (ADS)
Fan, Na; Zhao, Lian-Feng; Xie, Xiao-Bi; Ge, Zengxi; Yao, Zhen-Xing
2016-07-01
Real Earth media are not perfectly elastic. Instead, they attenuate propagating mechanical waves. This anelastic phenomenon in wave propagation can be modeled by a viscoelastic mechanical model consisting of several standard linear solids. Using this viscoelastic model, we approximate a constant Q over a frequency band of interest. We use a four-element viscoelastic model with a tradeoff between accuracy and computational costs to incorporate Q into 2D time-domain first-order velocity-stress wave equations. To improve the computational efficiency, we limit the Q in the model to a list of discrete values between 2 and 1000. The related stress and strain relaxation times that characterize the viscoelastic model are pre-calculated and stored in a database for use by the finite-difference calculation. A viscoelastic finite-difference scheme that is second-order in time and fourth-order in space is developed based on the MacCormack algorithm. The new method is validated by comparing the numerical result with analytical solutions that are calculated using the generalized reflection/transmission coefficient method. The synthetic seismograms exhibit greater than 95 per cent consistency in a two-layer viscoelastic model. The dispersion generated from the simulation is consistent with the Kolsky-Futterman dispersion relationship.
Optimal implicit 2-D finite differences to model wave propagation in poroelastic media
NASA Astrophysics Data System (ADS)
Itzá, Reymundo; Iturrarán-Viveros, Ursula; Parra, Jorge O.
2016-05-01
Numerical modeling of seismic waves in heterogeneous porous reservoir rocks is an important tool for the interpretation of seismic surveys in reservoir engineering. We apply globally optimal implicit staggered-grid finite-differences to model 2-D wave propagation in heterogeneous poroelastic media at a low-frequency range (<10kHz). We validate the numerical solution by comparing it to an analytical-transient solution obtaining clear seismic wavefields including fast P, slow P and S waves (for a porous media saturated with fluid). The numerical dispersion and stability conditions are derived using von Neumann analysis, showing that over a wide range of porous materials the Courant condition governs the stability and this optimal implicit scheme improves the stability of explicit schemes. High order explicit finite-differences (FD) can be replaced by some lower order optimal implicit FD so computational cost will not be as expensive while maintaining the accuracy. Here we compute weights for the optimal implicit FD scheme to attain an accuracy of γ = 10-8. The implicit spatial differentiation involves solving tridiagonal linear systems of equations through Thomas' algorithm.
Simulations of SH wave scattering due to cracks by the 2-D finite difference method
NASA Astrophysics Data System (ADS)
Suzuki, Y.; Kawahara, J.; Okamoto, T.; Miyashita, K.
2006-05-01
We simulate SH wave scattering by 2-D parallel cracks using the finite difference method (FDM), instead of the popularly used boundary integral equation method (BIEM). Here special emphasis is put on simplicity; we apply a standard FDM (fourth-order velocity-stress scheme with a staggered grid) to media in cluding traction-freecracks, which are expressed by arrays of grid points with zero traction. Two types of accuracy tests based oncomparison with a reliable BIEM, suggest that the present method gives practically sufficient accuracy, except for the wavefields in the vicinity of cracks, which can be well handled if the second-order FDM is used instead. As an application of this method, we also simulate wave propagation in media with randomly distributed cracks of the same length. We experimentally determine the attenuation and velocity dispersion induced by scattering from the synthetic seismograms, using a waveform averaging technique. It is shown that the results are well explained by a theory based on the Foldy approximation for crack densities of up to about 01. The presence of a free surface does not affect the validity of the theory. A preliminary experiment also suggests that the validity will not change even for multi-scale cracks.
Optimal implicit 2-D finite differences to model wave propagation in poroelastic media
NASA Astrophysics Data System (ADS)
Itzá, Reymundo; Iturrarán-Viveros, Ursula; Parra, Jorge O.
2016-08-01
Numerical modeling of seismic waves in heterogeneous porous reservoir rocks is an important tool for the interpretation of seismic surveys in reservoir engineering. We apply globally optimal implicit staggered-grid finite differences (FD) to model 2-D wave propagation in heterogeneous poroelastic media at a low-frequency range (<10 kHz). We validate the numerical solution by comparing it to an analytical-transient solution obtaining clear seismic wavefields including fast P and slow P and S waves (for a porous media saturated with fluid). The numerical dispersion and stability conditions are derived using von Neumann analysis, showing that over a wide range of porous materials the Courant condition governs the stability and this optimal implicit scheme improves the stability of explicit schemes. High-order explicit FD can be replaced by some lower order optimal implicit FD so computational cost will not be as expensive while maintaining the accuracy. Here, we compute weights for the optimal implicit FD scheme to attain an accuracy of γ = 10-8. The implicit spatial differentiation involves solving tridiagonal linear systems of equations through Thomas' algorithm.
NASA Astrophysics Data System (ADS)
Guan, Zhen; Heinonen, Vili; Lowengrub, John; Wang, Cheng; Wise, Steven M.
2016-09-01
In this paper we construct an energy stable finite difference scheme for the amplitude expansion equations for the two-dimensional phase field crystal (PFC) model. The equations are formulated in a periodic hexagonal domain with respect to the reciprocal lattice vectors to achieve a provably unconditionally energy stable and solvable scheme. To our knowledge, this is the first such energy stable scheme for the PFC amplitude equations. The convexity of each part in the amplitude equations is analyzed, in both the semi-discrete and fully-discrete cases. Energy stability is based on a careful convexity analysis for the energy (in both the spatially continuous and discrete cases). As a result, unique solvability and unconditional energy stability are available for the resulting scheme. Moreover, we show that the scheme is point-wise stable for any time and space step sizes. An efficient multigrid solver is devised to solve the scheme, and a few numerical experiments are presented, including grain rotation and shrinkage and grain growth studies, as examples of the strength and robustness of the proposed scheme and solver.
A convergent 2D finite-difference scheme for the Dirac–Poisson system and the simulation of graphene
Brinkman, D.; Heitzinger, C.; Markowich, P.A.
2014-01-15
We present a convergent finite-difference scheme of second order in both space and time for the 2D electromagnetic Dirac equation. We apply this method in the self-consistent Dirac–Poisson system to the simulation of graphene. The model is justified for low energies, where the particles have wave vectors sufficiently close to the Dirac points. In particular, we demonstrate that our method can be used to calculate solutions of the Dirac–Poisson system where potentials act as beam splitters or Veselago lenses.
High Order Finite Difference Methods with Subcell Resolution for 2D Detonation Waves
NASA Technical Reports Server (NTRS)
Wang, W.; Shu, C. W.; Yee, H. C.; Sjogreen, B.
2012-01-01
In simulating hyperbolic conservation laws in conjunction with an inhomogeneous stiff source term, if the solution is discontinuous, spurious numerical results may be produced due to different time scales of the transport part and the source term. This numerical issue often arises in combustion and high speed chemical reacting flows.
Simulations of P-SV wave scattering due to cracks by the 2-D finite difference method
NASA Astrophysics Data System (ADS)
Suzuki, Yuji; Shiina, Takahiro; Kawahara, Jun; Okamoto, Taro; Miyashita, Kaoru
2013-12-01
We simulate P-SV wave scattering by 2-D parallel cracks using the finite difference method (FDM). Here, special emphasis is put on simplicity; we apply a standard FDM (second-order velocity-stress scheme with a staggered grid) to media including traction-free, infinitesimally thin cracks, which are expressed in a simple manner. As an accuracy test of the present method, we calculate the displacement discontinuity along an isolated crack caused by harmonic waves using the method, which is compared with the corresponding results based on a reliable boundary integral equation method. The test resultantly indicates that the present method yields sufficient accuracy. As an application of this method, we also simulate wave propagation in media with randomly distributed cracks. We experimentally determine the attenuation and velocity dispersion induced by scattering from the synthetic seismograms, using a waveform averaging technique. It is shown that the results are well explained by a theory based on the Foldy approximation, if the crack density is sufficiently low. The theory appears valid with a crack density up to at least 0.1 for SV wave incidence, whereas the validity limit appears lower for P wave incidence.
NASA Astrophysics Data System (ADS)
Martowicz, A.; Ruzzene, M.; Staszewski, W. J.; Rimoli, J. J.; Uhl, T.
2014-03-01
The work deals with the reduction of numerical dispersion in simulations of wave propagation in solids. The phenomenon of numerical dispersion naturally results from time and spatial discretization present in a numerical model of mechanical continuum. Although discretization itself makes possible to model wave propagation in structures with complicated geometries and made of different materials, it inevitably causes simulation errors when improper time and length scales are chosen for the simulations domains. Therefore, by definition, any characteristic parameter for spatial and time resolution must create limitations on maximal wavenumber and frequency for a numerical model. It should be however noted that expected increase of the model quality and its functionality in terms of affordable wavenumbers, frequencies and speeds should not be achieved merely by denser mesh and reduced time integration step. The computational cost would be simply unacceptable. The authors present a nonlocal finite difference scheme with the coefficients calculated applying a Fourier series, which allows for considerable reduction of numerical dispersion. There are presented the results of analyses for 2D models, with isotropic and anisotropic materials, fulfilling the planar stress state. Reduced numerical dispersion is shown in the dispersion surfaces for longitudinal and shear waves propagating for different directions with respect to the mesh orientation and without dramatic increase of required number of nonlocal interactions. A case with the propagation of longitudinal wave in composite material is studied with given referential solution of the initial value problem for verification of the time-domain outcomes. The work gives a perspective of modeling of any type of real material dispersion according to measurements and with assumed accuracy.
NASA Astrophysics Data System (ADS)
Wang, Enjiang; Liu, Yang; Sen, Mrinal K.
2016-07-01
The 2D acoustic wave equation is commonly solved numerically by finite-difference (FD) methods in which the accuracy of solution is significantly affected by the FD stencils. The commonly used cross stencil can reach either only second-order accuracy for space domain dispersion-relation-based FD method or (2 M)th-order accuracy along eight specific propagation directions for time-space domain dispersion-relation-based FD method, if the conventional (2 M)th-order spatial FD and second-order temporal FD are used to discretize the equation. One other newly developed rhombus stencil can reach arbitrary even-order accuracy. However, this stencil adds significantly computational cost when the operator length is large. To achieve a balance between the solution accuracy and efficiency, we develop a new FD stencil to solve the 2D acoustic wave equation. This stencil is a combination of the cross stencil and rhombus stencil. A cross stencil with an operator length parameter M is used to approximate the spatial partial derivatives while a rhombus stencil with an operator length parameter N together with the conventional 2nd-order temporal FD is employed in approximating the temporal partial derivatives. Using this stencil, a new FD scheme is developed; we demonstrate that this scheme can reach (2 M)th-order accuracy in space and (2 N)th-order accuracy in time when spatial FD coefficients and temporal FD coefficients are derived from respective dispersion relation using Taylor-series expansion (TE) method. To further increase the accuracy, we derive the FD coefficients by employing the time-space domain dispersion relation of this FD scheme using TE. We also use least-squares (LS) optimization method to reduce dispersion at high wavenumbers. Dispersion analysis, stability analysis and modelling examples demonstrate that our new scheme has greater accuracy and better stability than conventional FD schemes, and thus can adopt large time steps. To reduce the extra computational
2-d Finite Element Code Postprocessor
Energy Science and Technology Software Center (ESTSC)
1996-07-15
ORION is an interactive program that serves as a postprocessor for the analysis programs NIKE2D, DYNA2D, TOPAZ2D, and CHEMICAL TOPAZ2D. ORION reads binary plot files generated by the two-dimensional finite element codes currently used by the Methods Development Group at LLNL. Contour and color fringe plots of a large number of quantities may be displayed on meshes consisting of triangular and quadrilateral elements. ORION can compute strain measures, interface pressures along slide lines, reaction forcesmore » along constrained boundaries, and momentum. ORION has been applied to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.« less
NASA Astrophysics Data System (ADS)
Choi, S.-J.; Giraldo, F. X.; Kim, J.; Shin, S.
2014-11-01
The non-hydrostatic (NH) compressible Euler equations for dry atmosphere were solved in a simplified two-dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and a finite difference method (FDM) for the vertical discretization. By using horizontal SEM, which decomposes the physical domain into smaller pieces with a small communication stencil, a high level of scalability can be achieved. By using vertical FDM, an easy method for coupling the dynamics and existing physics packages can be provided. The SEM uses high-order nodal basis functions associated with Lagrange polynomials based on Gauss-Lobatto-Legendre (GLL) quadrature points. The FDM employs a third-order upwind-biased scheme for the vertical flux terms and a centered finite difference scheme for the vertical derivative and integral terms. For temporal integration, a time-split, third-order Runge-Kutta (RK3) integration technique was applied. The Euler equations that were used here are in flux form based on the hydrostatic pressure vertical coordinate. The equations are the same as those used in the Weather Research and Forecasting (WRF) model, but a hybrid sigma-pressure vertical coordinate was implemented in this model. We validated the model by conducting the widely used standard tests: linear hydrostatic mountain wave, tracer advection, and gravity wave over the Schär-type mountain, as well as density current, inertia-gravity wave, and rising thermal bubble. The results from these tests demonstrated that the model using the horizontal SEM and the vertical FDM is accurate and robust provided sufficient diffusion is applied. The results with various horizontal resolutions also showed convergence of second-order accuracy due to the accuracy of the time integration scheme and that of the vertical direction, although high-order basis functions were used in the horizontal. By using the 2-D slice model, we effectively showed that the combined spatial
NASA Technical Reports Server (NTRS)
Gelinas, R. J.; Doss, S. K.; Vajk, J. P.; Djomehri, J.; Miller, K.
1983-01-01
The mathematical background regarding the moving finite element (MFE) method of Miller and Miller (1981) is discussed, taking into account a general system of partial differential equations (PDE) and the amenability of the MFE method in two dimensions to code modularization and to semiautomatic user-construction of numerous PDE systems for both Dirichlet and zero-Neumann boundary conditions. A description of test problem results is presented, giving attention to aspects of single square wave propagation, and a solution of the heat equation.
2-D Finite Element Heat Conduction
Energy Science and Technology Software Center (ESTSC)
1989-10-30
AYER is a finite element program which implicitly solves the general two-dimensional equation of thermal conduction for plane or axisymmetric bodies. AYER takes into account the effects of time (transient problems), in-plane anisotropic thermal conductivity, a three-dimensional velocity distribution, and interface thermal contact resistance. Geometry and material distributions are arbitrary, and input is via subroutines provided by the user. As a result, boundary conditions, material properties, velocity distributions, and internal power generation may be mademore » functions of, e.g., time, temperature, location, and heat flux.« less
Finite Element Analysis of 2-D Elastic Contacts Involving FGMs
NASA Astrophysics Data System (ADS)
Abhilash, M. N.; Murthy, H.
2014-05-01
The response of elastic indenters in contact with Functionally Graded Material (FGM) coated homogeneous elastic half space has been presented in the current paper. Finite element analysis has been used due to its ability to handle complex geometry, material, and boundary conditions. Indenters of different typical surface profiles have been considered and the problem has been idealized as a two-dimensional (2D) plane strain problem considering only normal loads. Initially, indenters were considered to be rigid and the results were validated with the solutions presented in the literature. The analysis has then been extended to the case of elastic indenters on FGM-coated half spaces and the results are discussed.
Automatic differentiation of the TACO2D finite element code using ADIFOR
Carle, A.; Fagan, M.
1996-04-01
The need for sensitivities in particular applications is becoming increasingly important in problems such as optimal design or control. In this study, the authors use ADIFOR to generate derivative code for TACO2D, a finite element heat transfer code. The study of TACO2D indicates that ADIFOR-generated derivatives yield accurate derivatives at a fraction of the time requirements of finite difference approximations, and space requirements proportional to the number of variables. The primary focus on TACO2D was for the design of chemical vapor deposition reactors.
ELLIPT2D: A Flexible Finite Element Code Written Python
Pletzer, A.; Mollis, J.C.
2001-03-22
The use of the Python scripting language for scientific applications and in particular to solve partial differential equations is explored. It is shown that Python's rich data structure and object-oriented features can be exploited to write programs that are not only significantly more concise than their counter parts written in Fortran, C or C++, but are also numerically efficient. To illustrate this, a two-dimensional finite element code (ELLIPT2D) has been written. ELLIPT2D provides a flexible and easy-to-use framework for solving a large class of second-order elliptic problems. The program allows for structured or unstructured meshes. All functions defining the elliptic operator are user supplied and so are the boundary conditions, which can be of Dirichlet, Neumann or Robbins type. ELLIPT2D makes extensive use of dictionaries (hash tables) as a way to represent sparse matrices.Other key features of the Python language that have been widely used include: operator over loading, error handling, array slicing, and the Tkinter module for building graphical use interfaces. As an example of the utility of ELLIPT2D, a nonlinear solution of the Grad-Shafranov equation is computed using a Newton iterative scheme. A second application focuses on a solution of the toroidal Laplace equation coupled to a magnetohydrodynamic stability code, a problem arising in the context of magnetic fusion research.
Predicting Fracture Using 2D Finite Element Modeling
MacNeil, J.A.M.; Adachi, J.D; Goltzman, D; Josse, R.G; Kovacs, C.S; Prior, J.C; Olszynski, W; Davison, K.S.; Kaiser, S.M
2013-01-01
A decrease in bone density at the hip or spine has been shown to increase the risk of fracture. A limitation of the bone mineral density (BMD) measurement is that it provides only a measure of a bone samples average density when projected onto a 2D surface. Effectively, what determines bone fracture is whether an applied load exceeds ultimate strength, with both bone tissue material properties (can be approximated through bone density), and geometry playing a role. The goal of this project was to use bone geometry and BMD obtained from radiographs and DXA measurements respectively to estimate fracture risk, using a two-dimensional finite element model (FEM) of the sagittal plane of lumbar vertebrae. The Canadian Multicenter Osteoporosis Study (CaMos) data was used for this study. There were 4194 men and women over the age of 50 years, with 786 having fractures. Each subject had BMD testing and radiographs of their lumbar vertebrae. A single two dimensional FEM of the first to fourth lumbar vertebra was automatically generated for each subject. Bone tissue stiffness was assigned based on the BMD of the individual vertebrae, and adjusted for patient age. Axial compression boundary conditions were applied with a force proportional to body mass. The resulting overall strain from the applied force was found. Men and women were analyzed separately. At baseline, the sensitivity of BMD to predict fragility fractures in women and men was 3.77 % and 0.86 %, while the sensitivity of FEM to predict fragility fractures for women and men was 10.8 % and 11.3 %. The FEM ROC curve demonstrated better performance compared to BMD. The relative risk of being considered at high fracture risk using FEM at baseline, was a better predictor of 5 year incident fragility fracture risk compared to BMD. PMID:21959170
2D resistivity inversion using conjugate gradients for a finite element discretization
NASA Astrophysics Data System (ADS)
Bortolozo, C. A.; Santos, F. M.; Porsani, J. L.
2014-12-01
In this work we present a DC 2D inversion algorithm using conjugate gradients relaxation to solve the maximum likelihood inverse equations. We apply, according to Zhang (1995), the maximum likelihood inverse theory developed by Tarantola and Valette (1982) to our 2D resistivity inversion. This algorithm was chosen to this research because it doesn't need to calculate the field's derivatives. Since conjugate gradient techniques only need the results of the sensitivity matrix Ã or its transpose ÃT multiplying a vector, the actual computation of the sensitivity matrix are not performed, according to the methodology described in Zhang (1995). In Zhang (1995), the terms Ãx and ÃTy, are dependent of the stiffness matrix K and its partial derivative ∂K⁄∂ρ. The inversion methodology described in Zhang (1995) is for the case of 3D electrical resistivity by finite differences discretization. So it was necessary to make a series of adjustments to obtain a satisfactory result for 2D electrical inversion using finite element method. The difference between the modeling of 3D resistivity with finite difference and the 2D finite element method are in the integration variable, used in the 2D case. In the 2D case the electrical potential are initially calculated in the transformed domain, including the stiffness matrix, and only in the end is transformed in Cartesian domain. In the case of 3D, described by Zhang (1995) this is done differently, the calculation is done directly in the Cartesian domain. In the literature was not found any work describing how to deal with this problem. Because the calculations of Ãx and ÃTy must be done without having the real stiffness matrix, the adaptation consist in calculate the stiffness matrix and its partial derivative using a set of integration variables. We transform those matrix in the same form has in the potential case, but with different sets of variables. The results will be presented and are very promising.
Accurate Finite Difference Algorithms
NASA Technical Reports Server (NTRS)
Goodrich, John W.
1996-01-01
Two families of finite difference algorithms for computational aeroacoustics are presented and compared. All of the algorithms are single step explicit methods, they have the same order of accuracy in both space and time, with examples up to eleventh order, and they have multidimensional extensions. One of the algorithm families has spectral like high resolution. Propagation with high order and high resolution algorithms can produce accurate results after O(10(exp 6)) periods of propagation with eight grid points per wavelength.
Nonstandard finite difference schemes
NASA Technical Reports Server (NTRS)
Mickens, Ronald E.
1995-01-01
The major research activities of this proposal center on the construction and analysis of nonstandard finite-difference schemes for ordinary and partial differential equations. In particular, we investigate schemes that either have zero truncation errors (exact schemes) or possess other significant features of importance for numerical integration. Our eventual goal is to bring these methods to bear on problems that arise in the modeling of various physical, engineering, and technological systems. At present, these efforts are extended in the direction of understanding the exact nature of these nonstandard procedures and extending their use to more complicated model equations. Our presentation will give a listing (obtained to date) of the nonstandard rules, their application to a number of linear and nonlinear, ordinary and partial differential equations. In certain cases, numerical results will be presented.
Gross, M.B.
1984-10-01
STEALTH is a family of computer codes that can be used to calculate a variety of physical processes in which the dynamic behavior of a continuum is involved. The version of STEALTH described in this volume is designed for calculations of fluid-structure interaction. This version of the program consists of a hydrodynamic version of STEALTH which has been coupled to a finite-element code, WHAMSE. STEALTH computes the transient response of the fluid continuum, while WHAMSE computes the transient response of shell and beam structures under external fluid loadings. The coupling between STEALTH and WHAMSE is performed during each cycle or step of a calculation. Separate calculations of fluid response and structural response are avoided, thereby giving a more accurate model of the dynamic coupling between fluid and structure. This volume provides the theoretical background, the finite-difference equations, the finite-element equations, a discussion of several sample problems, a listing of the input decks for the sample problems, a programmer's manual and a description of the input records for the STEALTH/WHAMSE computer program.
Numerical method of crack analysis in 2D finite magnetoelectroelastic media
NASA Astrophysics Data System (ADS)
Zhao, Minghao; Xu, Guangtao; Fan, Cuiying
2010-04-01
The present paper extends the hybrid extended displacement discontinuity fundamental solution method (HEDD-FSM) (Eng Anal Bound Elem 33:592-600, 2009) to analysis of cracks in 2D finite magnetoelectroelastic media. The solution of the crack is expressed approximately by a linear combination of fundamental solutions of the governing equations, which includes the extended point force fundamental solutions with sources placed at chosen points outside the domain of the problem under consideration, and the extended Crouch fundamental solutions with extended displacement discontinuities placed on the crack. The coefficients of the fundamental solutions are determined by letting the approximated solution satisfy the prescribed boundary conditions on the boundary of the domain and on the crack face. The Crouch fundamental solution for a parabolic element at the crack tip is derived to model the square root variations of near tip fields. The extended stress intensity factors are calculated under different electric and magnetic boundary conditions.
A framework for grand scale parallelization of the combined finite discrete element method in 2d
NASA Astrophysics Data System (ADS)
Lei, Z.; Rougier, E.; Knight, E. E.; Munjiza, A.
2014-09-01
Within the context of rock mechanics, the Combined Finite-Discrete Element Method (FDEM) has been applied to many complex industrial problems such as block caving, deep mining techniques (tunneling, pillar strength, etc.), rock blasting, seismic wave propagation, packing problems, dam stability, rock slope stability, rock mass strength characterization problems, etc. The reality is that most of these were accomplished in a 2D and/or single processor realm. In this work a hardware independent FDEM parallelization framework has been developed using the Virtual Parallel Machine for FDEM, (V-FDEM). With V-FDEM, a parallel FDEM software can be adapted to different parallel architecture systems ranging from just a few to thousands of cores.
Mimetic finite difference method
NASA Astrophysics Data System (ADS)
Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail
2014-01-01
The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathematical identities of the vector and tensor calculus. This article is the first comprehensive review of the 50-year long history of the mimetic methodology and describes in a systematic way the major mimetic ideas and their relevance to academic and real-life problems. The supporting applications include diffusion, electromagnetics, fluid flow, and Lagrangian hydrodynamics problems. The article provides enough details to build various discrete operators on unstructured polygonal and polyhedral meshes and summarizes the major convergence results for the mimetic approximations. Most of these theoretical results, which are presented here as lemmas, propositions and theorems, are either original or an extension of existing results to a more general formulation using polyhedral meshes. Finally, flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.
Effects of 2D and Finite Density Fluctuations on O-X Correlation Reflectometry
G.J. Kramer; R. Nazikian; E. Valeo
2001-07-05
The correlation between O-mode and X-mode reflectometer signals is studied with a 1D and 2D reflectometer model in order to explore its feasibilities as a q-profile diagnostic. It was found that 2D effects and finite fluctuation levels both decrease the O-X correlation. At very low fluctuation levels, which are usually present in the plasma core, there is good possibility to determine the local magnetic field strength and use that as a constraint for the equilibrium reconstruction.
Dynamic Analysis of 2D Electromagnetic Resonant Optical Scanner Using 3D Finite Element Method
NASA Astrophysics Data System (ADS)
Hirata, Katsuhiro; Hong, Sara; Maeda, Kengo
The optical scanner is a scanning device in which a laser beam is reflected by a mirror that can be rotated or oscillated. In this paper, we propose a new 2D electromagnetic resonant optical scanner that employs electromagnets and leaf springs. Torque characteristics and resonance characteristics of the scanner are analyzed using the 3D finite element method. The validity of the analysis is shown by comparing the characteristics inferred from the analysis with the characteristics of the prototype. Further, 2D resonance is investigated by introducing a superimposed-frequency current in a single coil.
2D-3D hybrid stabilized finite element method for tsunami runup simulations
NASA Astrophysics Data System (ADS)
Takase, S.; Moriguchi, S.; Terada, K.; Kato, J.; Kyoya, T.; Kashiyama, K.; Kotani, T.
2016-09-01
This paper presents a two-dimensional (2D)-three-dimensional (3D) hybrid stabilized finite element method that enables us to predict a propagation process of tsunami generated in a hypocentral region, which ranges from offshore propagation to runup to urban areas, with high accuracy and relatively low computational costs. To be more specific, the 2D shallow water equation is employed to simulate the propagation of offshore waves, while the 3D Navier-Stokes equation is employed for the runup in urban areas. The stabilized finite element method is utilized for numerical simulations for both of the 2D and 3D domains that are independently discretized with unstructured meshes. The multi-point constraint and transmission methods are applied to satisfy the continuity of flow velocities and pressures at the interface between the resulting 2D and 3D meshes, since neither their spatial dimensions nor node arrangements are consistent. Numerical examples are presented to demonstrate the performance of the proposed hybrid method to simulate tsunami behavior, including offshore propagation and runup to urban areas, with substantially lower computation costs in comparison with full 3D computations.
2D-3D hybrid stabilized finite element method for tsunami runup simulations
NASA Astrophysics Data System (ADS)
Takase, S.; Moriguchi, S.; Terada, K.; Kato, J.; Kyoya, T.; Kashiyama, K.; Kotani, T.
2016-05-01
This paper presents a two-dimensional (2D)-three-dimensional (3D) hybrid stabilized finite element method that enables us to predict a propagation process of tsunami generated in a hypocentral region, which ranges from offshore propagation to runup to urban areas, with high accuracy and relatively low computational costs. To be more specific, the 2D shallow water equation is employed to simulate the propagation of offshore waves, while the 3D Navier-Stokes equation is employed for the runup in urban areas. The stabilized finite element method is utilized for numerical simulations for both of the 2D and 3D domains that are independently discretized with unstructured meshes. The multi-point constraint and transmission methods are applied to satisfy the continuity of flow velocities and pressures at the interface between the resulting 2D and 3D meshes, since neither their spatial dimensions nor node arrangements are consistent. Numerical examples are presented to demonstrate the performance of the proposed hybrid method to simulate tsunami behavior, including offshore propagation and runup to urban areas, with substantially lower computation costs in comparison with full 3D computations.
NASA Astrophysics Data System (ADS)
Yan, Bo; Li, Yuguo; Liu, Ying
2016-07-01
In this paper, we present an adaptive finite element (FE) algorithm for direct current (DC) resistivity modeling in 2-D generally anisotropic conductivity structures. Our algorithm is implemented on an unstructured triangular mesh that readily accommodates complex structures such as topography and dipping layers and so on. We implement a self-adaptive, goal-oriented grid refinement algorithm in which the finite element analysis is performed on a sequence of refined grids. The grid refinement process is guided by an a posteriori error estimator. The problem is formulated in terms of total potentials where mixed boundary conditions are incorporated. This type of boundary condition is superior to the Dirichlet type of conditions and improves numerical accuracy considerably according to model calculations. We have verified the adaptive finite element algorithm using a two-layered earth with azimuthal anisotropy. The FE algorithm with incorporation of mixed boundary conditions achieves high accuracy. The relative error between the numerical and analytical solutions is less than 1% except in the vicinity of the current source location, where the relative error is up to 2.4%. A 2-D anisotropic model is used to demonstrate the effects of anisotropy upon the apparent resistivity in DC soundings.
Justification for a 2D versus 3D fingertip finite element model during static contact simulations.
Harih, Gregor; Tada, Mitsunori; Dolšak, Bojan
2016-10-01
The biomechanical response of a human hand during contact with various products has not been investigated in details yet. It has been shown that excessive contact pressure on the soft tissue can result in discomfort, pain and also cumulative traumatic disorders. This manuscript explores the benefits and limitations of a simplified two-dimensional vs. an anatomically correct three-dimensional finite element model of a human fingertip. Most authors still use 2D FE fingertip models due to their simplicity and reduced computational costs. However we show that an anatomically correct 3D FE fingertip model can provide additional insight into the biomechanical behaviour. The use of 2D fingertip FE models is justified when observing peak contact pressure values as well as displacement during the contact for the given studied cross-section. On the other hand, an anatomically correct 3D FE fingertip model provides a contact pressure distribution, which reflects the fingertip's anatomy. PMID:26856769
NASA Astrophysics Data System (ADS)
Zou, B.; Li, D. F.; Hu, H. J.; Zhang, H. W.; Lou, L. H.; Chen, M.; Lv, Z. Y.
Based on the verified two dimensional(2D) finite element model for river flow simulation, the effect of estuary training levees on the water flow and sediment movement in the Yellow River estuary is analyzed. For disclosing the effect of setting the two training levees on the flow and sediment motion, the calculation and analysis for the two projects, (one is no levees, the other is setting up two no levees) are given. The results show that when setting up two training levees, water flow is bound by levees and the water flows become more concentrated. As a result, velocity increases in the main channel, sediment carrying capacity of water flow increases correspondingly.
Finite-size scaling in a 2D disordered electron gas with spectral nodes
NASA Astrophysics Data System (ADS)
Sinner, Andreas; Ziegler, Klaus
2016-08-01
We study the DC conductivity of a weakly disordered 2D electron gas with two bands and spectral nodes, employing the field theoretical version of the Kubo–Greenwood conductivity formula. Disorder scattering is treated within the standard perturbation theory by summing up ladder and maximally crossed diagrams. The emergent gapless (diffusion) modes determine the behavior of the conductivity on large scales. We find a finite conductivity with an intermediate logarithmic finite-size scaling towards smaller conductivities but do not obtain the logarithmic divergence of the weak-localization approach. Our results agree with the experimentally observed logarithmic scaling of the conductivity in graphene with the formation of a plateau near {{e}2}/π h .
Finite-size scaling in a 2D disordered electron gas with spectral nodes.
Sinner, Andreas; Ziegler, Klaus
2016-08-01
We study the DC conductivity of a weakly disordered 2D electron gas with two bands and spectral nodes, employing the field theoretical version of the Kubo-Greenwood conductivity formula. Disorder scattering is treated within the standard perturbation theory by summing up ladder and maximally crossed diagrams. The emergent gapless (diffusion) modes determine the behavior of the conductivity on large scales. We find a finite conductivity with an intermediate logarithmic finite-size scaling towards smaller conductivities but do not obtain the logarithmic divergence of the weak-localization approach. Our results agree with the experimentally observed logarithmic scaling of the conductivity in graphene with the formation of a plateau near [Formula: see text]. PMID:27270084
2D to 3D conversion implemented in different hardware
NASA Astrophysics Data System (ADS)
Ramos-Diaz, Eduardo; Gonzalez-Huitron, Victor; Ponomaryov, Volodymyr I.; Hernandez-Fragoso, Araceli
2015-02-01
Conversion of available 2D data for release in 3D content is a hot topic for providers and for success of the 3D applications, in general. It naturally completely relies on virtual view synthesis of a second view given by original 2D video. Disparity map (DM) estimation is a central task in 3D generation but still follows a very difficult problem for rendering novel images precisely. There exist different approaches in DM reconstruction, among them manually and semiautomatic methods that can produce high quality DMs but they demonstrate hard time consuming and are computationally expensive. In this paper, several hardware implementations of designed frameworks for an automatic 3D color video generation based on 2D real video sequence are proposed. The novel framework includes simultaneous processing of stereo pairs using the following blocks: CIE L*a*b* color space conversions, stereo matching via pyramidal scheme, color segmentation by k-means on an a*b* color plane, and adaptive post-filtering, DM estimation using stereo matching between left and right images (or neighboring frames in a video), adaptive post-filtering, and finally, the anaglyph 3D scene generation. Novel technique has been implemented on DSP TMS320DM648, Matlab's Simulink module over a PC with Windows 7, and using graphic card (NVIDIA Quadro K2000) demonstrating that the proposed approach can be applied in real-time processing mode. The time values needed, mean Similarity Structural Index Measure (SSIM) and Bad Matching Pixels (B) values for different hardware implementations (GPU, Single CPU, and DSP) are exposed in this paper.
Moving finite elements in 2-D. Technical progress report, year 3
Gelinas, R.J.
1984-04-03
The moving finite element (MFE) method has emerged as a potentially potent and interesting method for solving partial differential equations (PDE's) with large gradients. The principal feature of the MFE method is that the grid node co-ordinates, themselves, are dependent variables and are calculated at each time step so as to minimize a PDE residual in some norm. This has the effect of moving the grid nodes continuously and systematically to those positions which minimize PDE numerical solution errors. Research on the MFE method to this time has been advanced by a relatively small number of groups and individual investigators. Of these, the presently proposing group at Science Applications, Inc. (SAI), in Pleasanton, California, has pursued simultaneously developments of the basic theory, numerical analysis, and real-world applications under sponsorship of the DOE and others. The results of our MFE research to date in both 1-D and 2-D transient PDE systems have been quite positive, as well as laden with indicators for further advancements. We report the progress of this third year of 2-D MFE research and indicate those research tasks which should now be pursued into their next logical stages of advancement for large-gradient PDE problems in 2-D.
Exponential Finite-Difference Technique
NASA Technical Reports Server (NTRS)
Handschuh, Robert F.
1989-01-01
Report discusses use of explicit exponential finite-difference technique to solve various diffusion-type partial differential equations. Study extends technique to transient-heat-transfer problems in one dimensional cylindrical coordinates and two and three dimensional Cartesian coordinates and to some nonlinear problems in one or two Cartesian coordinates.
Use of finite volume radiation for predicting the Knudsen minimum in 2D channel flow
Malhotra, Chetan P.; Mahajan, Roop L.
2014-12-09
In an earlier paper we employed an analogy between surface-to-surface radiation and free-molecular flow to model Knudsen flow through tubes and onto planes. In the current paper we extend the analogy between thermal radiation and molecular flow to model the flow of a gas in a 2D channel across all regimes of rarefaction. To accomplish this, we break down the problem of gaseous flow into three sub-problems (self-diffusion, mass-motion and generation of pressure gradient) and use the finite volume method for modeling radiation through participating media to model the transport in each sub-problem as a radiation problem. We first model molecular self-diffusion in the stationary gas by modeling the transport of the molecular number density through the gas starting from the analytical asymptote for free-molecular flow to the kinetic theory limit of gaseous self-diffusion. We then model the transport of momentum through the gas at unit pressure gradient to predict Poiseuille flow and slip flow in the 2D gas. Lastly, we predict the generation of pressure gradient within the gas due to molecular collisions by modeling the transport of the forces generated due to collisions per unit volume of gas. We then proceed to combine the three radiation problems to predict flow of the gas over the entire Knudsen number regime from free-molecular to transition to continuum flow and successfully capture the Knudsen minimum at Kn ∼ 1.
Diverse Geological Applications For Basil: A 2d Finite-deformation Computational Algorithm
NASA Astrophysics Data System (ADS)
Houseman, Gregory A.; Barr, Terence D.; Evans, Lynn
Geological processes are often characterised by large finite-deformation continuum strains, on the order of 100% or greater. Microstructural processes cause deformation that may be represented by a viscous constitutive mechanism, with viscosity that may depend on temperature, pressure, or strain-rate. We have developed an effective com- putational algorithm for the evaluation of 2D deformation fields produced by Newto- nian or non-Newtonian viscous flow. With the implementation of this algorithm as a computer program, Basil, we have applied it to a range of diverse applications in Earth Sciences. Viscous flow fields in 2D may be defined for the thin-sheet case or, using a velocity-pressure formulation, for the plane-strain case. Flow fields are represented using 2D triangular elements with quadratic interpolation for velocity components and linear for pressure. The main matrix equation is solved by an efficient and compact conjugate gradient algorithm with iteration for non-Newtonian viscosity. Regular grids may be used, or grids based on a random distribution of points. Definition of the prob- lem requires that velocities, tractions, or some combination of the two, are specified on all external boundary nodes. Compliant boundaries may also be defined, based on the idea that traction is opposed to and proportional to boundary displacement rate. In- ternal boundary segments, allowing fault-like displacements within a viscous medium have also been developed, and we find that the computed displacement field around the fault tip is accurately represented for Newtonian and non-Newtonian viscosities, in spite of the stress singularity at the fault tip. Basil has been applied by us and colleagues to problems that include: thin sheet calculations of continental collision, Rayleigh-Taylor instability of the continental mantle lithosphere, deformation fields around fault terminations at the outcrop scale, stress and deformation fields in and around porphyroblasts, and
A 2-D Interface Element for Coupled Analysis of Independently Modeled 3-D Finite Element Subdomains
NASA Technical Reports Server (NTRS)
Kandil, Osama A.
1998-01-01
Over the past few years, the development of the interface technology has provided an analysis framework for embedding detailed finite element models within finite element models which are less refined. This development has enabled the use of cascading substructure domains without the constraint of coincident nodes along substructure boundaries. The approach used for the interface element is based on an alternate variational principle often used in deriving hybrid finite elements. The resulting system of equations exhibits a high degree of sparsity but gives rise to a non-positive definite system which causes difficulties with many of the equation solvers in general-purpose finite element codes. Hence the global system of equations is generally solved using, a decomposition procedure with pivoting. The research reported to-date for the interface element includes the one-dimensional line interface element and two-dimensional surface interface element. Several large-scale simulations, including geometrically nonlinear problems, have been reported using the one-dimensional interface element technology; however, only limited applications are available for the surface interface element. In the applications reported to-date, the geometry of the interfaced domains exactly match each other even though the spatial discretization within each domain may be different. As such, the spatial modeling of each domain, the interface elements and the assembled system is still laborious. The present research is focused on developing a rapid modeling procedure based on a parametric interface representation of independently defined subdomains which are also independently discretized.
Exact ground state for the four-electron problem in a 2D finite honeycomb lattice
NASA Astrophysics Data System (ADS)
Trencsényi, Réka; Glukhov, Konstantin; Gulácsi, Zsolt
2014-07-01
Working in a subspace with dimensionality much smaller than the dimension of the full Hilbert space, we deduce exact four-particle ground states in 2D samples containing hexagonal repeat units and described by Hubbard type of models. The procedure identifies first a small subspace ? in which the ground state ? is placed, than deduces ? by exact diagonalization in ?. The small subspace is obtained by the repeated application of the Hamiltonian ? on a carefully chosen starting wave vector describing the most interacting particle configuration, and the wave vectors resulting from the application of ?, till the obtained system of equations closes in itself. The procedure which can be applied in principle at fixed but arbitrary system size and number of particles is interesting on its own since it provides exact information for the numerical approximation techniques which use a similar strategy, but apply non-complete basis for ?. The diagonalization inside ? provides an incomplete image of the low lying part of the excitation spectrum, but provides the exact ?. Once the exact ground state is obtained, its properties can be easily analysed. The ? is found always as a singlet state whose energy, interestingly, saturates in the ? limit. The unapproximated results show that the emergence probabilities of different particle configurations in the ground state presents 'Zittern' (trembling) characteristics which are absent in 2D square Hubbard systems. Consequently, the manifestation of the local Coulomb repulsion in 2D square and honeycomb types of systems presents differences, which can be a real source in the differences in the many-body behaviour.
Hallquist, J.O.
1982-02-01
This revised report provides an updated user's manual for DYNA2D, an explicit two-dimensional axisymmetric and plane strain finite element code for analyzing the large deformation dynamic and hydrodynamic response of inelastic solids. A contact-impact algorithm permits gaps and sliding along material interfaces. By a specialization of this algorithm, such interfaces can be rigidly tied to admit variable zoning without the need of transition regions. Spatial discretization is achieved by the use of 4-node solid elements, and the equations-of motion are integrated by the central difference method. An interactive rezoner eliminates the need to terminate the calculation when the mesh becomes too distorted. Rather, the mesh can be rezoned and the calculation continued. The command structure for the rezoner is described and illustrated by an example.
NASA Astrophysics Data System (ADS)
Schaa, R.; Gross, L.; du Plessis, J.
2016-04-01
We present a general finite-element solver, escript, tailored to solve geophysical forward and inverse modeling problems in terms of partial differential equations (PDEs) with suitable boundary conditions. Escript’s abstract interface allows geoscientists to focus on solving the actual problem without being experts in numerical modeling. General-purpose finite element solvers have found wide use especially in engineering fields and find increasing application in the geophysical disciplines as these offer a single interface to tackle different geophysical problems. These solvers are useful for data interpretation and for research, but can also be a useful tool in educational settings. This paper serves as an introduction into PDE-based modeling with escript where we demonstrate in detail how escript is used to solve two different forward modeling problems from applied geophysics (3D DC resistivity and 2D magnetotellurics). Based on these two different cases, other geophysical modeling work can easily be realized. The escript package is implemented as a Python library and allows the solution of coupled, linear or non-linear, time-dependent PDEs. Parallel execution for both shared and distributed memory architectures is supported and can be used without modifications to the scripts.
Mixed-RKDG Finite Element Methods for the 2-D Hydrodynamic Model for Semiconductor Device Simulation
Chen, Zhangxin; Cockburn, Bernardo; Jerome, Joseph W.; Shu, Chi-Wang
1995-01-01
In this paper we introduce a new method for numerically solving the equations of the hydrodynamic model for semiconductor devices in two space dimensions. The method combines a standard mixed finite element method, used to obtain directly an approximation to the electric field, with the so-called Runge-Kutta Discontinuous Galerkin (RKDG) method, originally devised for numerically solving multi-dimensional hyperbolic systems of conservation laws, which is applied here to the convective part of the equations. Numerical simulations showing the performance of the new method are displayed, and the results compared with those obtained by using Essentially Nonoscillatory (ENO) finite difference schemes. Frommore » the perspective of device modeling, these methods are robust, since they are capable of encompassing broad parameter ranges, including those for which shock formation is possible. The simulations presented here are for Gallium Arsenide at room temperature, but we have tested them much more generally with considerable success.« less
The Complex-Step-Finite-Difference method
NASA Astrophysics Data System (ADS)
Abreu, Rafael; Stich, Daniel; Morales, Jose
2015-07-01
We introduce the Complex-Step-Finite-Difference method (CSFDM) as a generalization of the well-known Finite-Difference method (FDM) for solving the acoustic and elastic wave equations. We have found a direct relationship between modelling the second-order wave equation by the FDM and the first-order wave equation by the CSFDM in 1-D, 2-D and 3-D acoustic media. We present the numerical methodology in order to apply the introduced CSFDM and show an example for wave propagation in simple homogeneous and heterogeneous models. The CSFDM may be implemented as an extension into pre-existing numerical techniques in order to obtain fourth- or sixth-order accurate results with compact three time-level stencils. We compare advantages of imposing various types of initial motion conditions of the CSFDM and demonstrate its higher-order accuracy under the same computational cost and dispersion-dissipation properties. The introduced method can be naturally extended to solve different partial differential equations arising in other fields of science and engineering.
NASA Astrophysics Data System (ADS)
Noji, H.
This study investigates the losses in a two conducting-layer REBCO cable fabricated by researchers at Furukawa Electric Co. Ltd. The losses were calculated using a combination of my electric circuit (EC) model with a two-dimensional finite element method (2D FEM). The helical pitches of the tapes in each layer, P1 and P2, were adjusted to equalize the current in both cable layers, although the loss calculation assumed infinite helical pitches and the same current in each layer at first. The results showed that the losses depended on the relative tape-position angle between the layers (θ/θ'), because the vertical field between adjacent tapes in the same layer varied with θ/θ'. When simulating the real cable, the helical pitches were adjusted and the layer currents were calculated by the EC model. These currents were input to the 2D FEM to compute the losses. The losses changed along the cable length because the difference between P1 and P2 altered the θ/θ' along this direction. The average angle-dependent and position-dependent losses were equal and closely approximated the measured losses. As an example to reduce the loss in this cable, the angle and the helical pitches were fixed at θ/θ' = 0.5 and P1 = P2 = 100 mm (S-direction). The calculation with these conditions indicated that the loss is about one order of magnitude lower than the measurement.
SIMULATIONS OF 2D AND 3D THERMOCAPILLARY FLOWS BY A LEAST-SQUARES FINITE ELEMENT METHOD. (R825200)
Numerical results for time-dependent 2D and 3D thermocapillary flows are presented in this work. The numerical algorithm is based on the Crank-Nicolson scheme for time integration, Newton's method for linearization, and a least-squares finite element method, together with a matri...
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.
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.
Finite element and finite difference methods in electromagnetic scattering
NASA Astrophysics Data System (ADS)
Morgan, Michael A.
Finite-difference and finite-element methods for the computational analysis of EM scattering phenomena are examined in chapters contributed by leading experts. Topics addressed include an FEM for composite scatterers, coupled finite- and boundary-element methods for EM scattering, absorbing boundary conditions for the direct solution PDEs arising in EM scattering problems, application of the control-region approximation to two-dimensional EM scattering, coupled potentials for EM fields in inhomogeneous media, the method of conforming boundary elements for transient electromagnetics, and the finite-difference time-domain method for numerical modeling of EM wave interactions with arbitrary structures. Extensive diagrams and graphs of typical results are provided.
NASA Technical Reports Server (NTRS)
Buczek, M. B.; Gregory, M. A.; Herakovich, C. T.
1983-01-01
CLFE2D is a two dimensional generalized plane strain finite element code, using a linear, four node, general quadrilateral, isoparametric element. The program is developed to calculate the displacements, strains, stresses, and strain energy densities in a finite width composite laminate. CLFE2D offers any combination of the following load types: nodal displacements, nodal forces, uniform normal strain, or hygrothermal. The program allows the user to input one set of three dimensional orthotropic material properties. The user can then specify the angle of material principal orientation for each element in the mesh. Output includes displacements, stresses, strains and strain densities at points selected by the user. An option is also available to plot the underformed and deformed finite element meshes.
Finite-size effects for anisotropic 2D Ising model with various boundary conditions
NASA Astrophysics Data System (ADS)
Izmailian, N. Sh
2012-12-01
We analyze the exact partition function of the anisotropic Ising model on finite M × N rectangular lattices under four different boundary conditions (periodic-periodic (pp), periodic-antiperiodic (pa), antiperiodic-periodic (ap) and antiperiodic-antiperiodic (aa)) obtained by Kaufman (1949 Phys. Rev. 76 1232), Wu and Hu (2002 J. Phys. A: Math. Gen. 35 5189) and Kastening (2002 Phys. Rev. E 66 057103)). We express the partition functions in terms of the partition functions Zα, β(J, k) with (α, β) = (0, 0), (1/2, 0), (0, 1/2) and (1/2, 1/2), J is an interaction coupling and k is an anisotropy parameter. Based on such expressions, we then extend the algorithm of Ivashkevich et al (2002 J. Phys. A: Math. Gen. 35 5543) to derive the exact asymptotic expansion of the logarithm of the partition function for all boundary conditions mentioned above. Our result is f = fbulk + ∑∞p = 0fp(ρ, k)S-p - 1, where f is the free energy of the system, fbulk is the free energy of the bulk, S = MN is the area of the lattice and ρ = M/N is the aspect ratio. All coefficients in this expansion are expressed through analytical functions. We have introduced the effective aspect ratio ρeff = ρ/sinh 2Jc and show that for pp and aa boundary conditions all finite size correction terms are invariant under the transformation ρeff → 1/ρeff. This article is part of ‘Lattice models and integrability’, a special issue of Journal of Physics A: Mathematical and Theoretical in honour of F Y Wu's 80th birthday.
Chin, Fee Wai; Chan, Soon Choy; Abdul Rahman, Sabariah; Noor Akmal, Sharifah; Rosli, Rozita
2016-01-01
The cytochrome P450, family 2, subfamily D, polypeptide 6 (CYP2D6) is an enzyme that is predominantly involved in the metabolism of tamoxifen. Genetic polymorphisms of the CYP2D6 gene may contribute to inter-individual variability in tamoxifen metabolism, which leads to the differences in clinical response to tamoxifen among breast cancer patients. In Malaysia, the knowledge on CYP2D6 genetic polymorphisms as well as metabolizer status in Malaysian breast cancer patients remains unknown. Hence, this study aimed to comprehensively identify CYP2D6 genetic polymorphisms among 80 Malaysian breast cancer patients. The genetic polymorphisms of all the 9 exons of CYP2D6 gene were identified using high-resolution melting analysis and confirmed by DNA sequencing. Seven CYP2D6 alleles consisting of CYP2D6*1, CYP2D6*2, CYP2D6*4, CYP2D6*10, CYP2D6*39, CYP2D6*49, and CYP2D6*75 were identified in this study. Among these alleles, CYP2D6*10 is the most common allele in both Malaysian Malay (54.8%) and Chinese (71.4%) breast cancer patients, whereas CYP2D6*4 in Malaysian Indian (28.6%) breast cancer patients. In relation to CYP2D6 genotype, CYP2D6*10/*10 is more frequently observed in both Malaysian Malay (28.9%) and Chinese (57.1%) breast cancer patients, whereas CYP2D6*4/*10 is more frequently observed in Malaysian Indian (42.8%) breast cancer patients. In terms of CYP2D6 phenotype, 61.5% of Malaysian Malay breast cancer patients are predicted as extensive metabolizers in which they are most likely to respond well to tamoxifen therapy. However, 57.1% of Chinese as well as Indian breast cancer patients are predicted as intermediate metabolizers and they are less likely to gain optimal benefit from the tamoxifen therapy. This is the first report of CYP2D6 genetic polymorphisms and phenotypes in Malaysian breast cancer patients for different ethnicities. These data may aid clinicians in selecting an optimal drug therapy for Malaysian breast cancer patients, hence improve the
Extreme value statistics of 2D Gaussian free field: effect of finite domains
NASA Astrophysics Data System (ADS)
Cao, X.; Rosso, A.; Santachiara, R.
2016-01-01
We study minima statistics of the 2D Gaussian free field (GFF) on circles in the unit disk with Dirichlet boundary condition. Free energy distributions of the associated random energy models are exactly calculated in the high temperature phase, and shown to satisfy the duality property, which enables us to predict the minima distribution by assuming the freezing scenario. Numerical tests are provided. Related questions concerning the GFF on a sphere are also considered.
TOPAZ - a finite element heat conduction code for analyzing 2-D solids
Shapiro, A.B.
1984-03-01
TOPAZ is a two-dimensional implicit finite element computer code for heat conduction analysis. This report provides a user's manual for TOPAZ and a description of the numerical algorithms used. Sample problems with analytical solutions are presented. TOPAZ has been implemented on the CRAY and VAX computers.
A 2D finite element wave equation solver based on triangular base elements
NASA Astrophysics Data System (ADS)
Van Eester, D.; Lerche, E.; Evrard, M.
2009-11-01
A finite element method based on the subdivision of the physical domain in triangular sub-domains in which simple local 'areale' coordinates are adopted is explored. The advantage of the method is that it straightforwardly allows grid refinement in regions where higher precision is required. The plasma model was kept simple for this 'proof-of-principle' exercise. Rather than accounting for the actual differential or integro-differential dielectric tensor, its locally uniform plasma equivalent was adopted for 3 possible choices: the cold plasma response, the full hot Stix/Swanson plasma tensor retaining all orders in finite Larmor radius (FLR) and the more common hot tensor, truncated at terms of second order in the Larmor radius.
A 2D finite element wave equation solver based on triangular base elements
Van Eester, D.; Lerche, E.; Evrard, M.
2009-11-26
A finite element method based on the subdivision of the physical domain in triangular sub-domains in which simple local 'areale' coordinates are adopted is explored. The advantage of the method is that it straightforwardly allows grid refinement in regions where higher precision is required. The plasma model was kept simple for this 'proof-of-principle' exercise. Rather than accounting for the actual differential or integro-differential dielectric tensor, its locally uniform plasma equivalent was adopted for 3 possible choices: the cold plasma response, the full hot Stix/Swanson plasma tensor retaining all orders in finite Larmor radius (FLR) and the more common hot tensor, truncated at terms of second order in the Larmor radius.
Finite element nonlinear flutter and fatigue life of 2-D panels with temperature effects
NASA Technical Reports Server (NTRS)
Mei, Chuh; Xue, David Y.
1991-01-01
A frequency domain method for two-dimensional nonlinear panel flutter with thermal effects obtained from a consistent finite element formulation is presented. The von Karman nonlinear strain-displacement relation is used to account for large deflections, and the quasi-steady first-order piston theory is employed for aerodynamic loading. The finite element frequency domain results are compared with analytical time domain solutions. In a limit-cycle motion, the panel frequency and stress can be determined, thus fatigue life can be predicted. The influence of temperature and dynamic pressure on panel fatigue life is presented. An endurance dynamic pressure can be established at a given temperature from the present method.
Coupling finite and boundary element methods for 2-D elasticity problems
NASA Technical Reports Server (NTRS)
Krishnamurthy, T.; Raju, I. S.; Sistla, R.
1993-01-01
A finite element-boundary element (FE-BE) coupling method for two-dimensional elasticity problems is developed based on a weighted residual variational method in which a portion of the domain of interest is modeled by FEs and the remainder of the region by BEs. The performance of the FE-BE coupling method is demonstrated via applications to a simple 'patch test' problem and three-crack problems. The method passed the patch tests for various modeling configurations and yielded accurate strain energy release rates for the crack problems studied.
NASA Technical Reports Server (NTRS)
Hermance, J. F.
1984-01-01
Electromagnetic induction in a laterally homogeneous earth is analyzed in terms of a source field with finite dimensions. Attention is focused on a time-varying two-dimensional current source directed parallel to the strike of a two-dimensional anomalous structure within the earth, i.e., the E-parallel mode. The spatially harmonic source field is expressed as discontinuities in the magnetic (or electric) field of the current in the source. The model is applied to describing the magnetic gradients across megatectonic features, and may be used to predict the magnetic fields encountered by a satellite orbiting above the ionosphere.
Sun, Liyun; Gu, Shaohua; Sun, Yaqiong; Zheng, Dan; Wu, Qihan; Li, Xin; Dai, Jianfeng; Dai, Jianliang; Ji, Chaoneng; Xie, Yi; Mao, Yumin
2005-04-01
This study reports the cloning and characterization of a novel human phosphatidic acid phosphatase type 2 isoform cDNAs (PAP2d) from the foetal brain cDNA library. The PAP2d gene is localized on chromosome 1p21.3. It contains six exons and spans 112 kb of the genomic DNA. By large-scale cDNA sequencing we found two splice variants of PAP2d, PAP2d_v1 and PAP2d_v2. The PAP2d_v1 cDNA is 1722 bp in length and spans an open reading frame from nucleotide 56 to 1021, encoding a 321aa protein. The PAP2d_v2 cDNA is 1707 bp in length encoding a 316aa protein from nucleotide 56-1006. The PAP2d_v1 cDNA is 15 bp longer than the PAP2d_v2 cDNA in the terminal of the fifth exon and it creates different ORF. Both of the proteins contain a well-conserved PAP2 motif. The PAP2d_v1 is mainly expressed in human brain, lung, kidney, testis and colon, while PAP2d_v2 is restricted to human placenta, skeletal muscle, and kidney. The two splice variants are co-expressed only in kidney. PMID:16010976
Finite-difference computations of rotor loads
NASA Technical Reports Server (NTRS)
Caradonna, F. X.; Tung, C.
1985-01-01
This paper demonstrates the current and future potential of finite-difference methods for solving real rotor problems which now rely largely on empiricism. The demonstration consists of a simple means of combining existing finite-difference, integral, and comprehensive loads codes to predict real transonic rotor flows. These computations are performed for hover and high-advance-ratio flight. Comparisons are made with experimental pressure data.
Finite-difference computations of rotor loads
NASA Technical Reports Server (NTRS)
Caradonna, F. X.; Tung, C.
1985-01-01
The current and future potential of finite difference methods for solving real rotor problems which now rely largely on empiricism are demonstrated. The demonstration consists of a simple means of combining existing finite-difference, integral, and comprehensive loads codes to predict real transonic rotor flows. These computations are performed for hover and high-advanced-ratio flight. Comparisons are made with experimental pressure data.
ZONE - a finite element mesh generator. [2-D, for CDC 7600
Burger, M.J.
1980-03-12
The ZONE computer program is a finite element mesh generator that produces the nodes and element description of any two-dimensional geometry. The geometry is subdivided into a mesh of quadrilateral and triangular zones arranged sequentially in an ordered march through the geometry. The order of march can be chosen so that the minimum bandwidth is obtained. The node points are defined in terms of the x and y coordinates in a global rectangular coordinate system. The zones generated are quadrilaterals or triangles defined by four node points in a counterclockwise sequence. Node points defining the outside boundary are generated for slide lines and to describe pressure boundary conditions. The mesh that is generated can be used as input to any two dimensional as well as any axisymmetrical structure program. The following points are taken up: program concept and characteristics; regions; layers; meridians (offset, circular arc, ellipse); rays; common characterstics - rays and meridians, ZONE input description; output files; examples; and program availability. Also generated is the input to the program PLOT. 15 figures. (RWR)
Accurate 2d finite element calculations for hydrogen in magnetic fields of arbitrary strength
NASA Astrophysics Data System (ADS)
Schimeczek, C.; Wunner, G.
2014-02-01
Recent observations of hundreds of hydrogen-rich magnetic white dwarf stars with magnetic fields up to 105 T (103 MG) have called for more comprehensive and accurate databases for wavelengths and oscillator strengths of the H atom in strong magnetic fields for all states evolving from the field-free levels with principal quantum numbers n≤10. We present a code to calculate the energy eigenvalues and wave functions of such states which is capable of covering the entire regime of field strengths B=0 T to B˜109 T. We achieve this high flexibility by using a two-dimensional finite element expansion of the wave functions in terms of B-splines in the directions parallel and perpendicular to the magnetic field, instead of using asymptotically valid basis expansions in terms of spherical harmonics or Landau orbitals. We have paid special attention to the automation of the program such that the data points for the magnetic field strengths at which the energy of a given state are calculated can be selected automatically. Furthermore, an elaborate method for varying the basis parameters is applied to ensure that the results reach a pre-selected precision, which also can be adjusted freely. Energies and wave functions are stored in a convenient format for further analysis, e.g. for the calculation of transition energies and oscillator strengths. The code has been tested to work for 300 states with an accuracy of better than 10-6 Rydberg across several symmetry subspaces over the entire regime of magnetic field strengths.
Study of the electrical conductivity at finite temperature in 2D Si- MOSFETs
Limouny, L. Kaaouachi, A. El Tata, O.; Daoudi, E.; Errai, M.; Dlimi, S.; Idrissi, H. El; Zatni, A.
2014-01-27
We investigate the low temperature density dependent conductivity of two dimensional electron systems in zero magnetic field for sample Si-15 MOSFETs. The first purpose of this paper is to establish that the knee of the conductivity σ{sub 0} (σ{sub 0} is the T = 0.3 conductivity obtained by linear extrapolation of the curves of σ (T) for different values of electron density, n{sub s}) as a function of the carrier densities n{sub s} for T = 0.3 K, observed by Lai et al. and Limouny et al. in previous work for two different samples, is independent of temperature. The second aim is the determination of the critical density, n{sub c}, of the metal-insulator transition. Many methods are used in this investigation of n{sub c} which have been already used for other samples. The motivation behind this last study is the observation of many values of n{sub c} that have been obtained from different methods and that are slightly different. We will use in this study three methods with the intention to infer which one is more appropriate to obtain n{sub c}.
NASA Astrophysics Data System (ADS)
Horritt, M. S.; Bates, P. D.; Mattinson, M. J.
2006-09-01
SummaryThe effects of mesh resolution and topographic data quality on the predictions of a 2D finite volume model of channel flow are investigated. 25 cm resolution side scan sonar swath bathymetry of a 7 km reach of the river Thames, UK, provides topography for a series of finite volume models with resolutions ranging from 2.5 to 50 m. Results from the coarser meshes are compared with the 2.5 m simulation which is used as a benchmark. The model shows greater sensitivity to mesh resolution than topographic sampling. Sensitivity to mesh resolution is attributed to two effects of roughly equal magnitude. Small elements are able to represent hydraulic features such as recirculation zones, and a more accurate representation of the domain boundary helps to drive these flow features. In practical terms, a models at a resolution of 20 and 50 m require 50 m cross-sections, whereas the 10 m model predictions are improved by using all the bathymetry data.
Numerical computation of transonic flows by finite-element and finite-difference methods
NASA Technical Reports Server (NTRS)
Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.
1978-01-01
Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.
Finite-difference modelling of wavefield constituents
NASA Astrophysics Data System (ADS)
Robertsson, Johan O. A.; van Manen, Dirk-Jan; Schmelzbach, Cedric; Van Renterghem, Cederic; Amundsen, Lasse
2015-11-01
The finite-difference method is among the most popular methods for modelling seismic wave propagation. Although the method has enjoyed huge success for its ability to produce full wavefield seismograms in complex models, it has one major limitation which is of critical importance for many modelling applications; to naturally output up- and downgoing and P- and S-wave constituents of synthesized seismograms. In this paper, we show how such wavefield constituents can be isolated in finite-difference-computed synthetics in complex models with high numerical precision by means of a simple algorithm. The description focuses on up- and downgoing and P- and S-wave separation of data generated using an isotropic elastic finite-difference modelling method. However, the same principles can also be applied to acoustic, electromagnetic and other wave equations.
Applications of an exponential finite difference technique
NASA Technical Reports Server (NTRS)
Handschuh, Robert F.; Keith, Theo G., Jr.
1988-01-01
An exponential finite difference scheme first presented by Bhattacharya for one dimensional unsteady heat conduction problems in Cartesian coordinates was extended. The finite difference algorithm developed was used to solve the unsteady diffusion equation in one dimensional cylindrical coordinates and was applied to two and three dimensional conduction problems in Cartesian coordinates. Heat conduction involving variable thermal conductivity was also investigated. The method was used to solve nonlinear partial differential equations in one and two dimensional Cartesian coordinates. Predicted results are compared to exact solutions where available or to results obtained by other numerical methods.
On the wavelet optimized finite difference method
NASA Technical Reports Server (NTRS)
Jameson, Leland
1994-01-01
When one considers the effect in the physical space, Daubechies-based wavelet methods are equivalent to finite difference methods with grid refinement in regions of the domain where small scale structure exists. Adding a wavelet basis function at a given scale and location where one has a correspondingly large wavelet coefficient is, essentially, equivalent to adding a grid point, or two, at the same location and at a grid density which corresponds to the wavelet scale. This paper introduces a wavelet optimized finite difference method which is equivalent to a wavelet method in its multiresolution approach but which does not suffer from difficulties with nonlinear terms and boundary conditions, since all calculations are done in the physical space. With this method one can obtain an arbitrarily good approximation to a conservative difference method for solving nonlinear conservation laws.
Finite-difference migration to zero offset
Li, Jianchao
1992-07-01
Migration to zero offset (MZO), also called dip moveout (DMO) or prestack partial migration, transforms prestack offset seismic data into approximate zero-offset data so as to remove reflection point smear and obtain quality stacked results over a range of reflector dips. MZO has become an important step in standard seismic data processing, and a variety of frequency-wavenumber (f-k) and integral MZO algorithms have been used in practice to date. Here, I present a finite-difference MZO algorithm applied to normal-moveout (NMO)-corrected, common-offset sections. This algorithm employs a traditional poststack 15-degree finite-difference migration algorithm and a special velocity function rather than the true migration velocity. This paper shows results of implementation of this MZO algorithm when velocity varies with depth, and discusses the possibility of applying this algorithm to cases where velocity varies with both depth and horizontal distance.
Finite-difference migration to zero offset
Li, Jianchao.
1992-01-01
Migration to zero offset (MZO), also called dip moveout (DMO) or prestack partial migration, transforms prestack offset seismic data into approximate zero-offset data so as to remove reflection point smear and obtain quality stacked results over a range of reflector dips. MZO has become an important step in standard seismic data processing, and a variety of frequency-wavenumber (f-k) and integral MZO algorithms have been used in practice to date. Here, I present a finite-difference MZO algorithm applied to normal-moveout (NMO)-corrected, common-offset sections. This algorithm employs a traditional poststack 15-degree finite-difference migration algorithm and a special velocity function rather than the true migration velocity. This paper shows results of implementation of this MZO algorithm when velocity varies with depth, and discusses the possibility of applying this algorithm to cases where velocity varies with both depth and horizontal distance.
Test of two methods for faulting on finite-difference calculations
Andrews, D.J.
1999-01-01
Tests of two fault boundary conditions show that each converges with second order accuracy as the finite-difference grid is refined. The first method uses split nodes so that there are disjoint grids that interact via surface traction. The 3D version described here is a generalization of a method I have used extensively in 2D; it is as accurate as the 2D version. The second method represents fault slip as inelastic strain in a fault zone. Offset of stress from its elastic value is seismic moment density. Implementation of this method is quite simple in a finite-difference scheme using velocity and stress as dependent variables.
Wong, Wang I; Hines, Melissa
2016-02-01
The popularity of using the ratio of the second to the fourth digit (2D:4D) to study influences of early androgen exposure on human behavior relies, in part, on a report that the ratio is sex-dimorphic and stable from age 2 years (Manning etal., 1998). However, subsequent research has rarely replicated this finding. Moreover, although 2D:4D has been correlated with many behaviors, these correlations are often inconsistent. Young children's 2D:4D-behavior correlations may be more consistent than those of older individuals, because young children have experienced fewer postnatal influences. To evaluate the usefulness of 2D:4D as a biomarker of prenatal androgen exposure in studies of 2D:4D-behavior correlations, we assessed its sex difference, temporal stability, and behavioral correlates over a 6- to 8-month period in 126, 2- to 3-year-old children, providing a rare same-sample replicability test. We found a moderate sex difference on both hands and high temporal stability. However, between-sex overlap and within-sex variability were also large. Only 3 of 24 correlations with sex-typed behaviors-scores on the Preschool Activities Inventory (PSAI), preference for a boy-typical toy, preference for a girl-typical toy, were significant and in the predicted direction, all of which involved the PSAI, partially confirming findings from another study. Correlation coefficients were larger for behaviors that showed larger sex differences. But, as in older samples, the overall pattern showed inconsistency across time, sex, and hand. Therefore, although sex-dimorphic and stable, 2D:4D-behavior correlations are no more consistent for young children than for older samples. Theoretical and methodological implications are discussed. PMID:26542674
Software suite for finite difference method models.
Arola, T; Hannula, M; Narra, N; Malmivuo, J; Hyttinen, J
2006-01-01
We have developed a software suite for finite difference method (FDM) model construction, visualization and quasi-static simulation to be used in bioelectric field modeling. The aim of the software is to provide a full path from medical image data to simulation of bioelectric phenomena and results visualization. It is written in Java and can be run on various platforms while still supporting all features included. The software can be distributed across a network utilizing dedicated servers for calculation intensive tasks. Supported visualization modes are both two- and three-dimensional modes. PMID:17946057
A nearly analytic exponential time difference method for solving 2D seismic wave equations
NASA Astrophysics Data System (ADS)
Zhang, Xiao; Yang, Dinghui; Song, Guojie
2014-02-01
In this paper, we propose a nearly analytic exponential time difference (NETD) method for solving the 2D acoustic and elastic wave equations. In this method, we use the nearly analytic discrete operator to approximate the high-order spatial differential operators and transform the seismic wave equations into semi-discrete ordinary differential equations (ODEs). Then, the converted ODE system is solved by the exponential time difference (ETD) method. We investigate the properties of NETD in detail, including the stability condition for 1-D and 2-D cases, the theoretical and relative errors, the numerical dispersion relation for the 2-D acoustic case, and the computational efficiency. In order to further validate the method, we apply it to simulating acoustic/elastic wave propagation in multilayer models which have strong contrasts and complex heterogeneous media, e.g., the SEG model and the Marmousi model. From our theoretical analyses and numerical results, the NETD can suppress numerical dispersion effectively by using the displacement and gradient to approximate the high-order spatial derivatives. In addition, because NETD is based on the structure of the Lie group method which preserves the quantitative properties of differential equations, it can achieve more accurate results than the classical methods.
NASA Technical Reports Server (NTRS)
Krueger, Ronald; Paris, Isbelle L.; OBrien, T. Kevin; Minguet, Pierre J.
2004-01-01
The influence of two-dimensional finite element modeling assumptions on the debonding prediction for skin-stiffener specimens was investigated. Geometrically nonlinear finite element analyses using two-dimensional plane-stress and plane-strain elements as well as three different generalized plane strain type approaches were performed. The computed skin and flange strains, transverse tensile stresses and energy release rates were compared to results obtained from three-dimensional simulations. The study showed that for strains and energy release rate computations the generalized plane strain assumptions yielded results closest to the full three-dimensional analysis. For computed transverse tensile stresses the plane stress assumption gave the best agreement. Based on this study it is recommended that results from plane stress and plane strain models be used as upper and lower bounds. The results from generalized plane strain models fall between the results obtained from plane stress and plane strain models. Two-dimensional models may also be used to qualitatively evaluate the stress distribution in a ply and the variation of energy release rates and mixed mode ratios with delamination length. For more accurate predictions, however, a three-dimensional analysis is required.
NASA Astrophysics Data System (ADS)
Beilina, Larisa
2016-08-01
We present domain decomposition finite element/finite difference method for the solution of hyperbolic equation. The domain decomposition is performed such that finite elements and finite differences are used in different subdomains of the computational domain: finite difference method is used on the structured part of the computational domain and finite elements on the unstructured part of the domain. Explicit discretizations for both methods are constructed such that the finite element and the finite difference schemes coincide on the common structured overlapping layer between computational subdomains. Then the resulting approach can be considered as a pure finite element scheme which avoids instabilities at the interfaces. We derive an energy estimate for the underlying hyperbolic equation with absorbing boundary conditions and illustrate efficiency of the domain decomposition method on the reconstruction of the conductivity function in three dimensions.
Efficient discretization in finite difference method
NASA Astrophysics Data System (ADS)
Rozos, Evangelos; Koussis, Antonis; Koutsoyiannis, Demetris
2015-04-01
Finite difference method (FDM) is a plausible and simple method for solving partial differential equations. The standard practice is to use an orthogonal discretization to form algebraic approximate formulations of the derivatives of the unknown function and a grid, much like raster maps, to represent the properties of the function domain. For example, for the solution of the groundwater flow equation, a raster map is required for the characterization of the discretization cells (flow cell, no-flow cell, boundary cell, etc.), and two raster maps are required for the hydraulic conductivity and the storage coefficient. Unfortunately, this simple approach to describe the topology comes along with the known disadvantages of the FDM (rough representation of the geometry of the boundaries, wasted computational resources in the unavoidable expansion of the grid refinement in all cells of the same column and row, etc.). To overcome these disadvantages, Hunt has suggested an alternative approach to describe the topology, the use of an array of neighbours. This limits the need for discretization nodes only for the representation of the boundary conditions and the flow domain. Furthermore, the geometry of the boundaries is described more accurately using a vector representation. Most importantly, graded meshes can be employed, which are capable of restricting grid refinement only in the areas of interest (e.g. regions where hydraulic head varies rapidly, locations of pumping wells, etc.). In this study, we test the Hunt approach against MODFLOW, a well established finite difference model, and the Finite Volume Method with Simplified Integration (FVMSI). The results of this comparison are examined and critically discussed.
TUNED FINITE-DIFFERENCE DIFFUSION OPERATORS
Maron, Jason; Low, Mordecai-Mark Mac E-mail: mordecai@amnh.org
2009-05-15
Finite-difference simulations of fluid dynamics and magnetohydrodynamics generally require an explicit diffusion operator, either to maintain stability by attenuating grid-scale structure, or to implement physical diffusivities such as viscosity or resistivity. If the goal is stability only, the diffusion must act at the grid scale, but should affect structure at larger scales as little as possible. For physical diffusivities the diffusion scale depends on the problem, and diffusion may act at larger scales as well. Diffusivity can undesirably limit the computational time step in both cases. We construct tuned finite-difference diffusion operators that minimally limit the time step while acting as desired near the diffusion scale. Such operators reach peak values at the diffusion scale rather than at the grid scale, but behave as standard operators at larger scales. These operators will be useful for simulations with high magnetic diffusivity or kinematic viscosity such as in the simulation of astrophysical dynamos with magnetic Prandtl number far from unity, or for numerical stabilization using hyperdiffusivity.
Wang, Xiang; Zauel, Roger R.; Rao, D. Sudhaker; Fyhrie, David P.
2009-01-01
Biomechanical stereology is proposed as a two-dimensional (2D) finite element (FE) method to estimate the ability of bone tissue to sustain damage and to separate patients with osteoporotic fracture from normal controls. Briefly, 2D nonlinear compact tension FE models were created from quantitative back scattered electron images taken of iliac crest bone specimens collected from the individuals with or without osteoporotic fracture history. The effects of bone mineral microstructure on predicted bone fracture toughness and microcrack propagation were examined. The 2D FE models were used as surrogates for the real bone tissues. The calculated microcrack propagation results and bone mechanical properties were examined as surrogates for measurements from mechanical testing of actual specimens. The results for the 2D FE simulation separated patients with osteoporotic fracture from normal controls even though only the variability in tissue mineral microstructure was used to build the models. The models were deliberately created to ignore all differences in mean mineralization. Hence, the current results support the following hypotheses: (1) that material heterogeneity is important to the separation of patients with osteoporotic fracture from normal controls and; and (2) that 2D nonlinear finite element modeling can produce surrogate mechanical parameters that separate patients with fracture from normal controls. PMID:18378204
Visualization of elastic wavefields computed with a finite difference code
Larsen, S.; Harris, D.
1994-11-15
The authors have developed a finite difference elastic propagation model to simulate seismic wave propagation through geophysically complex regions. To facilitate debugging and to assist seismologists in interpreting the seismograms generated by the code, they have developed an X Windows interface that permits viewing of successive temporal snapshots of the (2D) wavefield as they are calculated. The authors present a brief video displaying the generation of seismic waves by an explosive source on a continent, which propagate to the edge of the continent then convert to two types of acoustic waves. This sample calculation was part of an effort to study the potential of offshore hydroacoustic systems to monitor seismic events occurring onshore.
Comparison of 3-D finite element model of ashlar masonry with 2-D numerical models of ashlar masonry
NASA Astrophysics Data System (ADS)
Beran, Pavel
2016-06-01
3-D state of stress in heterogeneous ashlar masonry can be also computed by several suitable chosen 2-D numerical models of ashlar masonry. The results obtained from 2-D numerical models well correspond to the results obtained from 3-D numerical model. The character of thermal stress is the same. While using 2-D models the computational time is reduced more than hundredfold and therefore this method could be used for computation of thermal stresses during long time periods with 10 000 of steps.
Energy Science and Technology Software Center (ESTSC)
2004-08-01
AnisWave2D is a 2D finite-difference code for a simulating seismic wave propagation in fully anisotropic materials. The code is implemented to run in parallel over multiple processors and is fully portable. A mesh refinement algorithm has been utilized to allow the grid-spacing to be tailored to the velocity model, avoiding the over-sampling of high-velocity materials that usually occurs in fixed-grid schemes.
NASA Technical Reports Server (NTRS)
Hua, Chongyu; Volakis, John L.
1990-01-01
AUTOMESH-2D is a computer program specifically designed as a preprocessor for the scattering analysis of two dimensional bodies by the finite element method. This program was developed due to a need for reproducing the effort required to define and check the geometry data, element topology, and material properties. There are six modules in the program: (1) Parameter Specification; (2) Data Input; (3) Node Generation; (4) Element Generation; (5) Mesh Smoothing; and (5) Data File Generation.
NASA Technical Reports Server (NTRS)
Fix, G. J.; Rose, M. E.
1983-01-01
A least squares formulation of the system divu = rho, curlu = zeta is surveyed from the viewpoint of both finite element and finite difference methods. Closely related arguments are shown to establish convergence estimates.
Interfractional trend analysis of dose differences based on 2D transit portal dosimetry
NASA Astrophysics Data System (ADS)
Persoon, L. C. G. G.; Nijsten, S. M. J. J. G.; Wilbrink, F. J.; Podesta, M.; Snaith, J. A. D.; Lustberg, T.; van Elmpt, W. J. C.; van Gils, F.; Verhaegen, F.
2012-10-01
Dose delivery of a radiotherapy treatment can be influenced by a number of factors. It has been demonstrated that the electronic portal imaging device (EPID) is valuable for transit portal dosimetry verification. Patient related dose differences can emerge at any time during treatment and can be categorized in two types: (1) systematic—appearing repeatedly, (2) random—appearing sporadically during treatment. The aim of this study is to investigate how systematic and random information appears in 2D transit dose distributions measured in the EPID plane over the entire course of a treatment and how this information can be used to examine interfractional trends, building toward a methodology to support adaptive radiotherapy. To create a trend overview of the interfractional changes in transit dose, the predicted portal dose for the different beams is compared to a measured portal dose using a γ evaluation. For each beam of the delivered fraction, information is extracted from the γ images to differentiate systematic from random dose delivery errors. From the systematic differences of a fraction for a projected anatomical structures, several metrics are extracted like percentage pixels with |γ| > 1. We demonstrate for four example cases the trends and dose difference causes which can be detected with this method. Two sample prostate cases show the occurrence of a random and systematic difference and identify the organ that causes the difference. In a lung cancer case a trend is shown of a rapidly diminishing atelectasis (lung fluid) during the course of treatment, which was detected with this trend analysis method. The final example is a breast cancer case where we show the influence of set-up differences on the 2D transit dose. A method is presented based on 2D portal transit dosimetry to record dose changes throughout the course of treatment, and to allow trend analysis of dose discrepancies. We show in example cases that this method can identify the causes of
Hsu, Sen-Ming; Chang, Hung-Chun
2007-11-26
A full-vectorial finite element method based eigenvalue algorithm is developed to analyze the band structures of two-dimensional (2D) photonic crystals (PCs) with arbitray 3D anisotropy for in-planewave propagations, in which the simple transverse-electric (TE) or transverse-magnetic (TM) modes may not be clearly defined. By taking all the field components into consideration simultaneously without decoupling of the wave modes in 2D PCs into TE and TM modes, a full-vectorial matrix eigenvalue equation, with the square of the wavenumber as the eigenvalue, is derived. We examine the convergence behaviors of this algorithm and analyze 2D PCs with arbitrary anisotropy using this algorithm to demonstrate its correctness and usefulness by explaining the numerical results theoretically. PMID:19550864
Kim, S.
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
2D:4D Asymmetry and Gender Differences in Academic Performance
Nye, John V. C.; Androuschak, Gregory; Desierto, Desirée; Jones, Garett; Yudkevich, Maria
2012-01-01
Exposure to prenatal androgens affects both future behavior and life choices. However, there is still relatively limited evidence on its effects on academic performance. Moreover, the predicted effect of exposure to prenatal testosterone (T)–which is inversely correlated with the relative length of the second to fourth finger lengths (2D:4D)–would seem to have ambiguous effects on academic achievement since traits like aggressiveness or risk-taking are not uniformly positive for success in school. We provide the first evidence of a non-linear, quadratic, relationship between 2D:4D and academic achievement using samples from Moscow and Manila. We also find that there is a gender differentiated link between various measures of academic achievement and measured digit ratios. These effects are different depending on the field of study, choice of achievement measure, and use of the right hand or left digit ratios. The results seem to be asymmetric between Moscow and Manila where the right (left) hand generates inverted-U (U-shaped) curves in Moscow while the pattern for hands reverses in Manila. Drawing from unusually large and detailed samples of university students in two countries not studied in the digit literature, our work is the first to have a large cross country comparison that includes two groups with very different ethnic compositions. PMID:23056282
Adaptive finite difference for seismic wavefield modelling in acoustic media.
Yao, Gang; Wu, Di; Debens, Henry Alexander
2016-01-01
Efficient numerical seismic wavefield modelling is a key component of modern seismic imaging techniques, such as reverse-time migration and full-waveform inversion. Finite difference methods are perhaps the most widely used numerical approach for forward modelling, and here we introduce a novel scheme for implementing finite difference by introducing a time-to-space wavelet mapping. Finite difference coefficients are then computed by minimising the difference between the spatial derivatives of the mapped wavelet and the finite difference operator over all propagation angles. Since the coefficients vary adaptively with different velocities and source wavelet bandwidths, the method is capable to maximise the accuracy of the finite difference operator. Numerical examples demonstrate that this method is superior to standard finite difference methods, while comparable to Zhang's optimised finite difference scheme. PMID:27491333
Adaptive finite difference for seismic wavefield modelling in acoustic media
NASA Astrophysics Data System (ADS)
Yao, Gang; Wu, Di; Debens, Henry Alexander
2016-08-01
Efficient numerical seismic wavefield modelling is a key component of modern seismic imaging techniques, such as reverse-time migration and full-waveform inversion. Finite difference methods are perhaps the most widely used numerical approach for forward modelling, and here we introduce a novel scheme for implementing finite difference by introducing a time-to-space wavelet mapping. Finite difference coefficients are then computed by minimising the difference between the spatial derivatives of the mapped wavelet and the finite difference operator over all propagation angles. Since the coefficients vary adaptively with different velocities and source wavelet bandwidths, the method is capable to maximise the accuracy of the finite difference operator. Numerical examples demonstrate that this method is superior to standard finite difference methods, while comparable to Zhang’s optimised finite difference scheme.
Adaptive finite difference for seismic wavefield modelling in acoustic media
Yao, Gang; Wu, Di; Debens, Henry Alexander
2016-01-01
Efficient numerical seismic wavefield modelling is a key component of modern seismic imaging techniques, such as reverse-time migration and full-waveform inversion. Finite difference methods are perhaps the most widely used numerical approach for forward modelling, and here we introduce a novel scheme for implementing finite difference by introducing a time-to-space wavelet mapping. Finite difference coefficients are then computed by minimising the difference between the spatial derivatives of the mapped wavelet and the finite difference operator over all propagation angles. Since the coefficients vary adaptively with different velocities and source wavelet bandwidths, the method is capable to maximise the accuracy of the finite difference operator. Numerical examples demonstrate that this method is superior to standard finite difference methods, while comparable to Zhang’s optimised finite difference scheme. PMID:27491333
Impact of Structural Differences in Galactocerebrosides on the Behavior of 2D Monolayers.
Stefaniu, Cristina; Ries, Annika; Gutowski, Olof; Ruett, Uta; Seeberger, Peter H; Werz, Daniel B; Brezesinski, Gerald
2016-03-15
The molecular interactions of three biologically important galactocerebrosides have been studied in monolayers formed at the soft air/water interface as 2D model membranes. Highly surface-sensitive techniques as GIXD (grazing incidence X-ray diffraction), IRRAS (infrared reflection-absorption spectroscopy), and BAM (Brewster angle microscopy) have been used. The study reveals that small differences in the chemical structure have a relevant impact on the physical-chemical properties and intermolecular interactions. The presence of a 2-d-hydroxyl group in the fatty acid favored for GalCer C24:0 (2-OH) monolayers a higher hydration state of the headgroup at low lateral pressures (<25 mN/m) and a higher condensation effect above 30 mN/m. An opposite behavior was recorded for GalCer C24:0 and GalCer C24:1, for which the intermolecular interactions are defined by the weakly hydrated but strong H-bonded interconnected head groups. Additionally, the 15-cis-double bond in the fatty acid chain (nervonic acid) of GalCer C24:1 stabilized the LE phase but did not disturb the packing parameters of the LC phase as compared with the saturated compound GalCer C24:0. PMID:26907993
Zhou, Huaiyu; Zhao, Qunli; Das Singla, Lachhman; Min, Juan; He, Shenyi; Cong, Hua; Li, Ying; Su, Chunlei
2013-04-01
Toxoplasma gondii is an obligate intracellular protozoan that infects mammals and birds. Human infection during pregnancy may cause severe damage to the fetus. Reactivation of latent infection in immunocompromised patients can cause life-threatening encephalitis. T. gondii strains are highly diverse but only a few lineages (Type I, II and III) are widely spread. In mouse model, Type I strains are highly virulent, whereas Type II and III strains are intermediately or non virulent. It is not clear how much quantitative difference exists in proteomic profiles among these distinct T. gondii lineages. In the present study, the proteomic profiles of T. gondii tachyzoites from these lineages were investigated by two dimensional fluorescence difference gel electrophoresis (2D-DIGE) and mass spectrometry (MS) technologies. A total of 2321 protein spots were detected. Overall, the GT1 strain of Type I lineage and the strain PTG of Type II lineage have highly similar proteomic profiles and both are different from that of the CTG strain of Type III lineage. Eighty-four protein spots were differentially expressed by greater than 1.5-fold in relative abundance and 10 of them were identified to 7 T. gondii proteins in existing database. Investigation of the quantitative differences in proteomics among distinct T. gondii strains should facilitate our understanding of difference in biological processes and pathogenesis of distinct T. gondii genotypes, which will provide basic information to determine treatment regimen for different manifestation of toxoplasmosis. PMID:23340323
Calibration and simulation of ASM2d at different temperatures in a phosphorus removal pilot plant.
García-Usach, F; Ferrer, J; Bouzas, A; Seco, A
2006-01-01
In this work, an organic and nutrient removal pilot plant was used to study the temperature influence on phosphorus accumulating organisms. Three experiments were carried out at 13, 20 and 24.5 degrees C, achieving a high phosphorus removal percentage in all cases. The ASM2d model was calibrated at 13 and 20 degrees C and the Arrhenius equation constant was obtained for phosphorus removal processes showing that the temperature influences on the biological phosphorus removal subprocesses in a different degree. The 24.5 degrees C experiment was simulated using the model parameters obtained by means of the Arrhenius equation. The simulation results for the three experiments showed good correspondence with the experimental data, demonstrating that the model and the calibrated parameters were able to predict the pilot plant behaviour. PMID:16889256
Bailey, T S; Adams, M L; Chang, J H
2008-10-01
We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional cylindrical (RZ) geometry for arbitrary polygonal meshes. This discretization is a discontinuous finite element method that utilizes the piecewise linear basis functions developed by Stone and Adams. We describe an asymptotic analysis that shows this method to be accurate for many problems in the thick diffusion limit on arbitrary polygons, allowing this method to be applied to radiative transfer problems with these types of meshes. We also present numerical results for multiple problems on quadrilateral grids and compare these results to the well-known bi-linear discontinuous finite element method.
Stochastic finite-difference time-domain
NASA Astrophysics Data System (ADS)
Smith, Steven Michael
2011-12-01
This dissertation presents the derivation of an approximate method to determine the mean and the variance of electro-magnetic fields in the body using the Finite-Difference Time-Domain (FDTD) method. Unlike Monte Carlo analysis, which requires repeated FDTD simulations, this method directly computes the variance of the fields at every point in space at every sample of time in the simulation. This Stochastic FDTD simulation (S-FDTD) has at its root a new wave called the Variance wave, which is computed in the time domain along with the mean properties of the model space in the FDTD simulation. The Variance wave depends on the electro-magnetic fields, the reflections and transmission though the different dielectrics, and the variances of the electrical properties of the surrounding materials. Like the electro-magnetic fields, the Variance wave begins at zero (there is no variance before the source is turned on) and is computed in the time domain until all fields reach steady state. This process is performed in a fraction of the time of a Monte Carlo simulation and yields the first two statistical parameters (mean and variance). The mean of the field is computed using the traditional FDTD equations. Variance is computed by approximating the correlation coefficients between the constituitive properties and the use of the S-FDTD equations. The impetus for this work was the simulation time it takes to perform 3D Specific Absorption Rate (SAR) FDTD analysis of the human head model for cell phone power absorption in the human head due to the proximity of a cell phone being used. In many instances, Monte Carlo analysis is not performed due to the lengthy simulation times required. With the development of S-FDTD, these statistical analyses could be performed providing valuable statistical information with this information being provided in a small fraction of the time it would take to perform a Monte Carlo analysis.
Finite Mathematics and Discrete Mathematics: Is There a Difference?
ERIC Educational Resources Information Center
Johnson, Marvin L.
Discrete mathematics and finite mathematics differ in a number of ways. First, finite mathematics has a longer history and is therefore more stable in terms of course content. Finite mathematics courses emphasize certain particular mathematical tools which are useful in solving the problems of business and the social sciences. Discrete mathematics…
Veijola, Timo; Råback, Peter
2007-01-01
We present a straightforward method to solve gas damping problems for perforated structures in two dimensions (2D) utilising a Perforation Profile Reynolds (PPR) solver. The PPR equation is an extended Reynolds equation that includes additional terms modelling the leakage flow through the perforations, and variable diffusivity and compressibility profiles. The solution method consists of two phases: 1) determination of the specific admittance profile and relative diffusivity (and relative compressibility) profiles due to the perforation, and 2) solution of the PPR equation with a FEM solver in 2D. Rarefied gas corrections in the slip-flow region are also included. Analytic profiles for circular and square holes with slip conditions are presented in the paper. To verify the method, square perforated dampers with 16–64 holes were simulated with a three-dimensional (3D) Navier-Stokes solver, a homogenised extended Reynolds solver, and a 2D PPR solver. Cases for both translational (in normal to the surfaces) and torsional motion were simulated. The presented method extends the region of accurate simulation of perforated structures to cases where the homogenisation method is inaccurate and the full 3D Navier-Stokes simulation is too time-consuming.
Viscoelastic Finite Difference Modeling Using Graphics Processing Units
NASA Astrophysics Data System (ADS)
Fabien-Ouellet, G.; Gloaguen, E.; Giroux, B.
2014-12-01
Full waveform seismic modeling requires a huge amount of computing power that still challenges today's technology. This limits the applicability of powerful processing approaches in seismic exploration like full-waveform inversion. This paper explores the use of Graphics Processing Units (GPU) to compute a time based finite-difference solution to the viscoelastic wave equation. The aim is to investigate whether the adoption of the GPU technology is susceptible to reduce significantly the computing time of simulations. The code presented herein is based on the freely accessible software of Bohlen (2002) in 2D provided under a General Public License (GNU) licence. This implementation is based on a second order centred differences scheme to approximate time differences and staggered grid schemes with centred difference of order 2, 4, 6, 8, and 12 for spatial derivatives. The code is fully parallel and is written using the Message Passing Interface (MPI), and it thus supports simulations of vast seismic models on a cluster of CPUs. To port the code from Bohlen (2002) on GPUs, the OpenCl framework was chosen for its ability to work on both CPUs and GPUs and its adoption by most of GPU manufacturers. In our implementation, OpenCL works in conjunction with MPI, which allows computations on a cluster of GPU for large-scale model simulations. We tested our code for model sizes between 1002 and 60002 elements. Comparison shows a decrease in computation time of more than two orders of magnitude between the GPU implementation run on a AMD Radeon HD 7950 and the CPU implementation run on a 2.26 GHz Intel Xeon Quad-Core. The speed-up varies depending on the order of the finite difference approximation and generally increases for higher orders. Increasing speed-ups are also obtained for increasing model size, which can be explained by kernel overheads and delays introduced by memory transfers to and from the GPU through the PCI-E bus. Those tests indicate that the GPU memory size
High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains
NASA Astrophysics Data System (ADS)
Fisher, Travis C.; Carpenter, Mark H.
2013-11-01
Nonlinear entropy stability is used to derive provably stable high-order finite difference operators including boundary closure stencils, for the compressible Navier-Stokes equations. A comparison technique is used to derive a new Entropy Stable Weighted Essentially Non-Oscillatory (SSWENO) finite difference method, appropriate for simulations of problems with shocks. Viscous terms are approximated using conservative, entropy stable, narrow-stencil finite difference operators. The efficacy of the new discrete operators is demonstrated using both smooth and discontinuous test cases.
High-Order Entropy Stable Finite Difference Schemes for Nonlinear Conservation Laws: Finite Domains
NASA Technical Reports Server (NTRS)
Fisher, Travis C.; Carpenter, Mark H.
2013-01-01
Developing stable and robust high-order finite difference schemes requires mathematical formalism and appropriate methods of analysis. In this work, nonlinear entropy stability is used to derive provably stable high-order finite difference methods with formal boundary closures for conservation laws. Particular emphasis is placed on the entropy stability of the compressible Navier-Stokes equations. A newly derived entropy stable weighted essentially non-oscillatory finite difference method is used to simulate problems with shocks and a conservative, entropy stable, narrow-stencil finite difference approach is used to approximate viscous terms.
NASA Astrophysics Data System (ADS)
Li, Jianbao; Wang, Yue-Sheng; Zhang, Chuanzeng
2010-05-01
In this paper, a finite element method based on the ABAQUS code and user subroutine is presented to evaluate the propagation of acoustic waves in the two-dimensional phononic crystals with Archimedean-like tilings. Two systems composed of cylinder scatters embedded in a host in Ladybug and Bathroom lattices are considered. Complete and accurate band structures and transmission spectra are obtained to identify the band gaps and eigenmodes. We found that Archimedean-like structures can have some advantages over the traditional square lattice regarding the completeness of the gap and its position and width. Also, due to the same square primitive unit cell and the first Brillouin zone, the two square-like lattices have similar acoustic response in lower bands. The results indicate that the finite element method is precise for the band structure computation of the complex phononic crystals with Archimedean tilings.
NASA Astrophysics Data System (ADS)
Wendling, A.; Daniel, J. L.; Hivet, G.; Vidal-Sallé, E.; Boisse, P.
2015-12-01
Numerical simulation is a powerful tool to predict the mechanical behavior and the feasibility of composite parts. Among the available numerical approaches, as far as woven reinforced composites are concerned, 3D finite element simulation at the mesoscopic scale leads to a good compromise between realism and complexity. At this scale, the fibrous reinforcement is modeled by an interlacement of yarns assumed to be homogeneous that have to be accurately represented. Among the numerous issues induced by these simulations, the first one consists in providing a representative meshed geometrical model of the unit cell at the mesoscopic scale. The second one consists in enabling a fast data input in the finite element software (contacts definition, boundary conditions, elements reorientation, etc.) so as to obtain results within reasonable time. Based on parameterized 3D CAD modeling tool of unit-cells of dry fabrics already developed, this paper presents an efficient strategy which permits an automated meshing of the models with 3D hexahedral elements and to accelerate of several orders of magnitude the simulation data input. Finally, the overall modeling strategy is illustrated by examples of finite element simulation of the mechanical behavior of fabrics.
NASA Astrophysics Data System (ADS)
Le Hardy, D.; Favennec, Y.; Rousseau, B.
2016-08-01
The 2D radiative transfer equation coupled with specular reflection boundary conditions is solved using finite element schemes. Both Discontinuous Galerkin and Streamline-Upwind Petrov-Galerkin variational formulations are fully developed. These two schemes are validated step-by-step for all involved operators (transport, scattering, reflection) using analytical formulations. Numerical comparisons of the two schemes, in terms of convergence rate, reveal that the quadratic SUPG scheme proves efficient for solving such problems. This comparison constitutes the main issue of the paper. Moreover, the solution process is accelerated using block SOR-type iterative methods, for which the determination of the optimal parameter is found in a very cheap way.
Comparison of finite-difference and analytic microwave calculation methods
Friedlander, F.I.; Jackson, H.W.; Barmatz, M.; Wagner, P.
1996-12-31
Normal modes and power absorption distributions in microwave cavities containing lossy dielectric samples were calculated for problems of interest in materials processing. The calculations were performed both using a commercially available finite-difference electromagnetic solver and by numerical evaluation of exact analytic expressions. Results obtained by the two methods applied to identical physical situations were compared. The studies validate the accuracy of the finite-difference electromagnetic solver. Relative advantages of the analytic and finite-difference methods are discussed.
Full 2D observation of water surface elevation from SWOT under different flow conditions
NASA Astrophysics Data System (ADS)
Domeneghetti, Alessio; Schumann, Guy; Rui, Wei; Durand, Michael; Pavelsky, Tamlin
2016-04-01
The upcoming Surface Water and Ocean Topography (SWOT) satellite mission is a joint project of NASA, Centre National d'Etudes Spatiales (CNES, France), the Canadian Space Agency, and the Space Agency of the UK that will provide a first global, high-resolution observation of ocean and terrestrial water surface heights. Characterized by an observation swath of 120 km and an orbit repeat interval of about 21 days, SWOT will provide unprecedented bi-dimensional observations of rivers wider than 50-100 m. Despite many research activities that have investigated potential uses of remotely sensed data from SWOT, potentials and limitations of the spatial observations provided by the satellite mission for flood modeling still remain poorly understood and investigated. In this study we present a first analysis of the spatial observation of water surface elevation that is expected from SWOT for a 140 km reach of the middle-lower portion of the Po River, in Northern Italy. The river stretch is characterized by a main channel varying from 200-500 m in width and a floodplain that can be as wide as 5 km and that is delimited by a system of major embankments. The reconstruction of the hydraulic behavior of the Po River is performed by means of a quasi-2d model built with detailed topographic and bathymetric information (LiDAR, 2 m resolution), while the simulation of the spatial observation sensed by SWOT is performed with a SWOT simulator that mimics the satellite sensor characteristics. Referring to water surface elevations associated with different flow conditions (maximum, minimum and average flow reproduced by means of the quasi-2d numerical model) this work provides a first characterization of the spatial observations provided by SWOT and highlights the strengths and limitations of the expected products. By referring to a real river reach the analysis provides a credible example of the type of spatial observations that will be available after launch of SWOT and offers a first
Coupled 2D-3D finite element method for analysis of a skin panel with a discontinuous stiffener
NASA Technical Reports Server (NTRS)
Wang, J. T.; Lotts, C. G.; Davis, D. D., Jr.; Krishnamurthy, T.
1992-01-01
This paper describes a computationally efficient analysis method which was used to predict detailed stress states in a typical composite compression panel with a discontinuous hat stiffener. A global-local approach was used. The global model incorporated both 2D shell and 3D brick elements connected by newly developed transition elements. Most of the panel was modeled with 2D elements, while 3D elements were employed to model the stiffener flange and the adjacent skin. Both linear and geometrically nonlinear analyses were performed on the global model. The effect of geometric nonlinearity induced by the eccentric load path due to the discontinuous hat stiffener was significant. The local model used a fine mesh of 3D brick elements to model the region at the end of the stiffener. Boundary conditions of the local 3D model were obtained by spline interpolation of the nodal displacements from the global analysis. Detailed in-plane and through-the-thickness stresses were calculated in the flange-skin interface near the end of the stiffener.
Stress analysis of a rectangular implant in laminated composites using 2-D and 3-D finite elements
NASA Technical Reports Server (NTRS)
Chow, Wai T.; Graves, Michael J.
1992-01-01
An analysis method using the FEM based on the Hellinger-Reissner variation principle has been developed to determine the 3-D stresses and displacements near a rectangular implant inside a laminated composite material. Three-dimensional elements are employed in regions where the interlaminar stress is considered to be significant; 2-D elements are used in other areas. Uniaxially loaded graphite-epoxy laminates have been analyzed; the implant was modeled as four plies of 3501/6 epoxy located in the middle of the laminate. It is shown that the interlaminar stresses are an order of magnitude lower than the stress representing the applied far-field load. The stress concentration factors of both the interlaminar and in-plane stresses depend on the stacking sequence of the laminate.
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.
Lerche, Ernesto; Van Eester, Dirk
2011-12-23
Fourier analysis in the poloidal direction is a standard ingredient in present-day 2D wave equation solvers describing radio frequency waves in hot tokamak plasmas. Although a powerful and elegant technique, Fourier analysis has the disadvantage that a large number of modes is needed to describe the field pattern on a magnetic surface if a short wavelength mode exists on any - even very small - subpart of the particle trajectory. The present paper examines the potential of a method that does not suffer from this drawback: a finite element technique relying on simple linear or cubic area base functions that are defined on irregular elementary surfaces of triangular shape. The wave equation is solved in its weak Galerkin variational form and for realistic 2D tokamak geometry, accounting for the toroidal curvature but assuming the toroidal angle is ignorable, allowing to study the wave pattern for each of the independent toroidal modes excited by the antenna individually.The locally uniform full hot plasma dielectric tensor to all orders in finite Larmor radius was adopted. As the main intended application is the study of fast wave behavior (heating and current drive) at arbitrary harmonics, the wave vector complex amplitude appearing in the dielectric tensor is determined through a local dispersion root evaluation. High frequency fast wave propagation and damping is provided as an illustration in view of possible application of this type of current drive in future high density reactor-like tokamaks.
NASA Astrophysics Data System (ADS)
Ren, Xiaotao; Corcolle, Romain; Daniel, Laurent
2016-02-01
The use of soft magnetic composites (SMCs) in electrical engineering applications is growing. SMCs provide an effective alternative to laminated steels because they exhibit a high permeability with low eddy current losses. Losses are a critical feature in the design of electrical machines, and it is necessary to evaluate the role of microstructure and constitutive properties of SMCs during the predesign stage. In this paper we propose a simplified finite element approach to compute eddy current losses in these materials. The computations allow to quantify the role of exciting source and material properties on eddy current losses. This analysis can later be used in the development of homogenization models for SMC. Contribution to the topical issue "Numelec 2015 - Elected submissions", edited by Adel Razek
Comparison of different nonlinear solvers for 2D time-implicit stellar hydrodynamics
NASA Astrophysics Data System (ADS)
Viallet, M.; Baraffe, I.; Walder, R.
2013-07-01
Time-implicit schemes are attractive since they allow numerical time steps that are much larger than those permitted by the Courant-Friedrich-Lewy criterion characterizing time-explicit methods. This advantage comes, however, at a cost: the solution of a system of nonlinear equations is required at each time step. In this work, the nonlinear system results from the discretization of the hydrodynamical equations with the Crank-Nicholson scheme. We compare the cost of different methods, based on Newton-Raphson iterations, to solve this nonlinear system, and benchmark their performances against time-explicit schemes. Since our general scientific objective is to model stellar interiors, we use as test cases two realistic models for the convective envelope of a red giant and a young Sun. Focusing on 2D simulations, we show that the best performances are obtained with the quasi-Newton method proposed by Broyden. Another important concern is the accuracy of implicit calculations. Based on the study of an idealized problem, namely the advection of a single vortex by a uniform flow, we show that there are two aspects: i) the nonlinear solver has to be accurate enough to resolve the truncation error of the numerical discretization; and ii) the time step has be small enough to resolve the advection of eddies. We show that with these two conditions fulfilled, our implicit methods exhibit similar accuracy to time-explicit schemes, which have lower values for the time step and higher computational costs. Finally, we discuss in the conclusion the applicability of these methods to fully implicit 3D calculations.
NASA Astrophysics Data System (ADS)
Liu, Hong; Mo, Yu L.
1998-08-01
There are many textures such as woven fabrics having repeating Textron. In order to handle the textural characteristics of images with defects, this paper proposes a new method based on 2D wavelet transform. In the method, a new concept of different adaptive wavelet bases is used to match the texture pattern. The 2D wavelet transform has two different adaptive orthonormal wavelet bases for rows and columns which differ from Daubechies wavelet bases. The orthonormal wavelet bases for rows and columns are generated by genetic algorithm. The experiment result demonstrate the ability of the different adaptive wavelet bases to characterize the texture and locate the defects in the texture.
NASA Astrophysics Data System (ADS)
Sauer, Roger A.
2013-08-01
Recently an enriched contact finite element formulation has been developed that substantially increases the accuracy of contact computations while keeping the additional numerical effort at a minimum reported by Sauer (Int J Numer Meth Eng, 87: 593-616, 2011). Two enrich-ment strategies were proposed, one based on local p-refinement using Lagrange interpolation and one based on Hermite interpolation that produces C 1-smoothness on the contact surface. Both classes, which were initially considered for the frictionless Signorini problem, are extended here to friction and contact between deformable bodies. For this, a symmetric contact formulation is used that allows the unbiased treatment of both contact partners. This paper also proposes a post-processing scheme for contact quantities like the contact pressure. The scheme, which provides a more accurate representation than the raw data, is based on an averaging procedure that is inspired by mortar formulations. The properties of the enrichment strategies and the corresponding post-processing scheme are illustrated by several numerical examples considering sliding and peeling contact in the presence of large deformations.
2D warp-and-woof interwoven networks constructed by helical chains with different chirality.
Feng, Yuhua; Guo, Yang; OuYang, Yan; Liu, Zhanquan; Liao, Daizheng; Cheng, Peng; Yan, Shiping; Jiang, Zonghui
2007-09-21
Two unprecedented 2D entangled layers of warp-and-woof threads interwoven by left- and right-handed helical chains, {[Mn(salen)Au(CN)2]4(H2O)}n (salen = N,N'-ethylenebis(salicylideneaminato)) and {Mn(acacen)Ag(CN)2}n (acacen = N,N'-ethylenebis(acetylacetonylideneiminate)) 2, have been synthesized and characterized. PMID:17728880
NASA Technical Reports Server (NTRS)
Leonard, B. P.
1992-01-01
Judging by errors in the computational-fluid-dynamics literature in recent years, it is not generally well understood that (above first-order) there are significant differences in spatial truncation error between formulations of convection involving a finite-difference approximation of the first derivative, on the one hand, and a finite-volume model of flux differences across a control-volume cell, on the other. The difference between the two formulations involves a second-order truncation-error term (proportional to the third-derivative of the convected variable). Hence, for example, a third (or higher) order finite-difference approximation for the first-derivative convection term is only second-order accurate when written in conservative control-volume form as a finite-volume formulation, and vice versa.
Computer-Oriented Calculus Courses Using Finite Differences.
ERIC Educational Resources Information Center
Gordon, Sheldon P.
The so-called discrete approach in calculus instruction involves introducing topics from the calculus of finite differences and finite sums, both for motivation and as useful tools for applications of the calculus. In particular, it provides an ideal setting in which to incorporate computers into calculus courses. This approach has been…
Ghazi, A A; Hosseinpanah, F; Abdi, H; Hedayati, M; Hasheminia, M; Ghazi, S; Azizi, F
2016-06-01
Data regarding 1,25-dihydroxycholecalciferol in adolescents are limited. We aimed to determine serum levels of this active metabolite of vitamin D and the effects of different doses of vitamin D on its concentration in schoolchildren with high prevalence of vitamin D deficiency. In a previously published randomized double-blind, placebo-controlled trial, 210 subjects, aged 14-20 years, were assigned to 3 regimens of vitamin D treatment: group A (n=70) received 50 000 U oral cholecalciferol monthly, group B (n=70), 50 000 U bimonthly, and group C (n=70), placebo. Serum 25(OH)D, calcium, parathyroid hormone, and bone markers were measured at baseline and after 2 and 5 months of treatment. In the present study, serum levels of 1,25(OH)2D were measured in 97 boys and 95 girls. At baseline, girls had significantly higher concentrations of 1,25(OH)2D than boys (36, IQR: 24, 63 vs. 30, IQR: 15, 57.5 pmol/l; p<0.01). There was no significant correlation between serum levels of 25(OH)D and 1,25(OH)2D in the total population (Spearman rho=- 0.111; p=0.126), boys (Spearman rho=0.008; p=0.941), and girls (Spearman rho=0.036; p=0.729). Also, 1,25(OH)2D values did not change over time in different study groups. Moreover, total and sex-stratified analysis did not show any significant difference between different groups at different times of the study period. In an adolescent population with high prevalence of hypovitaminosis D especially in girls, 1,25(OH)2D values were higher in girls than boys. There was no significant change in 1,25(OH)2D concentrations with different doses of vitamin D. PMID:26975346
Hybrid finite element-finite difference method for thermal analysis of blood vessels.
Blanchard, C H; Gutierrez, G; White, J A; Roemer, R B
2000-01-01
A hybrid finite-difference/finite-element technique for the thermal analysis of blood vessels embedded in perfused tissue has been developed and evaluated. This method provides efficient and accurate solutions to the conjugated heat transfer problem of convection by blood coupled to conduction in the tissue. The technique uses a previously developed 3D automatic meshing method for creating a finite element mesh in the tissue surrounding the vessels, coupled iteratively with a 1-D marching finite difference method for the interior of the vessels. This hybrid technique retains the flexibility and ease of automated finite-element meshing techniques for modelling the complex geometry of blood vessels and irregularly shaped tissues, and speeds the solution time by using a simple finite-difference method to calculate the bulk mean temperatures within all blood vessels. The use of the 1D finite-difference technique in the blood vessels also eliminates the large computer memory requirements needed to accurately solve large vessel network problems when fine FE meshes are used in the interior of vessels. The accuracy of the hybrid technique has been verified against previously verified numerical solutions. In summary, the hybrid technique combines the accuracy and flexibility found in automated finite-element techniques, with the speed and reduction of computational memory requirements associated with the 1D finite-difference technique, something which has not been done before. This method, thus, has the potential to provide accurate, flexible and relatively fast solutions for the thermal analysis of coupled perfusion/blood vessel problems, and large vessel network problems. PMID:10949130
Coupled finite-difference/finite-element approach for wing-body aeroelasticity
NASA Technical Reports Server (NTRS)
Guruswamy, Guru P.
1992-01-01
Computational methods using finite-difference approaches for fluids and finite-element approaches for structures have individually advanced to solve almost full-aircraft configurations. However, coupled approaches to solve fluid/structural interaction problems are still in their early stages of development, particularly for complex geometries using complete equations such as the Euler/Navier-Stokes equations. Earlier work demonstrated the success of coupling finite-difference and finite-element methods for simple wing configurations using the Euler/Navier-Stokes equations. In this paper, the same approach is extended for general wing-body configurations. The structural properties are represented by beam-type finite elements. The flow is modeled using the Euler/Navier-Stokes equations. A general procedure to fully couple structural finite-element boundary conditions with fluid finite-difference boundary conditions is developed for wing-body configurations. Computations are made using moving grids that adapt to wing-body structural deformations. Results are illustrated for a typical wing-body configuration.
3D Finite Difference Modelling of Basaltic Region
NASA Astrophysics Data System (ADS)
Engell-Sørensen, L.
2003-04-01
The main purpose of the work was to generate realistic data to be applied for testing of processing and migration tools for basaltic regions. The project is based on the three - dimensional finite difference code (FD), TIGER, made by Sintef. The FD code was optimized (parallelized) by the author, to run on parallel computers. The parallel code enables us to model large-scale realistic geological models and to apply traditional seismic and micro seismic sources. The parallel code uses multiple processors in order to manipulate subsets of large amounts of data simultaneously. The general anisotropic code uses 21 elastic coefficients. Eight independent coefficients are needed as input parameters for the general TI medium. In the FD code, the elastic wave field computation is implemented by a higher order FD solution to the elastic wave equation and the wave fields are computed on a staggered grid, shifted half a node in one or two directions. The geological model is a gridded basalt model, which covers from 24 km to 37 km of a real shot line in horizontal direction and from the water surface to the depth of 3.5 km. The 2frac {1}{2}D model has been constructed using the compound modeling software from Norsk Hydro. The vertical parameter distribution is obtained from observations in two wells. At The depth of between 1100 m to 1500 m, a basalt horizon covers the whole sub surface layers. We have shown that it is possible to simulate a line survey in realistic (3D) geological models in reasonable time by using high performance computers. The author would like to thank Norsk Hydro, Statoil, GEUS, and SINTEF for very helpful discussions and Parallab for being helpful with the new IBM, p690 Regatta system.
A finite-difference contrast source inversion method
NASA Astrophysics Data System (ADS)
Abubakar, A.; Hu, W.; van den Berg, P. M.; Habashy, T. M.
2008-12-01
We present a contrast source inversion (CSI) algorithm using a finite-difference (FD) approach as its backbone for reconstructing the unknown material properties of inhomogeneous objects embedded in a known inhomogeneous background medium. Unlike the CSI method using the integral equation (IE) approach, the FD-CSI method can readily employ an arbitrary inhomogeneous medium as its background. The ability to use an inhomogeneous background medium has made this algorithm very suitable to be used in through-wall imaging and time-lapse inversion applications. Similar to the IE-CSI algorithm the unknown contrast sources and contrast function are updated alternately to reconstruct the unknown objects without requiring the solution of the full forward problem at each iteration step in the optimization process. The FD solver is formulated in the frequency domain and it is equipped with a perfectly matched layer (PML) absorbing boundary condition. The FD operator used in the FD-CSI method is only dependent on the background medium and the frequency of operation, thus it does not change throughout the inversion process. Therefore, at least for the two-dimensional (2D) configurations, where the size of the stiffness matrix is manageable, the FD stiffness matrix can be inverted using a non-iterative inversion matrix approach such as a Gauss elimination method for the sparse matrix. In this case, an LU decomposition needs to be done only once and can then be reused for multiple source positions and in successive iterations of the inversion. Numerical experiments show that this FD-CSI algorithm has an excellent performance for inverting inhomogeneous objects embedded in an inhomogeneous background medium.
Conservative properties of finite difference schemes for incompressible flow
NASA Technical Reports Server (NTRS)
Morinishi, Youhei
1995-01-01
The purpose of this research is to construct accurate finite difference schemes for incompressible unsteady flow simulations such as LES (large-eddy simulation) or DNS (direct numerical simulation). In this report, conservation properties of the continuity, momentum, and kinetic energy equations for incompressible flow are specified as analytical requirements for a proper set of discretized equations. Existing finite difference schemes in staggered grid systems are checked for satisfaction of the requirements. Proper higher order accurate finite difference schemes in a staggered grid system are then proposed. Plane channel flow is simulated using the proposed fourth order accurate finite difference scheme and the results compared with those of the second order accurate Harlow and Welch algorithm.
Techniques for correcting approximate finite difference solutions. [considering transonic flow
NASA Technical Reports Server (NTRS)
Nixon, D.
1978-01-01
A method of correcting finite-difference solutions for the effect of truncation error or the use of an approximate basic equation is presented. Applications to transonic flow problems are described and examples are given.
Comparison of different precondtioners for nonsymmtric finite volume element methods
Mishev, I.D.
1996-12-31
We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.
Finite-difference solutions of the 3-D eikonal equation
Fei, Tong; Fehler, M.C.; Hildebrand, S.T.
1995-12-31
Prestack Kirchhoff depth migration requires the computation of traveltimes from surface source and receiver locations to subsurface image locations. In 3-D problems, computational efficiency becomes important. Finite-difference solutions of the eikonal equation provide computationally efficient methods for generating the traveltime information. Here, a novel finite-difference solutions of the eikonal equation provide computationally efficient methods for generating the traveltime information. Here, a novel finite-difference method for computing the first arrival traveltime by solving the eikonal equation has been developed in Cartesian coordinates. The method, which is unconditionally stable and computationally efficient, can handle instabilities due to caustics and provide information about head waves. The comparison of finite-difference solutions of the acoustic wave equation with the traveltime solutions from the eikonal equation in various structure models demonstrate that the method developed here can provide correct first arrival traveltime information even in areas of complex velocity structure.
NASA Astrophysics Data System (ADS)
Key, K.
2013-12-01
This work announces the public release of an open-source inversion code named MARE2DEM (Modeling with Adaptively Refined Elements for 2D Electromagnetics). Although initially designed for the rapid inversion of marine electromagnetic data, MARE2DEM now supports a wide variety of acquisition configurations for both offshore and onshore surveys that utilize electric and magnetic dipole transmitters or magnetotelluric plane waves. The model domain is flexibly parameterized using a grid of arbitrarily shaped polygonal regions, allowing for complicated structures such as topography or seismically imaged horizons to be easily assimilated. MARE2DEM efficiently solves the forward problem in parallel by dividing the input data parameters into smaller subsets using a parallel data decomposition algorithm. The data subsets are then solved in parallel using an automatic adaptive finite element method that iterative solves the forward problem on successively refined finite element meshes until a specified accuracy tolerance is met, thus freeing the end user from the burden of designing an accurate numerical modeling grid. Regularized non-linear inversion for isotropic or anisotropic conductivity is accomplished with a new implementation of Occam's method referred to as fast-Occam, which is able to minimize the objective function in much fewer forward evaluations than the required by the original method. This presentation will review the theoretical considerations behind MARE2DEM and use a few recent offshore EM data sets to demonstrate its capabilities and to showcase the software interface tools that streamline model building and data inversion.
Combining different design strategies for rational affinity maturation of the MICA-NKG2D interface
Henager, Samuel H; Hale, Melissa A; Maurice, Nicholas J; Dunnington, Erin C; Swanson, Carter J; Peterson, Megan J; Ban, Joseph J; Culpepper, David J; Davies, Luke D; Sanders, Lisa K; McFarland, Benjamin J
2012-01-01
We redesigned residues on the surface of MICA, a protein that binds the homodimeric immunoreceptor NKG2D, to increase binding affinity with a series of rational, incremental changes. A fixed-backbone RosettaDesign protocol scored a set of initial mutations, which we tested by surface plasmon resonance for thermodynamics and kinetics of NKG2D binding, both singly and in combination. We combined the best four mutations at the surface with three affinity-enhancing mutations below the binding interface found with a previous design strategy. After curating design scores with three cross-validated tests, we found a linear relationship between free energy of binding and design score, and to a lesser extent, enthalpy and design score. Multiple mutants bound with substantial subadditivity, but in at least one case full additivity was observed when combining distant mutations. Altogether, combining the best mutations from the two strategies into a septuple mutant enhanced affinity by 50-fold, to 50 nM, demonstrating a simple, effective protocol for affinity enhancement. PMID:22761154
NASA Astrophysics Data System (ADS)
Vidal, F.; de Assis, J. T.; Lopes, R. T.; Lima, I.
2014-02-01
In recent years, bone quantification led to a deeper knowledge of the 3D microarchitecture. In this study the bone architecture of rats was investigated based on 2D/3D morphometric analysis using microcomputed tomography, aiming at determining the effect of the image acquisition pixel on the quality of some 2D/3D morphometric parameters, such as porosity and trabecular density.Six pairs of bone samples were used and the scans were carried out using high microcomputed tomography system, operating at three different pixel sizes of 33.3 μm, 15.0 μm and 9.5 μm. The results showed 2D parameters values lower than those obtained in the 3D analysis, mainly for trabecular density, separation and thickness.
Numerical techniques in linear duct acoustics. [finite difference and finite element analyses
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1980-01-01
Both finite difference and finite element analyses of small amplitude (linear) sound propagation in straight and variable area ducts with flow, as might be found in a typical turboject engine duct, muffler, or industrial ventilation system, are reviewed. Both steady state and transient theories are discussed. Emphasis is placed on the advantages and limitations associated with the various numerical techniques. Examples of practical problems are given for which the numerical techniques have been applied.
Cho, Hea-Young; Lee, Yong-Bok
2006-06-01
The aim of this study was to evaluate the bioequivalence of risperidone in healthy male subjects representing different CYP2D6 genotypes with respect to risperidone, 9-hydroxyrisperidone (9-OH-risperidone), and active moiety. A total of 506 Korean subjects were genotyped for CYP2D6*10 by means of allele-specific polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP). Based on the genotype analysis, 24 subjects, 7 homozygous for CYP2D6*1, 10 for *10, and 7 heterozygous for *10, were recruited and received a single oral dose of 2 mg risperidone tablet in this study. Serum concentrations of risperidone and 9-OHrisperidone up to 48 h were simultaneously determined. There were no significant differences of the active moiety, risperidone, and 9-OH-risperidone between the two preparations in AUC0-proportinal to, and Cmax. The 90% confidence intervals (CIs) for the ratio of means of the log-transformed AUC0-proportional to. and Cmax for the active moiety, risperidone, and 9-OH-risperidone were all within the bioequivalence acceptance criteria of 0.80-1.25. The CYP2D6*10 allele particularly was associated with higher serum concentrations of risperidone and the risperidone/9-OH-risperidone ratio compared with the CYP2D6*1 allele. The results demonstrate that the two preparations of risperidone are bioequivalent and it can be assumed that they are therapeutically equivalent and exchangeable in clinical practice. Furthermore, the pharmacokinetic parameters of risperidone and the risperidone/9-OH-risperidone ratio are highly dependent on the CYP2D6 genotypes. PMID:16833023
Practical aspects of prestack depth migration with finite differences
Ober, C.C.; Oldfield, R.A.; Womble, D.E.; Romero, L.A.; Burch, C.C.
1997-07-01
Finite-difference, prestack, depth migrations offers significant improvements over Kirchhoff methods in imaging near or under salt structures. The authors have implemented a finite-difference prestack depth migration algorithm for use on massively parallel computers which is discussed. The image quality of the finite-difference scheme has been investigated and suggested improvements are discussed. In this presentation, the authors discuss an implicit finite difference migration code, called Salvo, that has been developed through an ACTI (Advanced Computational Technology Initiative) joint project. This code is designed to be efficient on a variety of massively parallel computers. It takes advantage of both frequency and spatial parallelism as well as the use of nodes dedicated to data input/output (I/O). Besides giving an overview of the finite-difference algorithm and some of the parallelism techniques used, migration results using both Kirchhoff and finite-difference migration will be presented and compared. The authors start out with a very simple Cartoon model where one can intuitively see the multiple travel paths and some of the potential problems that will be encountered with Kirchhoff migration. More complex synthetic models as well as results from actual seismic data from the Gulf of Mexico will be shown.
Hsu, Sen-ming; Chang, Hung-chun
2008-12-22
To effectively investigate the fundamental characteristics of two-dimensional (2D) photonic crystals (PCs) with arbitrary 3D material anisotropy under the out-of-plane wave propagation, we establish a full-vectorial finite element method based eigenvalue algorithm to perform related analysis correctly. The band edge diagrams can be conveniently constructed from the band structures of varied propagation constants obtained from the algorithm, which is helpful for the analysis and design of photonic ban gap (PBG) fibers. Several PCs are analyzed to demonstrate the correctness of this numerical model. Our analysis results for simple PCs are checked with others' ones using different methods, including the transfer matrix method, the finite-difference frequency-domain (FDFD) method, and the plane-wave expansion method. And the validity of those for the most complex PC with arbitrary 3D anisotropy is supported by related liquid-crystal-filled PBG fiber mode analysis, which demonstrates the dependence of transmission properties on the PBGs, employing a full-vectorial finite element beam propagation method (FE-BPM). PMID:19104565
Comparison of 2D transmon coherence for different capacitive shunt fabrication methods
NASA Astrophysics Data System (ADS)
Yoder, Jonilyn; Kamal, Archana; Yan, Fei; Gudmundsen, Theodore; Welander, Paul; Gustavsson, Simon; Hover, David; Kerman, Andrew; Sears, Adam; Oliver, William
2015-03-01
Improvements in superconducting qubit coherence times and reproducibility have been demonstrated using capacitive shunting. In this study, we present a side-by-side comparison of two distinct methods for preparing the aluminum shunt capacitor material for 2D transmon superconducting qubit devices. The first method involved in situ wafer outgassing prior to molecular beam epitaxy aluminum evaporation. The second method involved ex situ wafer annealing prior to electron gun aluminum evaporation. Materials analysis for each process will be detailed. Experimental results, including qubit coherence times and superconducting coplanar waveguide resonator internal quality factors, will be presented for representative devices prepared using both methods. This work is sponsored by the Assistant Secretary of Defense for Research and Engineering under Air Force Contract FA8721-05-0002. Opinions, interpretations, conclusions, and recommendations are those of the authors and are not necessarily endorsed by the United States Government.
Improved finite-difference vibration analysis of pretwisted, tapered beams
NASA Technical Reports Server (NTRS)
Subrahmanyam, K. B.; Kaza, K. R. V.
1984-01-01
An improved finite difference procedure based upon second order central differences is developed. Several difficulties encountered in earlier works with fictitious stations that arise in using second order central differences, are eliminated by developing certain recursive relations. The need for forward or backward differences at the beam boundaries or other similar procedures is eliminated in the present theory. By using this improved theory, the vibration characteristics of pretwisted and tapered blades are calculated. Results of the second order theory are compared with published theoretical and experimental results and are found to be in good agreement. The present method generally produces close lower bound solutions and shows fast convergence. Thus, extrapolation procedures that are customary with first order finite-difference methods are unnecessary. Furthermore, the computational time and effort needed for this improved method are almost the same as required for the conventional first order finite-difference approach.
Finite-difference schemes for anisotropic diffusion
Es, Bram van; Koren, Barry; Blank, Hugo J. de
2014-09-01
In fusion plasmas diffusion tensors are extremely anisotropic due to the high temperature and large magnetic field strength. This causes diffusion, heat conduction, and viscous momentum loss, to effectively be aligned with the magnetic field lines. This alignment leads to different values for the respective diffusive coefficients in the magnetic field direction and in the perpendicular direction, to the extent that heat diffusion coefficients can be up to 10{sup 12} times larger in the parallel direction than in the perpendicular direction. This anisotropy puts stringent requirements on the numerical methods used to approximate the MHD-equations since any misalignment of the grid may cause the perpendicular diffusion to be polluted by the numerical error in approximating the parallel diffusion. Currently the common approach is to apply magnetic field-aligned coordinates, an approach that automatically takes care of the directionality of the diffusive coefficients. This approach runs into problems at x-points and at points where there is magnetic re-connection, since this causes local non-alignment. It is therefore useful to consider numerical schemes that are tolerant to the misalignment of the grid with the magnetic field lines, both to improve existing methods and to help open the possibility of applying regular non-aligned grids. To investigate this, in this paper several discretization schemes are developed and applied to the anisotropic heat diffusion equation on a non-aligned grid.
Hoffman, E.L.; Ammerman, D.J.
1995-04-01
A series of tests investigating dynamic pulse buckling of a cylindrical shell under axial impact is compared to several 2D and 3D finite element simulations of the event. The purpose of the work is to investigate the performance of various analysis codes and element types on a problem which is applicable to radioactive material transport packages, and ultimately to develop a benchmark problem to qualify finite element analysis codes for the transport package design industry. Four axial impact tests were performed on 4 in-diameter, 8 in-long, 304 L stainless steel cylinders with a 3/16 in wall thickness. The cylinders were struck by a 597 lb mass with an impact velocity ranging from 42.2 to 45.1 ft/sec. During the impact event, a buckle formed at each end of the cylinder, and one of the two buckles became unstable and collapsed. The instability occurred at the top of the cylinder in three tests and at the bottom in one test. Numerical simulations of the test were performed using the following codes and element types: PRONTO2D with axisymmetric four-node quadrilaterals; PRONTO3D with both four-node shells and eight-node hexahedrons; and ABAQUS/Explicit with axisymmetric two-node shells and four-node quadrilaterals, and 3D four-node shells and eight-node hexahedrons. All of the calculations are compared to the tests with respect to deformed shape and impact load history. As in the tests, the location of the instability is not consistent in all of the calculations. However, the calculations show good agreement with impact load measurements with the exception of an initial load spike which is proven to be the dynamic response of the load cell to the impact. Finally, the PRONIT02D calculation is compared to the tests with respect to strain and acceleration histories. Accelerometer data exhibited good qualitative agreement with the calculations. The strain comparisons show that measurements are very sensitive to gage placement.
Diverse 2D structures obtained by adsorption of charged ABA triblock copolymer on different surfaces
NASA Astrophysics Data System (ADS)
Kontturi, Katri S.; Vesterinen, Arja-Helena; Seppälä, Jukka; Laine, Janne
2012-11-01
In the larger context of 2D polymeric structures, the morphologies obtained by adsorption and subsequent drying of charged, ABA type amphiphilic triblock copolymer of poly[2-(dimethylamino)ethyl metacrylate] (PDMAEMA) and poly(propylene oxide) (PPO) were investigated with atomic force microscopy and X-ray photoelectron spectroscopy as well as in situ adsorption analysis with quartz crystal microbalance with dissipation monitoring. Hydrophilic silica and hydrophobic polystyrene (PS) were used as substrates for adsorption. The structures emerging from the self-assembly of adsorbing polymer were profoundly influenced by composition of the aqueous solution and the choice of substrate. When adsorbed from dilute polymer solution where the concentration is so low that the polymer does not yet show surface-active behavior, the triblock copolymer unimers associated on hydrophilic silica surface forming large, irregular clustered aggregates, with sizes increasing with electrolyte concentration of the solution. On a hydrophobic PS substrate, on the other hand, unimers spread much more evenly, forming clear surface patterns. The roughness of these patterned structures was tuned with the electrolyte concentration of the solution. Adsorption from a more concentrated polymer solution, where the surface-activity of the polymer is perceptible, resulted in the formation of a smooth film with complete coverage over the hydrophilic silica substrate when the electrolyte concentration was high. On PS, on the other hand, nucleation of evenly scattered globular, disk-like micelles was induced. Besides the dry film morphology, the even distribution of the irreversibly adsorbed polymer over the PS surface was likely to serve as an optimal platform for the build-up of reversible hydrophobically bound multilayers at high electrolyte concentration. The multilayer formation was reversible because a decrease in the electrolyte concentration of the solution re-introduces strong electrostatic
Compact finite difference method for American option pricing
NASA Astrophysics Data System (ADS)
Zhao, Jichao; Davison, Matt; Corless, Robert M.
2007-09-01
A compact finite difference method is designed to obtain quick and accurate solutions to partial differential equation problems. The problem of pricing an American option can be cast as a partial differential equation. Using the compact finite difference method this problem can be recast as an ordinary differential equation initial value problem. The complicating factor for American options is the existence of an optimal exercise boundary which is jointly determined with the value of the option. In this article we develop three ways of combining compact finite difference methods for American option price on a single asset with methods for dealing with this optimal exercise boundary. Compact finite difference method one uses the implicit condition that solutions of the transformed partial differential equation be nonnegative to detect the optimal exercise value. This method is very fast and accurate even when the spatial step size h is large (h[greater-or-equal, slanted]0.1). Compact difference method two must solve an algebraic nonlinear equation obtained by Pantazopoulos (1998) at every time step. This method can obtain second order accuracy for space x and requires a moderate amount of time comparable with that required by the Crank Nicolson projected successive over relaxation method. Compact finite difference method three refines the free boundary value by a method developed by Barone-Adesi and Lugano [The saga of the American put, 2003], and this method can obtain high accuracy for space x. The last two of these three methods are convergent, moreover all the three methods work for both short term and long term options. Through comparison with existing popular methods by numerical experiments, our work shows that compact finite difference methods provide an exciting new tool for American option pricing.
NASA Astrophysics Data System (ADS)
Zhu, Lu; Liu, Yuanyuan; Chen, Suhua; Hu, Fei; Chen, Zhizhang (David)
2015-04-01
Synthetic aperture imaging radiometer (SAIR) has the potential to meet the spatial resolution requirement of passive millimeter remote sensing from space. A new two-dimensional (2-D) imaging radiometer at millimeter wave (MMW) band is described in this paper; it uses a one-dimensional (1-D) synthetic aperture digital radiometer (SADR) to obtain an image on one dimension and a rotary platform to provide a scan on the second dimension. Due to the ill-posed inverse problem of SADR, we proposed a new reconstruction algorithm based on Finite Difference (FD) regularization to improve brightness temperature images. Experimental results show that the proposed 2-D MMW radiometer can give the brightness temperature images of natural scenes and the FD regularization reconstruction algorithm is able to improve the quality of brightness temperature images.
A comparison of the finite difference and finite element methods for heat transfer calculations
NASA Technical Reports Server (NTRS)
Emery, A. F.; Mortazavi, H. R.
1982-01-01
The finite difference method and finite element method for heat transfer calculations are compared by describing their bases and their application to some common heat transfer problems. In general it is noted that neither method is clearly superior, and in many instances, the choice is quite arbitrary and depends more upon the codes available and upon the personal preference of the analyst than upon any well defined advantages of one method. Classes of problems for which one method or the other is better suited are defined.
Finite-Difference Algorithms For Computing Sound Waves
NASA Technical Reports Server (NTRS)
Davis, Sanford
1993-01-01
Governing equations considered as matrix system. Method variant of method described in "Scheme for Finite-Difference Computations of Waves" (ARC-12970). Present method begins with matrix-vector formulation of fundamental equations, involving first-order partial derivatives of primitive variables with respect to space and time. Particular matrix formulation places time and spatial coordinates on equal footing, so governing equations considered as matrix system and treated as unit. Spatial and temporal discretizations not treated separately as in other finite-difference methods, instead treated together by linking spatial-grid interval and time step via common scale factor related to speed of sound.
Finite difference modeling of rotor flows including wake effects
NASA Technical Reports Server (NTRS)
Caradonna, F. X.; Desopper, A.; Tung, C.
1982-01-01
Rotary wing finite difference methods are investigated. The main concern is the specification of boundary conditions to properly account for the effect of the wake on the blade. Examples are given of an approach where wake effects are introduced by specifying an equivalent angle of attack. An alternate approach is also given where discrete vortices are introduced into the finite difference grid. The resulting computations of hovering and high advance ratio cases compare well with experiment. Some consideration is also given to the modeling of low to moderate advance ratio flows.
NASA Technical Reports Server (NTRS)
Strong, Stuart L.; Meade, Andrew J., Jr.
1992-01-01
Preliminary results are presented of a finite element/finite difference method (semidiscrete Galerkin method) used to calculate compressible boundary layer flow about airfoils, in which the group finite element scheme is applied to the Dorodnitsyn formulation of the boundary layer equations. The semidiscrete Galerkin (SDG) method promises to be fast, accurate and computationally efficient. The SDG method can also be applied to any smoothly connected airfoil shape without modification and possesses the potential capability of calculating boundary layer solutions beyond flow separation. Results are presented for low speed laminar flow past a circular cylinder and past a NACA 0012 airfoil at zero angle of attack at a Mach number of 0.5. Also shown are results for compressible flow past a flat plate for a Mach number range of 0 to 10 and results for incompressible turbulent flow past a flat plate. All numerical solutions assume an attached boundary layer.
Selecting step sizes in sensitivity analysis by finite differences
NASA Technical Reports Server (NTRS)
Iott, J.; Haftka, R. T.; Adelman, H. M.
1985-01-01
This paper deals with methods for obtaining near-optimum step sizes for finite difference approximations to first derivatives with particular application to sensitivity analysis. A technique denoted the finite difference (FD) algorithm, previously described in the literature and applicable to one derivative at a time, is extended to the calculation of several simultaneously. Both the original and extended FD algorithms are applied to sensitivity analysis for a data-fitting problem in which derivatives of the coefficients of an interpolation polynomial are calculated with respect to uncertainties in the data. The methods are also applied to sensitivity analysis of the structural response of a finite-element-modeled swept wing. In a previous study, this sensitivity analysis of the swept wing required a time-consuming trial-and-error effort to obtain a suitable step size, but it proved to be a routine application for the extended FD algorithm herein.
NASA Technical Reports Server (NTRS)
Saleem, M.; Pulliam, T.; Cheer, A. Y.
1993-01-01
Implicit difference operator spectra are presently computed by applying eigensystem analysis techniques to finite-difference formulations of 2D Euler and Navier-Stokes equations, and attention is given to these iterative methods' convergence and stability characteristics by taking into account the effects of grid geometry, time-step, numerical viscosity, and boundary conditions. On the basis of the eigenvalue distributions for various flow configurations, the feasibility of applying such convergence-acceleration techniques as eigenvalue annihilation and relaxation is discussed. Spectrum-shifting is applied to NASA-Ames' ARC2D flow code, achieving a 20-33 percent efficiency.
NASA Astrophysics Data System (ADS)
Ying, Jinyong; Xie, Dexuan
2015-10-01
The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model for calculating electrostatics of ionic solvated biomolecule. In this paper, a new finite element and finite difference hybrid method is presented to solve PBE efficiently based on a special seven-overlapped box partition with one central box containing the solute region and surrounded by six neighboring boxes. In particular, an efficient finite element solver is applied to the central box while a fast preconditioned conjugate gradient method using a multigrid V-cycle preconditioning is constructed for solving a system of finite difference equations defined on a uniform mesh of each neighboring box. Moreover, the PBE domain, the box partition, and an interface fitted tetrahedral mesh of the central box can be generated adaptively for a given PQR file of a biomolecule. This new hybrid PBE solver is programmed in C, Fortran, and Python as a software tool for predicting electrostatics of a biomolecule in a symmetric 1:1 ionic solvent. Numerical results on two test models with analytical solutions and 12 proteins validate this new software tool, and demonstrate its high performance in terms of CPU time and memory usage.
Modelling the core convection using finite element and finite difference methods
NASA Astrophysics Data System (ADS)
Chan, K. H.; Li, Ligang; Liao, Xinhao
2006-08-01
Applications of both parallel finite element and finite difference methods to thermal convection in a rotating spherical shell modelling the fluid dynamics of the Earth's outer core are presented. The numerical schemes are verified by reproducing the convection benchmark test by Christensen et al. [Christensen, U.R., Aubert, J., Cardin, P., Dormy, E., Gibbons, S., Glatzmaier, G.A., Grote, E., Honkura, Y., Jones, C., Kono, M., Matsushima, M., Sakuraba, A., Takahashi, F., Tilgner, A., Wilcht, J., Zhang, K., 2001. A numerical dynamo benchmark. Phys. Earth Planet. Interiors 128, 25-34.]. Both global average and local characteristics agree satisfactorily with the benchmark solution. With the element-by-element (EBE) parallelization technique, the finite element code demonstrates nearly optimal linear scalability in computational speed. The finite difference code is also efficient and scalable by utilizing a parallel library Aztec [Tuminaro, R.S., Heroux, M., Hutchinson, S.A., Shadid, J.N., 1999. Official AZTEC User's Guide: Version 2.1.].
Maximov, Philipp Y; McDaniel, Russell E; Fernandes, Daphne J; Korostyshevskiy, Valeriy R; Bhatta, Puspanjali; Mürdter, Thomas E; Flockhart, David A; Jordan, V Craig
2014-01-01
Background and Purpose Tamoxifen is a prodrug that is metabolically activated by 4-hydroxylation to the potent primary metabolite 4-hydroxytamoxifen (4OHT) or via another primary metabolite N-desmethyltamoxifen (NDMTAM) to a biologically active secondary metabolite endoxifen through a cytochrome P450 2D6 variant system (CYP2D6). To elucidate the mechanism of action of tamoxifen and the importance of endoxifen for its effect, we determined the anti-oestrogenic efficacy of tamoxifen and its metabolites, including endoxifen, at concentrations corresponding to serum levels measured in breast cancer patients with various CYP2D6 genotypes (simulating tamoxifen treatment). Experimental Approach The biological effects of tamoxifen and its metabolites on cell growth and oestrogen-responsive gene modulation were evaluated in a panel of oestrogen receptor-positive breast cancer cell lines. Actual clinical levels of tamoxifen metabolites in breast cancer patients were used in vitro along with actual levels of oestrogens observed in premenopausal patients taking tamoxifen. Key Results Tamoxifen and its primary metabolites (4OHT and NDMTAM) only partially inhibited the stimulant effects of oestrogen on cells. The addition of endoxifen at concentrations corresponding to different CYP2D6 genotypes was found to enhance the anti-oestrogenic effect of tamoxifen and its metabolites with an efficacy that correlated with the concentration of endoxifen; at concentrations corresponding to the extensive metabolizer genotype it further inhibited the actions of oestrogen. In contrast, lower concentrations of endoxifen (intermediate and poor metabolizers) had little or no anti-oestrogenic effects. Conclusions and Implications Endoxifen may be a clinically relevant metabolite in premenopausal patients as it provides additional anti-oestrogenic actions during tamoxifen treatment. PMID:25073551
Comparison of finite difference and finite element solutions to the variably saturated flow equation
NASA Astrophysics Data System (ADS)
Simpson, M. J.; Clement, T. P.
2003-01-01
Numerical solutions to the equation governing variably saturated flow are usually obtained using either the finite difference (FD) method or the finite element (FE) method. A detailed comparison of these methods shows that the main difference between them is in how the numerical schemes spatially average the variation of material properties. Further differences are also observed in the way that flux boundaries are represented in FE and FD methods. A modified finite element (MFE) algorithm is used to explore the significance of these differences. The MFE algorithm enables a direct comparison with a typical FD solution scheme, and explicitly demonstrates the differences between FE and FD methods. The MFE algorithm provides an improved approximation to the partial differential equation over the usual FD approach while being computationally simpler to implement than the standard FE solution. One of the main limitations of the MFE algorithm is that the algorithm was developed by imposing several restrictions upon the more general FE solution; however, the MFE is shown to be preferable over the usual FE and FD solutions for some of the test problems considered in this study. The comparison results show that the FE (or MFE) solution can avoid the erroneous results encountered in the FD solution for coarsely discretized problems. The improvement in the FE solution is attributed to the broader hydraulic conductivity averaging and differences in the representation of flux type boundaries.
Using the Finite Difference Calculus to Sum Powers of Integers.
ERIC Educational Resources Information Center
Zia, Lee
1991-01-01
Summing powers of integers is presented as an example of finite differences and antidifferences in discrete mathematics. The interrelation between these concepts and their analogues in differential calculus, the derivative and integral, is illustrated and can form the groundwork for students' understanding of differential and integral calculus.…
Scheme For Finite-Difference Computations Of Waves
NASA Technical Reports Server (NTRS)
Davis, Sanford
1992-01-01
Compact algorithms generating and solving finite-difference approximations of partial differential equations for propagation of waves obtained by new method. Based on concept of discrete dispersion relation. Used in wave propagation to relate frequency to wavelength and is key measure of wave fidelity.
Direct Finite-Difference Simulations Of Turbulent Flow
NASA Technical Reports Server (NTRS)
Rai, Man Mohan; Moin, Parviz
1991-01-01
Report discusses use of upwind-biased finite-difference numerical-integration scheme to simulate evolution of small disturbances and fully developed turbulence in three-dimensional flow of viscous, incompressible fluid in channel. Involves use of computational grid sufficiently fine to resolve motion of fluid at all relevant length scales.
Finite difference methods for the solution of unsteady potential flows
NASA Technical Reports Server (NTRS)
Caradonna, F. X.
1982-01-01
Various problems which are confronted in the development of an unsteady finite difference potential code are reviewed mainly in the context of what is done for a typical small disturbance and full potential method. The issues discussed include choice of equations, linearization and conservation, differencing schemes, and algorithm development. A number of applications, including unsteady three dimensional rotor calculations, are demonstrated.
2D-PAGE protein analysis of dinoflagellate Alexandrium minutum based on three different temperatures
NASA Astrophysics Data System (ADS)
Latib, Norhidayu Abdul; Norshaha, Safida Anira; Usup, Gires; Yusof, Nurul Yuziana Mohd
2015-09-01
Harmful algae bloom or red tide seems to be considered as threat to ecosystem, especially to human consumption because of the production of neurotoxin by dinoflagellates species such as Alexandrium minutum which can lead to paralytic shellfish poisoning. The aim of this study is to determine the most suitable method for protein extraction of A. minutum followed by determination of differential protein expression of A. minutum on three different temperatures (15°C, 26°C and 31.5°C). After the optimization, the protein extract was subjected to two-dimensional polyacrylamide gel electrophoresis (2-DE) to compare the intensity and distribution of the protein spots. Based on quantitative and qualitative protein assessment, use of Trizol reagent is the most suitable method to extract protein from A. minutum. 2-DE analysis of the samples results in different distribution and intensity of the protein spots were compared between 15°C, 26°C and 31.5°C.
Matrix Cracking in Four Different 2D SiC/SiC Composite Systems
NASA Technical Reports Server (NTRS)
Morscher, Gregory N.
2003-01-01
Silicon carbide fiber reinforced, silicon carbide matrix composites are some of the most advanced composite systems for high-temperature, high-stress applications in oxidizing environments. A basic area that needs to be understood for the purpose of material behavior modeling and optimization is the architectural, constituent, and mechanistic factors that contribute to non-linear stress-strain behavior. The mechanism that causes non-linear stress-strain in dense-matrix composites is the formation and propagation of bridged matrix cracks. In addition, the occurrence and propagation of matrix cracks controls the time-dependent strength-properties of these materials in oxidizing environments at elevated temperatures. A modal acoustic emission technique has been used to monitor and estimate the stress-dependent matrix cracking. Two different SiC matrix systems, chemical vapor infiltrated (CVI) and melt-infiltrated (MI), with two different SiC fiber reinforcement, Hi-Nicalon (trademark) and Sylramic (trademark) were compared. Even though the averages of the range where matrix cracking occurred for the composites varied by more than 0.1% in strain and almost 200 MPa in stress, the range or distribution for matrix cracking could be reduced to a narrow band of stress for CVI SiC and MI SiC composites if it were assumed that all matrix cracks emanate outside of the load-bearing fiber, interphase, CVI preform minicomposite. A simple relationship was determined to describe stress-dependent matrix cracking which can then be used to estimate the onset of large, bridged matrix cracks or for material behavior models.
Native N-terminus nitrophorin 2 from the kissing bug: similarities to and differences from NP2(D1A).
Berry, Robert E; Muthu, Dhanasekaran; Shokhireva, Tatiana K; Garrett, Sarah A; Zhang, Hongjun; Walker, F Ann
2012-09-01
The first amino acid of mature native nitrophorin 2 is aspartic acid, and when expressed in E. coli, the wild-type gene of the mature protein retains the methionine-0, which is produced by translation of the start codon. This form of NP2, (M0)NP2, has been found to have different properties from its D1A mutant, for which the Met0 is cleaved by the methionine aminopeptidase of E. coli (R. E. Berry, T. K. Shokhireva, I. Filippov, M. N. Shokhirev, H. Zhang, F. A. Walker, Biochemistry 2007, 46, 6830). Native N-terminus nitrophorin 2 ((ΔM0)NP2) has been prepared by employing periplasmic expression of NP2 in E. coli using the pelB leader sequence from Erwinia carotovora, which is present in the pET-26b expression plasmid (Novagen). This paper details the similarities and differences between the three different N-terminal forms of nitrophorin 2, (M0)NP2, NP2(D1A), and (ΔM0)NP2. It is found that the NMR spectra of high- and low-spin (ΔM0)NP2 are essentially identical to those of NP2(D1A), but the rate and equilibrium constants for histamine and NO dissociation/association of the two are different. PMID:22976966
Hyun, Eugin; Jin, Young-Seok; Lee, Jong-Hun
2016-01-01
For an automotive pedestrian detection radar system, fast-ramp based 2D range-Doppler Frequency Modulated Continuous Wave (FMCW) radar is effective for distinguishing between moving targets and unwanted clutter. However, when a weak moving target such as a pedestrian exists together with strong clutter, the pedestrian may be masked by the side-lobe of the clutter even though they are notably separated in the Doppler dimension. To prevent this problem, one popular solution is the use of a windowing scheme with a weighting function. However, this method leads to a spread spectrum, so the pedestrian with weak signal power and slow Doppler may also be masked by the main-lobe of clutter. With a fast-ramp based FMCW radar, if the target is moving, the complex spectrum of the range- Fast Fourier Transform (FFT) is changed with a constant phase difference over ramps. In contrast, the clutter exhibits constant phase irrespective of the ramps. Based on this fact, in this paper we propose a pedestrian detection for highly cluttered environments using a coherent phase difference method. By detecting the coherent phase difference from the complex spectrum of the range-FFT, we first extract the range profile of the moving pedestrians. Then, through the Doppler FFT, we obtain the 2D range-Doppler map for only the pedestrian. To test the proposed detection scheme, we have developed a real-time data logging system with a 24 GHz FMCW transceiver. In laboratory tests, we verified that the signal processing results from the proposed method were much better than those expected from the conventional 2D FFT-based detection method. PMID:26805835
Hyun, Eugin; Jin, Young-Seok; Lee, Jong-Hun
2016-01-01
For an automotive pedestrian detection radar system, fast-ramp based 2D range-Doppler Frequency Modulated Continuous Wave (FMCW) radar is effective for distinguishing between moving targets and unwanted clutter. However, when a weak moving target such as a pedestrian exists together with strong clutter, the pedestrian may be masked by the side-lobe of the clutter even though they are notably separated in the Doppler dimension. To prevent this problem, one popular solution is the use of a windowing scheme with a weighting function. However, this method leads to a spread spectrum, so the pedestrian with weak signal power and slow Doppler may also be masked by the main-lobe of clutter. With a fast-ramp based FMCW radar, if the target is moving, the complex spectrum of the range- Fast Fourier Transform (FFT) is changed with a constant phase difference over ramps. In contrast, the clutter exhibits constant phase irrespective of the ramps. Based on this fact, in this paper we propose a pedestrian detection for highly cluttered environments using a coherent phase difference method. By detecting the coherent phase difference from the complex spectrum of the range-FFT, we first extract the range profile of the moving pedestrians. Then, through the Doppler FFT, we obtain the 2D range-Doppler map for only the pedestrian. To test the proposed detection scheme, we have developed a real-time data logging system with a 24 GHz FMCW transceiver. In laboratory tests, we verified that the signal processing results from the proposed method were much better than those expected from the conventional 2D FFT-based detection method. PMID:26805835
NASA Astrophysics Data System (ADS)
Bayona, Victor; Kindelan, Manuel
2013-10-01
Laminar flame propagation is an important problem in combustion modelling for which great advances have been achieved both in its theoretical understanding and in the numerical solution of the governing equations in 2D and 3D. Most of these numerical simulations use finite difference techniques on simple geometries (channels, ducts, ...) with equispaced nodes. The objective of this work is to explore the applicability of the radial basis function generated finite difference (RBF-FD) method to laminar flame propagation modelling. This method is specially well suited for the solution of problems with complex geometries and irregular boundaries. Another important advantage is that the method is independent of the dimension of the problem and, therefore, it is very easy to apply in 3D problems with complex geometries. In this work we use the RBF-FD method to compute 2D and 3D numerical results that simulate premixed laminar flames with different Lewis numbers propagating in open ducts.
NASA Astrophysics Data System (ADS)
Autovino, Dario; Negm, Amro; Rallo, Giovanni; Provenzano, Giuseppe
2016-04-01
In Mediterranean countries characterized by limited water resources for agricultural and societal sectors, irrigation management plays a major role to improve water use efficiency at farm scale, mainly where irrigation systems are correctly designed to guarantee a suitable application efficiency and the uniform water distribution throughout the field. In the last two decades, physically-based agro-hydrological models have been developed to simulate mass and energy exchange processes in the soil-plant-atmosphere (SPA) system. Mechanistic models like HYDRUS 2D/3D (Šimunek et al., 2011) have been proposed to simulate all the components of water balance, including actual crop transpiration fluxes estimated according to a soil potential-dependent sink term. Even though the suitability of these models to simulate the temporal dynamics of soil and crop water status has been reported in the literature for different horticultural crops, a few researches have been considering arboreal crops where the higher gradients of root water uptake are the combination between the localized irrigation supply and the three dimensional root system distribution. The main objective of the paper was to assess the performance of HYDRUS-2D model to evaluate soil water contents and transpiration fluxes of an olive orchard irrigated with two different water distribution systems. Experiments were carried out in Castelvetrano (Sicily) during irrigation seasons 2011 and 2012, in a commercial farm specialized in the production of table olives (Olea europaea L., var. Nocellara del Belice), representing the typical variety of the surrounding area. During the first season, irrigation water was provided by a single lateral placed along the plant row with four emitters per plant (ordinary irrigation), whereas during the second season a grid of emitters laid on the soil was installed in order to irrigate the whole soil surface around the selected trees. The model performance was assessed based on the
Finite-difference lattice-Boltzmann methods for binary fluids.
Xu, Aiguo
2005-06-01
We investigate two-fluid Bhatnagar-Gross-Krook (BGK) kinetic methods for binary fluids. The developed theory works for asymmetric as well as symmetric systems. For symmetric systems it recovers Sirovich's theory and is summarized in models A and B. For asymmetric systems it contributes models C, D, and E which are especially useful when the total masses and/or local temperatures of the two components are greatly different. The kinetic models are discretized based on an octagonal discrete velocity model. The discrete-velocity kinetic models and the continuous ones are required to describe the same hydrodynamic equations. The combination of a discrete-velocity kinetic model and an appropriate finite-difference scheme composes a finite-difference lattice Boltzmann method. The validity of the formulated methods is verified by investigating (i) uniform relaxation processes, (ii) isothermal Couette flow, and (iii) diffusion behavior. PMID:16089910
Time dependent wave envelope finite difference analysis of sound propagation
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1984-01-01
A transient finite difference wave envelope formulation is presented for sound propagation, without steady flow. Before the finite difference equations are formulated, the governing wave equation is first transformed to a form whose solution tends not to oscillate along the propagation direction. This transformation reduces the required number of grid points by an order of magnitude. Physically, the transformed pressure represents the amplitude of the conventional sound wave. The derivation for the wave envelope transient wave equation and appropriate boundary conditions are presented as well as the difference equations and stability requirements. To illustrate the method, example solutions are presented for sound propagation in a straight hard wall duct and in a two dimensional straight soft wall duct. The numerical results are in good agreement with exact analytical results.
Experimentally constructing finite difference algorithms in numerical relativity
NASA Astrophysics Data System (ADS)
Anderson, Matthew; Neilsen, David; Matzner, Richard
2002-04-01
Computational studies of gravitational waves require numerical algorithms with long-term stability (necessary for convergence). However, constructing stable finite difference algorithms (FDA) for the ADM formulation of the Einstein equations, especially in multiple dimensions, has proven difficult. Most FDA's are constructed using rules of thumb gained from experience with simple model equations. To search for FDA's with improved stability, we adopt a brute-force approach, where we systematically test thousands of numerical schemes. We sort the spatial derivatives of the Einstein equations into groups, and parameterize each group by finite difference type (centered or upwind) and order. Furthermore, terms proportional to the constraints are added to the evolution equations with additional parameters. A spherically symmetric, excised Schwarzschild black hole (one dimension) and linearized waves in multiple dimensions are used as model systems to evaluate the different numerical schemes.
Finite element-finite difference thermal/structural analysis of large space truss structures
NASA Technical Reports Server (NTRS)
Warren, Andrew H.; Arelt, Joseph E.; Eskew, William F.; Rogers, Karen M.
1992-01-01
A technique of automated and efficient thermal-structural processing of truss structures that interfaces the finite element and finite difference method was developed. The thermal-structural analysis tasks include development of the thermal and structural math models, thermal analysis, development of an interface and data transfer between the models, and finally an evaluation of the thermal stresses and displacements in the structure. Consequently, the objective of the developed technique was to minimize the model development time, in order to assure an automatic transfer of data between the thermal and structural models as well as to minimize the computer resources needed for the analysis itself. The method and techniques described are illustrated on the thermal/structural analysis of the Space Station Freedom main truss.
Algorithmic vs. finite difference Jacobians for infrared atmospheric radiative transfer
NASA Astrophysics Data System (ADS)
Schreier, Franz; Gimeno García, Sebastián; Vasquez, Mayte; Xu, Jian
2015-10-01
Jacobians, i.e. partial derivatives of the radiance and transmission spectrum with respect to the atmospheric state parameters to be retrieved from remote sensing observations, are important for the iterative solution of the nonlinear inverse problem. Finite difference Jacobians are easy to implement, but computationally expensive and possibly of dubious quality; on the other hand, analytical Jacobians are accurate and efficient, but the implementation can be quite demanding. GARLIC, our "Generic Atmospheric Radiation Line-by-line Infrared Code", utilizes algorithmic differentiation (AD) techniques to implement derivatives w.r.t. atmospheric temperature and molecular concentrations. In this paper, we describe our approach for differentiation of the high resolution infrared and microwave spectra and provide an in-depth assessment of finite difference approximations using "exact" AD Jacobians as a reference. The results indicate that the "standard" two-point finite differences with 1 K and 1% perturbation for temperature and volume mixing ratio, respectively, can exhibit substantial errors, and central differences are significantly better. However, these deviations do not transfer into the truncated singular value decomposition solution of a least squares problem. Nevertheless, AD Jacobians are clearly recommended because of the superior speed and accuracy.
Finite difference seismic modeling of axial magma chambers
Swift, S.A.; Dougherty, M.E.; Stephen, R.A. )
1990-11-01
The authors tested the feasibility of using finite difference methods to model seismic propagation at {approximately}10 Hx through a two-dimensional representation of an axial magma chamber with a thin, liquid lid. This technique produces time series of displacement or pressure at seafloor receivers to mimic a seismic refraction experiment and snapshots of P and S energy propagation. The results indicate that the implementation is stable for models with sharp velocity contrasts and complex geometries. The authors observe a high-energy, downward-traveling shear phase, observable only with borehole receivers, that would be useful in studying the nature and shape of magma chambers. The ability of finite difference methods to model high-order wave phenomena makes this method ideal for testing velocity models of spreading axes and for planning near-axis drilling of the East Pacific Rise in order to optimize the benefits from shear wave imaging of sub-axis structure.
Calculation of sensitivity derivatives in thermal problems by finite differences
NASA Technical Reports Server (NTRS)
Haftka, R. T.; Malkus, D. S.
1981-01-01
The optimum design of a structure subject to temperature constraints is considered. When mathematical optimization techniques are used, derivatives of the temperature constraints with respect to the design variables are usually required. In the case of large aerospace structures, such as the Space Shuttle, the computation of these derivatives can become prohibitively expensive. Analytical methods and a finite difference approach have been considered in studies conducted to improve the efficiency of the calculation of the derivatives. The present investigation explores two possibilities for enhancing the effectiveness of the finite difference approach. One procedure involves the simultaneous solution of temperatures and derivatives. The second procedure makes use of the optimum selection of the magnitude of the perturbations of the design variables to achieve maximum accuracy.
Semianalytical computation of path lines for finite-difference models
Pollock, D.W.
1988-01-01
A semianalytical particle tracking method was developed for use with velocities generated from block-centered finite-difference ground-water flow models. Based on the assumption that each directional velocity component varies linearly within a grid cell in its own coordinate directions, the method allows an analytical expression to be obtained describing the flow path within an individual grid cell. Given the intitial position of a particle anywhere in a cell, the coordinates of any other point along its path line within the cell, and the time of travel between them, can be computed directly. For steady-state systems, the exit point for a particle entering a cell at any arbitrary location can be computed in a single step. By following the particle as it moves from cell to cell, this method can be used to trace the path of a particle through any multidimensional flow field generated from a block-centered finite-difference flow model. -Author
NASA Technical Reports Server (NTRS)
Krueger, Ronald; Minguet, Pierre J.; Bushnell, Dennis M. (Technical Monitor)
2002-01-01
The influence of two-dimensional finite element modeling assumptions on the debonding prediction for skin-stiffener specimens was investigated. Geometrically nonlinear finite element analyses using two-dimensional plane-stress and plane strain elements as well as three different generalized plane strain type approaches were performed. The computed deflections, skin and flange strains, transverse tensile stresses and energy release rates were compared to results obtained from three-dimensional simulations. The study showed that for strains and energy release rate computations the generalized plane strain assumptions yielded results closest to the full three-dimensional analysis. For computed transverse tensile stresses the plane stress assumption gave the best agreement. Based on this study it is recommended that results from plane stress and plane strain models be used as upper and lower bounds. The results from generalized plane strain models fall between the results obtained from plane stress and plane strain models. Two-dimensional models may also be used to qualitatively evaluate the stress distribution in a ply and the variation of energy release rates and mixed mode ratios with lamination length. For more accurate predictions, however, a three-dimensional analysis is required.
Finite difference discretisation of a model for biological nerve conduction
NASA Astrophysics Data System (ADS)
Aderogba, A. A.; Chapwanya, M.; Jejeniwa, O. A.
2016-06-01
A nonstandard finite difference method is proposed for the discretisation of the semilinear FitzHugh-Nagumo reaction diffusion equation. The equation has been useful in describing, for example, population models, biological models, heat and mass transfer models, and many other applications. The proposed approach involves splitting the equation into the space independent and the time independent sub equation. Numerical simulations for the full equation are presented.
Optimized Finite-Difference Coefficients for Hydroacoustic Modeling
NASA Astrophysics Data System (ADS)
Preston, L. A.
2014-12-01
Responsible utilization of marine renewable energy sources through the use of current energy converter (CEC) and wave energy converter (WEC) devices requires an understanding of the noise generation and propagation from these systems in the marine environment. Acoustic noise produced by rotating turbines, for example, could adversely affect marine animals and human-related marine activities if not properly understood and mitigated. We are utilizing a 3-D finite-difference acoustic simulation code developed at Sandia that can accurately propagate noise in the complex bathymetry in the near-shore to open ocean environment. As part of our efforts to improve computation efficiency in the large, high-resolution domains required in this project, we investigate the effects of using optimized finite-difference coefficients on the accuracy of the simulations. We compare accuracy and runtime of various finite-difference coefficients optimized via criteria such as maximum numerical phase speed error, maximum numerical group speed error, and L-1 and L-2 norms of weighted numerical group and phase speed errors over a given spectral bandwidth. We find that those coefficients optimized for L-1 and L-2 norms are superior in accuracy to those based on maximal error and can produce runtimes of 10% of the baseline case, which uses Taylor Series finite-difference coefficients at the Courant time step limit. We will present comparisons of the results for the various cases evaluated as well as recommendations for utilization of the cases studied. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
Calculating rotordynamic coefficients of seals by finite-difference techniques
NASA Technical Reports Server (NTRS)
Dietzen, F. J.; Nordmann, R.
1987-01-01
For modelling the turbulent flow in a seal the Navier-Stokes equations in connection with a turbulence (kappa-epsilon) model are solved by a finite-difference method. A motion of the shaft round the centered position is assumed. After calculating the corresponding flow field and the pressure distribution, the rotor-dynamic coefficients of the seal can be determined. These coefficients are compared with results obtained by using the bulk flow theory of Childs and with experimental results.
Finite difference time domain grid generation from AMC helicopter models
NASA Technical Reports Server (NTRS)
Cravey, Robin L.
1992-01-01
A simple technique is presented which forms a cubic grid model of a helicopter from an Aircraft Modeling Code (AMC) input file. The AMC input file defines the helicopter fuselage as a series of polygonal cross sections. The cubic grid model is used as an input to a Finite Difference Time Domain (FDTD) code to obtain predictions of antenna performance on a generic helicopter model. The predictions compare reasonably well with measured data.
Finite difference time domain calculations of antenna mutual coupling
NASA Technical Reports Server (NTRS)
Luebbers, Raymond J.; Kunz, Karl S.
1991-01-01
The Finite Difference Time Domain (FDTD) technique was applied to a wide variety of electromagnetic analysis problems, including shielding and scattering. However, the method has not been exclusively applied to antennas. Here, calculations of self and mutual admittances between wire antennas are made using FDTD and compared with results obtained during the method of moments. The agreement is quite good, indicating the possibilities for FDTD application to antenna impedance and coupling.
Finite difference time domain calculations of antenna mutual coupling
NASA Technical Reports Server (NTRS)
Luebbers, Raymond J.; Kunz, Karl S.
1991-01-01
The Finite Difference Time Domain (FDTD) technique has been applied to a wide variety of electromagnetic analysis problems, including shielding and scattering. However, the method has not been extensively applied to antennas. In this short paper calculations of self and mutual admittances between wire antennas are made using FDTD and compared with results obtained using the Method of Moments. The agreement is quite good, indicating the possibilities for FDTD application to antenna impedance and coupling.
Finite difference methods for the solution of unsteady potential flows
NASA Technical Reports Server (NTRS)
Caradonna, F. X.
1985-01-01
A brief review is presented of various problems which are confronted in the development of an unsteady finite difference potential code. This review is conducted mainly in the context of what is done for a typical small disturbance and full potential methods. The issues discussed include choice of equation, linearization and conservation, differencing schemes, and algorithm development. A number of applications including unsteady three-dimensional rotor calculation, are demonstrated.
Finite difference schemes for long-time integration
NASA Technical Reports Server (NTRS)
Haras, Zigo; Taasan, Shlomo
1993-01-01
Finite difference schemes for the evaluation of first and second derivatives are presented. These second order compact schemes were designed for long-time integration of evolution equations by solving a quadratic constrained minimization problem. The quadratic cost function measures the global truncation error while taking into account the initial data. The resulting schemes are applicable for integration times fourfold, or more, longer than similar previously studied schemes. A similar approach was used to obtain improved integration schemes.
Dispersion-relation-preserving finite difference schemes for computational acoustics
NASA Technical Reports Server (NTRS)
Tam, Christopher K. W.; Webb, Jay C.
1993-01-01
Time-marching dispersion-relation-preserving (DRP) schemes can be constructed by optimizing the finite difference approximations of the space and time derivatives in wave number and frequency space. A set of radiation and outflow boundary conditions compatible with the DRP schemes is constructed, and a sequence of numerical simulations is conducted to test the effectiveness of the DRP schemes and the radiation and outflow boundary conditions. Close agreement with the exact solutions is obtained.
High Order Finite Difference Methods for Multiscale Complex Compressible Flows
NASA Technical Reports Server (NTRS)
Sjoegreen, Bjoern; Yee, H. C.
2002-01-01
The classical way of analyzing finite difference schemes for hyperbolic problems is to investigate as many as possible of the following points: (1) Linear stability for constant coefficients; (2) Linear stability for variable coefficients; (3) Non-linear stability; and (4) Stability at discontinuities. We will build a new numerical method, which satisfies all types of stability, by dealing with each of the points above step by step.
Introduction to finite-difference methods for numerical fluid dynamics
Scannapieco, E.; Harlow, F.H.
1995-09-01
This work is intended to be a beginner`s exercise book for the study of basic finite-difference techniques in computational fluid dynamics. It is written for a student level ranging from high-school senior to university senior. Equations are derived from basic principles using algebra. Some discussion of partial-differential equations is included, but knowledge of calculus is not essential. The student is expected, however, to have some familiarity with the FORTRAN computer language, as the syntax of the computer codes themselves is not discussed. Topics examined in this work include: one-dimensional heat flow, one-dimensional compressible fluid flow, two-dimensional compressible fluid flow, and two-dimensional incompressible fluid flow with additions of the equations of heat flow and the {Kappa}-{epsilon} model for turbulence transport. Emphasis is placed on numerical instabilities and methods by which they can be avoided, techniques that can be used to evaluate the accuracy of finite-difference approximations, and the writing of the finite-difference codes themselves. Concepts introduced in this work include: flux and conservation, implicit and explicit methods, Lagrangian and Eulerian methods, shocks and rarefactions, donor-cell and cell-centered advective fluxes, compressible and incompressible fluids, the Boussinesq approximation for heat flow, Cartesian tensor notation, the Boussinesq approximation for the Reynolds stress tensor, and the modeling of transport equations. A glossary is provided which defines these and other terms.
Finite difference program for calculating hydride bed wall temperature profiles
Klein, J.E.
1992-10-29
A QuickBASIC finite difference program was written for calculating one dimensional temperature profiles in up to two media with flat, cylindrical, or spherical geometries. The development of the program was motivated by the need to calculate maximum temperature differences across the walls of the Tritium metal hydrides beds for thermal fatigue analysis. The purpose of this report is to document the equations and the computer program used to calculate transient wall temperatures in stainless steel hydride vessels. The development of the computer code was motivated by the need to calculate maximum temperature differences across the walls of the hydrides beds in the Tritium Facility for thermal fatigue analysis.
Fuzzy logic to improve efficiency of finite element and finite difference schemes
Garcia, M.D.; Heger, A.S.
1994-05-01
This paper explores possible applications of logic in the areas of finite element and finite difference methods applied to engineering design problems. The application of fuzzy logic to both front-end selection of computational options and within the numerical computation itself are proposed. Further, possible methods of overcoming these limitations through the application of methods are explored. Decision strategy is a fundamental limitation in performing finite element calculations, such as selecting the optimum coarseness of the grid, numerical integration algorithm, element type, implicit versus explicit schemes, and the like. This is particularly true of novice analysts who are confronted with a myriad of choices in performing a calculation. The advantage of having the myriad of options available to the analyst is, however, that it improves and optimizes the design process if the appropriate ones are selected. Unfortunately, the optimum choices are not always apparent and only through the process of elimination or prior extensive experience can the optimum choices or combination of choices be selected. The knowledge of expert analysts could be integrated into a fuzzy ``front-end`` rule-based package to optimize the design process. The use of logic to capture the heuristic and human knowledge for selecting optimum solution strategies sets the framework for these proposed strategies.
An Analysis of Finite-Difference and Finite-Volume Formulations of Convervation Laws
NASA Astrophysics Data System (ADS)
Vinokur, Marcel
1989-03-01
Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations-potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.
An analysis of finite-difference and finite-volume formulations of conservation laws
NASA Astrophysics Data System (ADS)
Vinokur, Marcel
1986-06-01
Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.
An analysis of finite-difference and finite-volume formulations of conservation laws
NASA Technical Reports Server (NTRS)
Vinokur, Marcel
1986-01-01
Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations--potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomeclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.
An analysis of finite-difference and finite-volume formulations of conservation laws
NASA Technical Reports Server (NTRS)
Vinokur, Marcel
1989-01-01
Finite-difference and finite-volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws. A new coordinate-free formulation of systems of conservation laws is developed, which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system. The analysis considers general types of equations: potential, Euler, and Navier-Stokes. Three-dimensional unsteady flows with time-varying grids are described using a single, consistent nomenclature for both formulations. Grid motion due to a non-inertial reference frame as well as flow adaptation is covered. In comparing the two formulations, it is found useful to distinguish between differences in numerical methods and differences in grid definition. The former plays a role for non-Cartesian grids, and results in only cosmetic differences in the manner in which geometric terms are handled. The differences in grid definition for the two formulations is found to be more important, since it affects the manner in which boundary conditions, zonal procedures, and grid singularities are handled at computational boundaries. The proper interpretation of strong and weak conservation-law forms for quasi-one-dimensional and axisymmetric flows is brought out.
NASA Astrophysics Data System (ADS)
Nale, J. P.; Gosain, A. K.; Khosa, R.
2015-12-01
Pinder River, one of major headstreams of River Ganga, originates in Pindari Glaciers of Kumaon Himalayas and after passing through rugged gorges meets Alaknanda at Karanprayag forming one of the five celestial confluences of Upper Ganga region. While other sub-basins of Upper Ganga are facing severe ecological losses, Pinder basin is still in its virginal state and is well known for its beautiful valleys besides being host to unique and rare biodiversity. A proposed 252 MW run-of-river hydroelectric project at Devsari on this river has been a major concern on account of its perceived potential for egregious environmental and social impacts. In this context, the study presented tries to analyse the expected changes in aquatic habitat conditions after this project is operational (with different operation policies). SWAT hydrological modelling platform has been used to derive stream flow simulations under various scenarios ranging from the present to the likely future conditions. To analyse the habitat conditions, a two dimensional hydraulic-habitat model 'River-2D', a module of iRIC software, is used. Snow trout has been identified as the target keystone species and its habitat preferences, in the form of flow depths, flow velocity and substrate condition, are obtained from diverse sources of related literature and are provided as Habitat Suitability Indices to River-2D. Bed morphology constitutes an important River-2D input and has been obtained, for the designated 1 km long study reach of Pinder upto Karanprayag, from a combination of actual field observations and supplemented by SRTM 1 Arc-Second Global digital elevation data. Monthly Weighted Usable Area for three different life stages (Spawning, Juvenile and Adult) of Snow Trout are obtained corresponding to seven different flow discharges ranging from 10 cumec to 1000 cumec. Comparing the present and proposed future river flow conditions obtained from SWAT modelling, losses in Weighted Usable Area, for the
NASA Astrophysics Data System (ADS)
Abudaram, Yaakov Jack
This work is concerned with a new method to apply consistent and known pretension to silicone rubber membranes intended for micro air vehicles as well as an understanding in the science of developed pre-tension in membranes constrained by 2- D and 3-D frames and structures. Pre-tension has a marked effect on the static and dynamic response of membrane wings and controls the overall deflections, as such control and measurement of the membrane pre-tension is important. Two different 2-D frame geometries were fabricated to evaluate the technique. For open-cell frames, the pretension was not uniform, whereas it was for closed-cell frames. Results show developed full-field stress and strain fields as a function of membrane attachment temperature and frame geometry along with experimental iterations to prove repeatability. The membranes can be stretched to a specific pretension according to the temperature at which it adheres to frames. Strain fields in membranes attached to 3-D frames at various temperatures are modeled through FEA utilizing Abaqus to be able to predict the developed membrane deformations, stresses, and strains. Rigid frames with various curvatures are built via appropriate molds and then adhered to silicone rubber membranes and elevated to various temperatures to achieve different pre-strains for experimental validation. Additional experiments are conducted for more complex frame geometries involving both convex and concave topologies embedded within frames. Results are then compared with the Abaqus outputs to validate the accuracy of the FEA model. Highly compliant wings have been used for MAV platforms, where the wing structure is determined by some combination of carbon fiber composites and a membrane skin, adhered in between the layers of composite material. Another new technique of attaching membranes firmly on wing structures is introduced, which involves the application of a technology known as corona treatment coupled with another method of
Explicit Finite Difference Methods for the Delay Pseudoparabolic Equations
Amirali, I.; Amiraliyev, G. M.; Cakir, M.; Cimen, E.
2014-01-01
Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown. PMID:24688392
Explicit finite difference methods for the delay pseudoparabolic equations.
Amirali, I; Amiraliyev, G M; Cakir, M; Cimen, E
2014-01-01
Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown. PMID:24688392
Macroscopic traffic modeling with the finite difference method
Mughabghab, S.; Azarm, A.; Stock, D.
1996-03-15
A traffic congestion forecasting model (ATOP), developed in the present investigation, is described briefly. Several macroscopic models, based on the solution of the partial differential equation of conservation of vehicles by the finite difference method, were tested using actual traffic data. The functional form, as well as the parameters, of the equation of state which describes the relation between traffic speed and traffic density, were determined for a section of the Long Island Expressway. The Lax method and the forward difference technique were applied. The results of extensive tests showed that the Lax method, in addition to giving very good agreement with the traffic data, produces stable solutions.
Lilliu, S.; Maragliano, C.; Hampton, M.; Elliott, M.; Stefancich, M.; Chiesa, M.; Dahlem, M. S.; Macdonald, J. E.
2013-01-01
We report a simple technique for mapping Electrostatic Force Microscopy (EFM) bias sweep data into 2D images. The method allows simultaneous probing, in the same scanning area, of the contact potential difference and the second derivative of the capacitance between tip and sample, along with the height information. The only required equipment consists of a microscope with lift-mode EFM capable of phase shift detection. We designate this approach as Scanning Probe Potential Electrostatic Force Microscopy (SPP-EFM). An open-source MATLAB Graphical User Interface (GUI) for images acquisition, processing and analysis has been developed. The technique is tested with Indium Tin Oxide (ITO) and with poly(3-hexylthiophene) (P3HT) nanowires for organic transistor applications. PMID:24284731
SU-E-T-422: Correlation Between 2D Passing Rates and 3D Dose Differences for Pretreatment VMAT QA
Jin, X; Xie, C
2014-06-01
Purpose: Volumetric modulated arc therapy (VMAT) quality assurance (QA) is typically using QA methods and action levels taken from fixedbeam intensity-modulated radiotherapy (IMRT) QA methods. However, recent studies demonstrated that there is no correlation between the percent gamma passing rate (%GP) and the magnitude of dose discrepancy between the planned dose and the actual delivered dose for IMRT. The purpose of this study is to investigate whether %GP is correlated with clinical dosimetric difference for VMAT. Methods: Twenty nasopharyngeal cancer (NPC) patients treated with dual-arc simultaneous integrated boost VMAT and 20 esophageal cancer patients treated with one-arc VMAT were enrolled in this study. Pretreatment VMAT QA was performed by a 3D diode array ArcCheck. Acceptance criteria of 2%/2mm, 3%/3mm, and 4%/4mm were applied for 2D %GP. Dose values below 10% of the per-measured normalization maximum dose were ignored.Mean DVH values obtained from 3DVH software and TPS were calculated and percentage dose differences were calculated. Statistical correlation between %GP and percent dose difference was studied by using Pearson correlation. Results: The %GP for criteria 2%/2mm, 3%/3mm, and 4%/4mm were 82.33±4.45, 93.47±2.31, 97.13±2.41, respectively. Dose differences calculated from 3DVH and TPS for beam isocenter, mean dose of PTV, maximum dose of PTV, D2 of PTV and D98 of PTV were -1.04±3.24, -0.74±1.71, 2.92±3.62, 0.89±3.29, -1.46±1.97, respectively. No correction were found between %GP and dose differences. Conclusion: There are weak correlations between the 2D %GP and dose differences calculated from 3DVH. The %GP acceptance criteria of 3%/3mm usually applied for pretreatment QA of IMRT and VMAT is not indicating strong clinical correlation with 3D dose difference. 3D dose reconstructions on patient anatomy may be necessary for physicist to predict the accuracy of delivered dose for VMAT QA.
Brittle damage models in DYNA2D
Faux, D.R.
1997-09-01
DYNA2D is an explicit Lagrangian finite element code used to model dynamic events where stress wave interactions influence the overall response of the system. DYNA2D is often used to model penetration problems involving ductile-to-ductile impacts; however, with the advent of the use of ceramics in the armor-anti-armor community and the need to model damage to laser optics components, good brittle damage models are now needed in DYNA2D. This report will detail the implementation of four brittle damage models in DYNA2D, three scalar damage models and one tensor damage model. These new brittle damage models are then used to predict experimental results from three distinctly different glass damage problems.
Nardi, Daniele; Meloni, Roberta; Orlandi, Marco; Olivetti-Belardinelli, Marta
2014-01-01
One of the spatial abilities that has recently revealed a remarkable variability in performance is that of using terrain slope to reorient. Previous studies have shown a very large disadvantage for females when the slope of the floor is the only information useful for encoding a goal location. However, the source of this sex difference is still unclear. The slope of the environment provides a directional source of information that is perceived through dissociable visual and kinesthetic sensory modalities. Here we focused on the visual information, and examined whether there are sex differences in the perception of a slope presented through 2-D images with a desktop computer connected to an eye-tracking device. Participants had to identify and point to the uphill direction by looking at different orientations of two virtual, slanted environments (one indoor and one outdoor). Men were quicker and more accurate than women, indicating that the female difficulty with slope emerges at an early, unisensory, perceptual level. However, the eye-tracking data revealed no sex differences in the slope cues used, providing no support to the hypothesis of sex-specific, visual-processing strategies. Interestingly, performance correlated with a test of mental rotation, and we speculate that the disadvantage in mental rotation ability might be an important factor responsible for females' difficulty using slope. PMID:25109016
NASA Astrophysics Data System (ADS)
Deb Nath, S. K.; Peyada, N. K.
2015-12-01
In the present study, we have developed a code using Matlab software for solving a rectangular aluminum plate having void, notch, at different boundary conditions discretizing a two dimensional (2D) heat conduction equation by the finite difference technique. We have solved a 2D mixed boundary heat conduction problem analytically using Fourier integrals (Deb Nath et al., 2006; 2007; 2007; Deb Nath and Ahmed, 2008; Deb Nath, 2008; Deb Nath and Afsar, 2009; Deb Nath and Ahmed, 2009; 2009; Deb Nath et al., 2010; Deb Nath, 2013) and the same problem is also solved using the present code developed by the finite difference technique (Ahmed et al., 2005; Deb Nath, 2002; Deb Nath et al., 2008; Ahmed and Deb Nath, 2009; Deb Nath et al., 2011; Mohiuddin et al., 2012). To verify the soundness of the present heat conduction code results using the finite difference method, the distribution of temperature at some sections of a 2D heated plate obtained by the analytical method is compared with those of the plate obtained by the present finite difference method. Interpolation technique is used as an example when the boundary of the plate does not pass through the discretized grid points of the plate. Sometimes hot and cold fluids are passed through rectangular channels in industries and many types of technical equipment. The distribution of temperature of plates including notches, slots with different temperature boundary conditions are studied. Transient heat transfer in several pure metallic plates is also studied to find out the required time to reach equilibrium temperature. So, this study will help find design parameters of such structures.
Seismic imaging using finite-differences and parallel computers
Ober, C.C.
1997-12-31
A key to reducing the risks and costs of associated with oil and gas exploration is the fast, accurate imaging of complex geologies, such as salt domes in the Gulf of Mexico and overthrust regions in US onshore regions. Prestack depth migration generally yields the most accurate images, and one approach to this is to solve the scalar wave equation using finite differences. As part of an ongoing ACTI project funded by the US Department of Energy, a finite difference, 3-D prestack, depth migration code has been developed. The goal of this work is to demonstrate that massively parallel computers can be used efficiently for seismic imaging, and that sufficient computing power exists (or soon will exist) to make finite difference, prestack, depth migration practical for oil and gas exploration. Several problems had to be addressed to get an efficient code for the Intel Paragon. These include efficient I/O, efficient parallel tridiagonal solves, and high single-node performance. Furthermore, to provide portable code the author has been restricted to the use of high-level programming languages (C and Fortran) and interprocessor communications using MPI. He has been using the SUNMOS operating system, which has affected many of his programming decisions. He will present images created from two verification datasets (the Marmousi Model and the SEG/EAEG 3D Salt Model). Also, he will show recent images from real datasets, and point out locations of improved imaging. Finally, he will discuss areas of current research which will hopefully improve the image quality and reduce computational costs.
Application of a finite difference technique to thermal wave propagation
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1975-01-01
A finite difference formulation is presented for thermal wave propagation resulting from periodic heat sources. The numerical technique can handle complex problems that might result from variable thermal diffusivity, such as heat flow in the earth with ice and snow layers. In the numerical analysis, the continuous temperature field is represented by a series of grid points at which the temperature is separated into real and imaginary terms. Next, computer routines previously developed for acoustic wave propagation are utilized in the solution for the temperatures. The calculation procedure is illustrated for the case of thermal wave propagation in a uniform property semi-infinite medium.
Application of a finite difference technique to thermal wave propagation
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1975-01-01
A finite difference formulation is presented for thermal wave propagation resulting from periodic heat sources. The numerical technique can handle complex problems that might result from variable thermal diffusivity, such as heat flow in the earth with ice and snow layers. In the numerical analysis, the continuous temperature field is represented by a series of grid points at which the temperature is separated into real and imaginary terms. Computer routines previously developed for acoustic wave propagation are utilized in the solution for the temperatures. The calculation procedure is illustrated for the case of thermal wave propagation in a uniform property semi-infinite medium.
FDIPS: Finite Difference Iterative Potential-field Solver
NASA Astrophysics Data System (ADS)
Toth, Gabor; van der Holst, Bartholomeus; Huang, Zhenguang
2016-06-01
FDIPS is a finite difference iterative potential-field solver that can generate the 3D potential magnetic field solution based on a magnetogram. It is offered as an alternative to the spherical harmonics approach, as when the number of spherical harmonics is increased, using the raw magnetogram data given on a grid that is uniform in the sine of the latitude coordinate can result in inaccurate and unreliable results, especially in the polar regions close to the Sun. FDIPS is written in Fortran 90 and uses the MPI library for parallel execution.
Compact finite difference schemes with spectral-like resolution
NASA Technical Reports Server (NTRS)
Lele, Sanjiva K.
1992-01-01
The present finite-difference schemes for the evaluation of first-order, second-order, and higher-order derivatives yield improved representation of a range of scales and may be used on nonuniform meshes. Various boundary conditions may be invoked, and both accurate interpolation and spectral-like filtering can be accomplished by means of schemes for derivatives at mid-cell locations. This family of schemes reduces to the Pade schemes when the maximal formal accuracy constraint is imposed with a specific computational stencil. Attention is given to illustrative applications of these schemes in fluid dynamics.
A finite difference approach to microstrip antenna design
Barth, M.J.; Bevensee, R.M.; Pennock, S.T.
1986-12-01
Microstrip antennas have received increased attention in recent years, due to their size and cost advantages. Analysis of the microstrip structure has proved difficult due to the presence of the dielectric substrate, particularly for complex geometries. One possible approach to a solution is the use of a finite difference computer code to model a proposed microstrip antenna design. The models are easily constructed and altered, and code versions are available which allow input impedance or far-field patterns to be calculated. Results for some simple antenna geometries will be presented.
Finite difference time domain modeling of spiral antennas
NASA Technical Reports Server (NTRS)
Penney, Christopher W.; Beggs, John H.; Luebbers, Raymond J.
1992-01-01
The objectives outlined in the original proposal for this project were to create a well-documented computer analysis model based on the finite-difference, time-domain (FDTD) method that would be capable of computing antenna impedance, far-zone radiation patterns, and radar cross-section (RCS). The ability to model a variety of penetrable materials in addition to conductors is also desired. The spiral antennas under study by this project meet these requirements since they are constructed of slots cut into conducting surfaces which are backed by dielectric materials.
Pencil: Finite-difference Code for Compressible Hydrodynamic Flows
NASA Astrophysics Data System (ADS)
Brandenburg, Axel; Dobler, Wolfgang
2010-10-01
The Pencil code is a high-order finite-difference code for compressible hydrodynamic flows with magnetic fields. It is highly modular and can easily be adapted to different types of problems. The code runs efficiently under MPI on massively parallel shared- or distributed-memory computers, like e.g. large Beowulf clusters. The Pencil code is primarily designed to deal with weakly compressible turbulent flows. To achieve good parallelization, explicit (as opposed to compact) finite differences are used. Typical scientific targets include driven MHD turbulence in a periodic box, convection in a slab with non-periodic upper and lower boundaries, a convective star embedded in a fully nonperiodic box, accretion disc turbulence in the shearing sheet approximation, self-gravity, non-local radiation transfer, dust particle evolution with feedback on the gas, etc. A range of artificial viscosity and diffusion schemes can be invoked to deal with supersonic flows. For direct simulations regular viscosity and diffusion is being used. The code is written in well-commented Fortran90.
NASA Astrophysics Data System (ADS)
Ahn, Jai Seok
2014-01-01
A finite difference method (FDM) applicable to a two dimensional (2D) quantum dot was developed as a non-conventional approach to the theoretical understandings of quantum devices. This method can be applied to a realistic potential with an arbitrary shape. Using this method, the Hamiltonian in a tri-diagonal matrix could be obtained from any 2D potential, and the Hamiltonian could be diagonalized numerically for the eigenvalues. The legitimacy of this method was first checked by comparing the results with a finite round well with the analytic solutions. Two truncated harmonic wells were examined as a realistic model potential for lateral double quantum dots (DQDs) and for triple quantum dots (TQDs). The successful applications of the 2D FDM were observed with the entanglements in the DQDs. The level-splitting and anticrossing behaviors of the DQDs could be obtained by varying the distance between the dots and by introducing asymmetry in the well-depths. The 2D FDM results for linear/triangular TQDs were compared with the tight binding approximations.
Hoffman, E.L.; Ammerman, D.J.
1993-08-01
A series of tests investigating dynamic pulse buckling of a cylindrical shell under axial impact is compared to several finite element simulations of the event. The purpose of the study is to compare the performance of the various analysis codes and element types with respect to a problem which is applicable to radioactive material transport packages, and ultimately to develop a benchmark problem to qualify finite element analysis codes for the transport package design industry.
Finite Difference Elastic Wave Field Simulation On GPU
NASA Astrophysics Data System (ADS)
Hu, Y.; Zhang, W.
2011-12-01
Numerical modeling of seismic wave propagation is considered as a basic and important aspect in investigation of the Earth's structure, and earthquake phenomenon. Among various numerical methods, the finite-difference method is considered one of the most efficient tools for the wave field simulation. However, with the increment of computing scale, the power of computing has becoming a bottleneck. With the development of hardware, in recent years, GPU shows powerful computational ability and bright application prospects in scientific computing. Many works using GPU demonstrate that GPU is powerful . Recently, GPU has not be used widely in the simulation of wave field. In this work, we present forward finite difference simulation of acoustic and elastic seismic wave propagation in heterogeneous media on NVIDIA graphics cards with the CUDA programming language. We also implement perfectly matched layers on the graphics cards to efficiently absorb outgoing waves on the fictitious edges of the grid Simulations compared with the results on CPU platform shows reliable accuracy and remarkable efficiency. This work proves that GPU can be an effective platform for wave field simulation, and it can also be used as a practical tool for real-time strong ground motion simulation.
Arrayed waveguide grating using the finite difference beam propagation method
NASA Astrophysics Data System (ADS)
Toledo, M. C. F.; Alayo, M. I.
2013-03-01
The purpose of this work is to analyze by simulation the coupling effects occurring in Arrayed Waveguide Grating (AWG) using the finite difference beam propagation method (FD-BPM). Conventional FD-BPM techniques do not immediately lend themselves to the analysis of large structures such as AWG. Cooper et al.1 introduced a description of the coupling between the interface of arrayed waveguides and star couplers using the numerically-assisted coupled-mode theory. However, when the arrayed waveguides are spatially close, such that, there is strong coupling between them, and coupled-mode theory is not adequate. On the other hand, Payne2 developed an exact eigenvalue equation for the super modes of a straight arrayed waveguide which involve a computational overhead. In this work, an integration of both methods is accomplished in order to describe the behavior of the propagation of light in guided curves. This new method is expected to reduce the necessary effort for simulation while also enabling the simulation of large and curved arrayed waveguides using a fully vectorial finite difference technique.
Seismic Analysis of a Rockfill Dam by FLAC Finite Difference Code
Miglio, Livia; Pagliaroli, Alessandro; Lanzo, Giuseppe; Miliziano, Salvatore
2008-07-08
The paper presents the results of numerical analyses carried out with FLAC finite difference code aiming at investigating the seismic response of rockfill dams. In particular the hysteretic damping model, recently incorporated within the code, coupled with a perfectly plastic yield criterion, was employed. As first step, 1D and 2D calibration analyses were performed and comparisons with the results supplied by well known linear equivalent and fully non linear codes were carried out. Then the seismic response of E1 Infiernillo rockfill dam was investigated during two weak and strong seismic events. Benefits and shortcomings of using the hysteretic damping model are discussed in the light of the results obtained from calibration studies and field-scale analyses.
Enhancing finite differences with radial basis functions: Experiments on the Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Flyer, Natasha; Barnett, Gregory A.; Wicker, Louis J.
2016-07-01
Polynomials are used together with polyharmonic spline (PHS) radial basis functions (RBFs) to create local RBF-finite-difference (RBF-FD) weights on different node layouts for spatial discretizations that can be viewed as enhancements of the classical finite differences (FD). The presented method replicates the convergence properties of FD but for arbitrary node layouts. It is tested on the 2D compressible Navier-Stokes equations at low Mach number, relevant to atmospheric flows. Test cases are taken from the numerical weather prediction community and solved on bounded domains. Thus, attention is given on how to handle boundaries with the RBF-FD method, as well as a novel implementation for hyperviscosity. Comparisons are done on Cartesian, hexagonal, and quasi-uniform node layouts. Consideration and guidelines are given on PHS order, polynomial degree and stencil size. The main advantages of the present method are: 1) capturing the basic physics of the problem surprisingly well, even at very coarse resolutions, 2) high-order accuracy without the need of tuning a shape parameter, and 3) the inclusion of polynomials eliminates stagnation (saturation) errors. A MATLAB code is given to calculate the differentiation weights for this novel approach.
High-Accuracy Finite Difference Equations for Simulation of Photonic Structures
Hadley, G.R.
1999-04-23
Progress towards the development of such algorithms as been reported for waveguide analysis'-3and vertical-cavity laser simulation. In all these cases, the higher accuracy order was obtained for a single spatial dimension. More recently, this concept was extended to differencing of the Helmholtz Equation on a 2-D grid, with uniform regions treated to 4th order and dielectric interfaces to 3'd order5. No attempt was made to treat corners properly. In this talk I will describe the extension of this concept to allow differencing of the Helmholtz Equation on a 2-D grid to 6* order in uniform regions and 5* order at dielectric interfaces. In addition, the first known derivation of a finite difference equation for a dielectric comer that allows correct satisfaction of all boundary conditions will be presented. This equation is only accurate to first order, but as will be shown, results in simulations that are third-order-accurate. In contrast to a previous approach3 that utilized a generalized Douglas scheme to increase the accuracy order of the difference second derivative, the present method invokes the Helmholtz Equation itself to convert derivatives of high order in a single direction into mixed
Implicit Predictor-Corrector finite difference scheme for the ideal MHD simulations
NASA Astrophysics Data System (ADS)
Tsai, T.; Yu, H.; Lai, S.
2012-12-01
A innovative simulation code for ideal magnetohydrodynamics (MHD) is developed. We present a multiple-dimensional MHD code based on high-order implicit predictor-corrector finite difference scheme (high-order IPCFD scheme). High-order IPCFD scheme adopts high-order predictor-corrector scheme for the time integration and high-order central difference method as the spatial derivative solver. We use Elimination-of-the-Runoff-Errors (ERE) technology to avoid the numerical oscillations and numerical instability in the simulation results. In one-dimensional MHD problem, our simulation results show good agreement with the Brio & Wu MHD shock tube problem. The divergent B constraint remains fully satisfied, that is the divergent B equals to zero throughout the simulation. When solving the two-dimensional (2D) linear wave in MHD plasma, we clearly obtain the group-velocity Friedrichs diagrams of the MHD waves. Here we demonstrate 2D simulation results of rotor problem, Orszag-Tang vortex system, vortex type K-H instability, and kink type K-H instability by using our IPCFD MHD code and discuss the advantage of our simulation code.
Eyler, L.L.; Budden, M.J.
1985-03-01
The objective of this work is to assess prediction capabilities and features of the MAGNUM-2D computer code in relation to its intended use in the Basalt Waste Isolation Project (BWIP). This objective is accomplished through a code verification and benchmarking task. Results are documented which support correctness of prediction capabilities in areas of intended model application. 10 references, 43 figures, 11 tables.
Elastic finite-difference method for irregular grids
Oprsal, I.; Zahradnik, J.
1999-01-01
Finite-difference (FD) modeling of complicated structures requires simple algorithms. This paper presents a new elastic FD method for spatially irregular grids that is simple and, at the same time, saves considerable memory and computing time. Features like faults, low-velocity layers, cavities, and/or nonplanar surfaces are treated on a fine grid, while the remaining parts of the model are, with equal accuracy, represented on a coarse grid. No interpolation is needed between the fine and coarse parts due to the rectangular grid cells. Relatively abrupt transitions between the small and large grid steps produce no numerical artifacts in the present method. Planar or nonplanar free surfaces, including underground cavities, are treated in a way similar to internal grid points but with consideration of the zero-valued elastic parameters and density outside the free surface (vacuum formalism). A theoretical proof that vacuum formalism fulfills the free-surface conditions is given. Numerical validation is performed through comparison with independent methods, comparing FD with explicitly prescribed boundary conditions and finite elements. Memory and computing time needed in the studied models was only about 10 to 40% of that employing regular square grids of equal accuracy. A practical example of a synthetic seismic section, showing clear signatures of a coal seam and cavity, is presented. The method can be extended to three dimensions.
NASA Technical Reports Server (NTRS)
Baumeister, Kenneth J.; Kreider, Kevin L.
1996-01-01
An explicit finite difference iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.
NASA Technical Reports Server (NTRS)
Baumeister, K. J.; Kreider, K. L.
1996-01-01
An explicit finite difference iteration scheme is developed to study harmonic sound propagation in ducts. To reduce storage requirements for large 3D problems, the time dependent potential form of the acoustic wave equation is used. To insure that the finite difference scheme is both explicit and stable, time is introduced into the Fourier transformed (steady-state) acoustic potential field as a parameter. Under a suitable transformation, the time dependent governing equation in frequency space is simplified to yield a parabolic partial differential equation, which is then marched through time to attain the steady-state solution. The input to the system is the amplitude of an incident harmonic sound source entering a quiescent duct at the input boundary, with standard impedance boundary conditions on the duct walls and duct exit. The introduction of the time parameter eliminates the large matrix storage requirements normally associated with frequency domain solutions, and time marching attains the steady-state quickly enough to make the method favorable when compared to frequency domain methods. For validation, this transient-frequency domain method is applied to sound propagation in a 2D hard wall duct with plug flow.
Wang, Wei; Shu, Chi-Wang; Yee, H.C.; Sjögreen, Björn
2012-01-01
A new high order finite-difference method utilizing the idea of Harten ENO subcell resolution method is proposed for chemical reactive flows and combustion. In reaction problems, when the reaction time scale is very small, e.g., orders of magnitude smaller than the fluid dynamics time scales, the governing equations will become very stiff. Wrong propagation speed of discontinuity may occur due to the underresolved numerical solution in both space and time. The present proposed method is a modified fractional step method which solves the convection step and reaction step separately. In the convection step, any high order shock-capturing method can be used. In the reaction step, an ODE solver is applied but with the computed flow variables in the shock region modified by the Harten subcell resolution idea. For numerical experiments, a fifth-order finite-difference WENO scheme and its anti-diffusion WENO variant are considered. A wide range of 1D and 2D scalar and Euler system test cases are investigated. Studies indicate that for the considered test cases, the new method maintains high order accuracy in space for smooth flows, and for stiff source terms with discontinuities, it can capture the correct propagation speed of discontinuities in very coarse meshes with reasonable CFL numbers.
3D finite-difference seismic migration with parallel computers
Ober, C.C.; Gjertsen, R.; Minkoff, S.; Womble, D.E.
1998-11-01
The ability to image complex geologies such as salt domes in the Gulf of Mexico and thrusts in mountainous regions is essential for reducing the risk associated with oil exploration. Imaging these structures, however, is computationally expensive as datasets can be terabytes in size. Traditional ray-tracing migration methods cannot handle complex velocity variations commonly found near such salt structures. Instead the authors use the full 3D acoustic wave equation, discretized via a finite difference algorithm. They reduce the cost of solving the apraxial wave equation by a number of numerical techniques including the method of fractional steps and pipelining the tridiagonal solves. The imaging code, Salvo, uses both frequency parallelism (generally 90% efficient) and spatial parallelism (65% efficient). Salvo has been tested on synthetic and real data and produces clear images of the subsurface even beneath complicated salt structures.
Finite difference modeling of Biot's poroelastic equations atseismic frequencies
Masson, Y.J.; Pride, S.R.; Nihei, K.T.
2006-02-24
Across the seismic band of frequencies (loosely defined as<10 kHz), a seismic wave propagating through a porous material willcreate flow in the pore space that is laminar; that is, in thislow-frequency "seismic limit," the development of viscous boundary layersin the pores need not be modeled. An explicit time steppingstaggered-grid finite difference scheme is presented for solving Biot'sequations of poroelasticity in this low-frequency limit. A key part ofthis work is the establishment of rigorous stability conditions. It isdemonstrated that over a wide range of porous material properties typicalof sedimentary rock and despite the presenceof fluid pressure diffusion(Biot slow waves), the usual Courant condition governs the stability asif the problem involved purely elastic waves. The accuracy of the methodis demonstrated by comparing to exact analytical solutions for both fastcompressional waves and slow waves. Additional numerical modelingexamples are also presented.
A finite-difference method for transonic airfoil design.
NASA Technical Reports Server (NTRS)
Steger, J. L.; Klineberg, J. M.
1972-01-01
This paper describes an inverse method for designing transonic airfoil sections or for modifying existing profiles. Mixed finite-difference procedures are applied to the equations of transonic small disturbance theory to determine the airfoil shape corresponding to a given surface pressure distribution. The equations are solved for the velocity components in the physical domain and flows with embedded shock waves can be calculated. To facilitate airfoil design, the method allows alternating between inverse and direct calculations to obtain a profile shape that satisfies given geometric constraints. Examples are shown of the application of the technique to improve the performance of several lifting airfoil sections. The extension of the method to three dimensions for designing supercritical wings is also indicated.
Accurate finite difference methods for time-harmonic wave propagation
NASA Technical Reports Server (NTRS)
Harari, Isaac; Turkel, Eli
1994-01-01
Finite difference methods for solving problems of time-harmonic acoustics are developed and analyzed. Multidimensional inhomogeneous problems with variable, possibly discontinuous, coefficients are considered, accounting for the effects of employing nonuniform grids. A weighted-average representation is less sensitive to transition in wave resolution (due to variable wave numbers or nonuniform grids) than the standard pointwise representation. Further enhancement in method performance is obtained by basing the stencils on generalizations of Pade approximation, or generalized definitions of the derivative, reducing spurious dispersion, anisotropy and reflection, and by improving the representation of source terms. The resulting schemes have fourth-order accurate local truncation error on uniform grids and third order in the nonuniform case. Guidelines for discretization pertaining to grid orientation and resolution are presented.
Effects of sources on time-domain finite difference models.
Botts, Jonathan; Savioja, Lauri
2014-07-01
Recent work on excitation mechanisms in acoustic finite difference models focuses primarily on physical interpretations of observed phenomena. This paper offers an alternative view by examining the properties of models from the perspectives of linear algebra and signal processing. Interpretation of a simulation as matrix exponentiation clarifies the separate roles of sources as boundaries and signals. Boundary conditions modify the matrix and thus its modal structure, and initial conditions or source signals shape the solution, but not the modal structure. Low-frequency artifacts are shown to follow from eigenvalues and eigenvectors of the matrix, and previously reported artifacts are predicted from eigenvalue estimates. The role of source signals is also briefly discussed. PMID:24993210
Finite-difference modeling of commercial aircraft using TSAR
Pennock, S.T.; Poggio, A.J.
1994-11-15
Future aircraft may have systems controlled by fiber optic cables, to reduce susceptibility to electromagnetic interference. However, the digital systems associated with the fiber optic network could still experience upset due to powerful radio stations, radars, and other electromagnetic sources, with potentially serious consequences. We are modeling the electromagnetic behavior of commercial transport aircraft in support of the NASA Fly-by-Light/Power-by-Wire program, using the TSAR finite-difference time-domain code initially developed for the military. By comparing results obtained from TSAR with data taken on a Boeing 757 at the Air Force Phillips Lab., we hope to show that FDTD codes can serve as an important tool in the design and certification of U.S. commercial aircraft, helping American companies to produce safe, reliable air transportation.
Parallelization of implicit finite difference schemes in computational fluid dynamics
NASA Technical Reports Server (NTRS)
Decker, Naomi H.; Naik, Vijay K.; Nicoules, Michel
1990-01-01
Implicit finite difference schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods are considerably more difficult and non-intuitive. The parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta-diagonal matrices is discussed. Three-dimensional cases are emphasized and schemes that minimize the total execution time are presented. Partitioning and scheduling schemes for alleviating the effects of the global data dependencies are described. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed.
Finite difference time domain implementation of surface impedance boundary conditions
NASA Technical Reports Server (NTRS)
Beggs, John H.; Luebbers, Raymond J.; Yee, Kane S.; Kunz, Karl S.
1991-01-01
Surface impedance boundary conditions are employed to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In the finite difference solution, they also can be utilized to avoid using small cells, made necessary by shorter wavelengths in conducting media throughout the solution volume. The standard approach is to approximate the surface impedance over a very small bandwidth by its value at the center frequency, and then use that result in the boundary condition. Here, two implementations of the surface impedance boundary condition are presented. One implementation is a constant surface impedance boundary condition and the other is a dispersive surface impedance boundary condition that is applicable over a very large frequency bandwidth and over a large range of conductivities. Frequency domain results are presented in one dimension for two conductivity values and are compared with exact results. Scattering width results from an infinite square cylinder are presented as a two dimensional demonstration. Extensions to three dimensions should be straightforward.
An optimized finite-difference scheme for wave propagation problems
NASA Technical Reports Server (NTRS)
Zingg, D. W.; Lomax, H.; Jurgens, H.
1993-01-01
Two fully-discrete finite-difference schemes for wave propagation problems are presented, a maximum-order scheme and an optimized (or spectral-like) scheme. Both combine a seven-point spatial operator and an explicit six-stage time-march method. The maximum-order operator is fifth-order in space and is sixth-order in time for a linear problem with periodic boundary conditions. The phase and amplitude errors of the schemes obtained using Fourier analysis are given and compared with a second-order and a fourth-order method. Numerical experiments are presented which demonstrate the usefulness of the schemes for a range of problems. For some problems, the optimized scheme leads to a reduction in global error compared to the maximum-order scheme with no additional computational expense.
Application of a new finite difference algorithm for computational aeroacoustics
NASA Technical Reports Server (NTRS)
Goodrich, John W.
1995-01-01
Acoustic problems have become extremely important in recent years because of research efforts such as the High Speed Civil Transport program. Computational aeroacoustics (CAA) requires a faithful representation of wave propagation over long distances, and needs algorithms that are accurate and boundary conditions that are unobtrusive. This paper applies a new finite difference method and boundary algorithm to the Linearized Euler Equations (LEE). The results demonstrate the ability of a new fourth order propagation algorithm to accurately simulate the genuinely multidimensional wave dynamics of acoustic propagation in two space dimensions with the LEE. The results also show the ability of a new outflow boundary condition and fourth order algorithm to pass the evolving solution from the computational domain with no perceptible degradation of the solution remaining within the domain.
Improved finite difference schemes for transonic potential calculations
NASA Technical Reports Server (NTRS)
Hafez, M.; Osher, S.; Whitlow, W., Jr.
1984-01-01
Engquist and Osher (1980) have introduced a finite difference scheme for solving the transonic small disturbance equation, taking into account cases in which only compression shocks are admitted. Osher et al. (1983) studied a class of schemes for the full potential equation. It is proved that these schemes satisfy a new discrete 'entropy inequality' which rules out expansion shocks. However, the conducted analysis is restricted to steady two-dimensional flows. The present investigation is concerned with the adoption of a heuristic approach. The full potential equation in conservation form is solved with the aid of a modified artificial density method, based on flux biasing. It is shown that, with the current scheme, expansion shocks are not possible.
NASA Astrophysics Data System (ADS)
Mejdoubi, Abdelilah; Brosseau, Christian
2006-03-01
Currently, there is a great interest in tailoring the polarization properties of composite materials with the goal of controlling the dielectric behavior. This paper reports finite-difference time-domain (FDTD) modeling of the dielectric behavior of two-dimensional (2D) lossless two-phase heterostructures. More specifically, we present extensive results of 2D FDTD computations on the quasistatic effective permittivity of a single inclusion, with arbitrarily complex geometry (regular polygons and fractals), embedded in a plane. The uniaxial perfectly matched layer-absorbing boundary condition is found adequate for truncating the boundary of the 2D space because it leads to only very small backreflections. The effectiveness of the method is demonstrated by the variety of geometries modeled, i.e., regular polygons and fractals, and permittivity contrast ratios which allows us to distinguish between effects of surface fraction and effects of morphology. Our calculations show that geometrical effects can give rise to significant modifications of the surface fraction dependence of the permittivity. The results are compared with Maxwell-Garnett (MG) and symmetric Bruggeman (SBG) formulas. As expected the effective permittivity in the situations considered here deviates from the MG and SBG results at high surface fractions and/or high permittivity ratios between the inclusion and the host medium. In addition, the results show that a two-phase composite containing a fractal-boundary inclusion, e.g., Koch's snowflake, can have a permittivity which is several tens of percent lower between the first and the fourth iteration of the structure at a fixed perimeter-to-surface ratio. This feature is consistent with the fact that as the surface fraction becomes higher, the inclusion rough boundaries dominate the overall geometry. We believe that simplified modeling such as the modeling done here can serve as a useful purpose in understanding the interplay between the structure and
Barão, Valentim Adelino Ricardo; Assunção, Wirley Gonçalves; Tabata, Lucas Fernando; de Sousa, Edson Antonio Capello; Rocha, Eduardo Passos
2008-11-01
The study aimed to evaluate the effect of different mucosa thickness and resiliency on stress distribution of implant-retained overdentures using a two-dimensional finite element analysis. Models were used in order to simulate two situations. In group A, model represented an edentulous mandible supporting an overdenture retained by two-splinted-implants connected with bar-clip system while in group B, model simulated an edentulous mandible supporting an overdenture retained by two-splinted-implants connected with bar-clip system associated with two-distally placed o'ring system. In each group, mucosa assumed three characteristics of thickness (1, 3 and 5 mm) in the resiliencies: hard, resilient and soft, respectively. Evaluation was performed on Ansys software. Group A showed higher stress values regardless of the mucosa characteristics. Overall, stress decreased at the supporting tissues as mucosa thickness and resiliency increased. Regarding supporting tissues, cortical bone showed the highest stress values. The use of bar-clip attachment system with distally placed o'ring attachment design optimized the stress distribution. PMID:18783845
Dastmalchi, Siavoush; Hamzeh-Mivehroud, Maryam; Asadpour-Zeynali, Karim
2012-01-01
Histamine H3 receptor subtype has been the target of several recent drug development programs. Quantitative structure-activity relationship (QSAR) methods are used to predict the pharmaceutically relevant properties of drug candidates whenever it is applicable. The aim of this study was to compare the predictive powers of three different QSAR techniques, namely, multiple linear regression (MLR), artificial neural network (ANN), and HASL as a 3D QSAR method, in predicting the receptor binding affinities of arylbenzofuran histamine H3 receptor antagonists. Genetic algorithm coupled partial least square as well as stepwise multiple regression methods were used to select a number of calculated molecular descriptors to be used in MLR and ANN-based QSAR studies. Using the leave-group-out cross-validation technique, the performances of the MLR and ANN methods were evaluated. The calculated values for the mean absolute percentage error (MAPE), ranging from 2.9 to 3.6, and standard deviation of error of prediction (SDEP), ranging from 0.31 to 0.36, for both MLR and ANN methods were statistically comparable, indicating that both methods perform equally well in predicting the binding affinities of the studied compounds toward the H3 receptors. On the other hand, the results from 3D-QSAR studies using HASL method were not as good as those obtained by 2D methods. It can be concluded that simple traditional approaches such as MLR method can be as reliable as those of more advanced and sophisticated methods like ANN and 3D-QSAR analyses. PMID:25317190
Optimizations on Designing High-Resolution Finite-Difference Schemes
NASA Technical Reports Server (NTRS)
Liu, Yen; Koomullil, George; Kwak, Dochan (Technical Monitor)
1994-01-01
We describe a general optimization procedure for both maximizing the resolution characteristics of existing finite differencing schemes as well as designing finite difference schemes that will meet the error tolerance requirements of numerical solutions. The procedure is based on an optimization process. This is a generalization of the compact scheme introduced by Lele in which the resolution is improved for single, one-dimensional spatial derivative, whereas in the present approach the complete scheme, after spatial and temporal discretizations, is optimized on a range of parameters of the scheme and the governing equations. The approach is to linearize and Fourier analyze the discretized equations to check the resolving power of the scheme for various wave number ranges in the solution and optimize the resolution to satisfy the requirements of the problem. This represents a constrained nonlinear optimization problem which can be solved to obtain the nodal weights of discretization. An objective function is defined in the parametric space of wave numbers, Courant number, Mach number and other quantities of interest. Typical criterion for defining the objective function include the maximization of the resolution of high wave numbers for acoustic and electromagnetic wave propagations and turbulence calculations. The procedure is being tested on off-design conditions of non-uniform mesh, non-periodic boundary conditions, and non-constant wave speeds for scalar and system of equations. This includes the solution of wave equations and Euler equations using a conventional scheme with and without optimization and the design of an optimum scheme for the specified error tolerance.
NASA Technical Reports Server (NTRS)
Bauld, N. R., Jr.; Goree, J. G.; Tzeng, L.-S.
1985-01-01
It is pointed out that edge delamination is a serious failure mechanism for laminated composite materials. Various numerical methods have been utilized in attempts to calculate the interlaminar stress components which precede delamination in a laminate. There are, however, discrepancies regarding the results provided by different methods, taking into account a finite-difference procedure, a perturbation procedure, and finite element approaches. The present investigation has the objective to assess the capacity of a finite difference method to predict the character and magnitude of the interlaminar stress distributions near an interface corner. A second purpose of the investigation is to determine if predictions by finite element method in-plane, interlaminar stress components near an interface corner represent actual laminate behavior.
Coulon, Marjorie; Deputte, Bertrand L.; Heyman, Yvan; Baudoin, Claude
2009-01-01
Background In order to maintain cohesion of groups, social animals need to process social information efficiently. Visual individual recognition, which is distinguished from mere visual discrimination, has been studied in only few mammalian species. In addition, most previous studies used either a small number of subjects or a few various views as test stimuli. Dairy cattle, as a domestic species allow the testing of a good sample size and provide a large variety of test stimuli due to the morphological diversity of breeds. Hence cattle are a suitable model for studying individual visual recognition. This study demonstrates that cattle display visual individual recognition and shows the effect of both familiarity and coat diversity in discrimination. Methodology/Principal Findings We tested whether 8 Prim'Holstein heifers could recognize 2D-images of heads of one cow (face, profiles, ¾ views) from those of other cows. Experiments were based on a simultaneous discrimination paradigm through instrumental conditioning using food rewards. In Experiment 1, all images represented familiar cows (belonging to the same social group) from the Prim'Holstein breed. In Experiments 2, 3 and 4, images were from unfamiliar (unknown) individuals either from the same breed or other breeds. All heifers displayed individual recognition of familiar and unfamiliar individuals from their own breed. Subjects reached criterion sooner when recognizing a familiar individual than when recognizing an unfamiliar one (Exp 1: 3.1±0.7 vs. Exp 2: 5.2±1.2 sessions; Z = 1.99, N = 8, P = 0.046). In addition almost all subjects recognized unknown individuals from different breeds, however with greater difficulty. Conclusions/Significance Our results demonstrated that cattle have efficient individual recognition based on categorization capacities. Social familiarity improved their performance. The recognition of individuals with very different coat characteristics from the subjects was
Nonlinear wave propagation using three different finite difference schemes (category 2 application)
NASA Technical Reports Server (NTRS)
Pope, D. Stuart; Hardin, J. C.
1995-01-01
Three common finite difference schemes are used to examine the computation of one-dimensional nonlinear wave propagation. The schemes are studied for their responses to numerical parameters such as time step selection, boundary condition implementation, and discretization of governing equations. The performance of the schemes is compared and various numerical phenomena peculiar to each is discussed.
A finite difference model for free surface gravity drainage
Couri, F.R.; Ramey, H.J. Jr.
1993-09-01
The unconfined gravity flow of liquid with a free surface into a well is a classical well test problem which has not been well understood by either hydrologists or petroleum engineers. Paradigms have led many authors to treat an incompressible flow as compressible flow to justify the delayed yield behavior of a time-drawdown test. A finite-difference model has been developed to simulate the free surface gravity flow of an unconfined single phase, infinitely large reservoir into a well. The model was verified with experimental results in sandbox models in the literature and with classical methods applied to observation wells in the Groundwater literature. The simulator response was also compared with analytical Theis (1935) and Ramey et al. (1989) approaches for wellbore pressure at late producing times. The seepage face in the sandface and the delayed yield behavior were reproduced by the model considering a small liquid compressibility and incompressible porous medium. The potential buildup (recovery) simulated by the model evidenced a different- phenomenon from the drawdown, contrary to statements found in the Groundwater literature. Graphs of buildup potential vs time, buildup seepage face length vs time, and free surface head and sand bottom head radial profiles evidenced that the liquid refills the desaturating cone as a flat moving surface. The late time pseudo radial behavior was only approached after exaggerated long times.
Finite difference time domain analysis of chirped dielectric gratings
NASA Technical Reports Server (NTRS)
Hochmuth, Diane H.; Johnson, Eric G.
1993-01-01
The finite difference time domain (FDTD) method for solving Maxwell's time-dependent curl equations is accurate, computationally efficient, and straight-forward to implement. Since both time and space derivatives are employed, the propagation of an electromagnetic wave can be treated as an initial-value problem. Second-order central-difference approximations are applied to the space and time derivatives of the electric and magnetic fields providing a discretization of the fields in a volume of space, for a period of time. The solution to this system of equations is stepped through time, thus, simulating the propagation of the incident wave. If the simulation is continued until a steady-state is reached, an appropriate far-field transformation can be applied to the time-domain scattered fields to obtain reflected and transmitted powers. From this information diffraction efficiencies can also be determined. In analyzing the chirped structure, a mesh is applied only to the area immediately around the grating. The size of the mesh is then proportional to the electric size of the grating. Doing this, however, imposes an artificial boundary around the area of interest. An absorbing boundary condition must be applied along the artificial boundary so that the outgoing waves are absorbed as if the boundary were absent. Many such boundary conditions have been developed that give near-perfect absorption. In this analysis, the Mur absorbing boundary conditions are employed. Several grating structures were analyzed using the FDTD method.
NASA Astrophysics Data System (ADS)
Düll, Wolf-Patrick; Schneider, Guido; Wayne, C. Eugene
2016-05-01
In 1968 V.E. Zakharov derived the Nonlinear Schrödinger equation for the two-dimensional water wave problem in the absence of surface tension, that is, for the evolution of gravity driven surface water waves, in order to describe slow temporal and spatial modulations of a spatially and temporarily oscillating wave packet. In this paper we give a rigorous proof that the wave packets in the two-dimensional water wave problem in a canal of finite depth can be approximated over a physically relevant timespan by solutions of the Nonlinear Schrödinger equation.
Chitcholtan, Kenny; Asselin, Eric; Parent, Sophie; Sykes, Peter H.; Evans, John J.
2013-01-01
Three-dimensional (3D) in vitro models have an invaluable role in understanding the behaviour of tumour cells in a well defined microenvironment. This is because some aspects of tumour characteristics cannot be fully recapitulated in a cell monolayer (2D). In the present study, we compared growth patterns, expression of signalling molecules, and metabolism-associated proteins of endometrial cancer cell lines in 3D and 2D cell cultures. Cancer cells formed spherical structures in 3D reconstituted basement membrane (3D rBM), and the morphological appearance was cell line dependent. Cell differentiation was observed after 8 days in the 3D rBM. There was reduced proliferation, detected by less expression of PCNA in 3D rBM than in 2D cell monolayers. The addition of exogenous epidermal growth factor (EGF) to cancer cells induced phosphorylation of EGFR and Akt in both cell culture conditions. The uptake of glucose was selectively altered in the 3D rBM, but there was a lack of association with Glut-1 expression. The secretion of vascular endothelial growth factor (VEGF) and prostaglandin E{sub 2} (PGE{sub 2}) was selectively altered in 3D rBM, and it was cell line dependent. Our data demonstrated that 3D rBM as an in vitro model can influence proliferation and metabolism of endometrial cancer cell behaviour compared to 2D cell monolayer. Changes are specific to individual cell types. The use of 3D rBM is, therefore, important in the in vitro study of targeted anticancer therapies.
Marsden, O; Bogey, C; Bailly, C
2014-03-01
The feasibility of using numerical simulation of fluid dynamics equations for the detailed description of long-range infrasound propagation in the atmosphere is investigated. The two dimensional (2D) Navier Stokes equations are solved via high fidelity spatial finite differences and Runge-Kutta time integration, coupled with a shock-capturing filter procedure allowing large amplitudes to be studied. The accuracy of acoustic prediction over long distances with this approach is first assessed in the linear regime thanks to two test cases featuring an acoustic source placed above a reflective ground in a homogeneous and weakly inhomogeneous medium, solved for a range of grid resolutions. An atmospheric model which can account for realistic features affecting acoustic propagation is then described. A 2D study of the effect of source amplitude on signals recorded at ground level at varying distances from the source is carried out. Modifications both in terms of waveforms and arrival times are described. PMID:24606252
Nonlinear triggered lightning models for use in finite difference calculations
NASA Technical Reports Server (NTRS)
Rudolph, Terence; Perala, Rodney A.; Ng, Poh H.
1989-01-01
Two nonlinear triggered lightning models have been developed for use in finite difference calculations. Both are based on three species of air chemistry physics and couple nonlinearly calculated air conductivity to Maxwell's equations. The first model is suitable for use in three-dimensional modeling and has been applied to the analysis of triggered lightning on the NASA F106B Thunderstorm Research Aircraft. The model calculates number densities of positive ions, negative ions, and electrons as a function of time and space through continuity equations, including convective derivative terms. The set of equations is closed by using experimentally determined mobilities, and the mobilities are also used to determine the air conductivity. Results from the model's application to the F106B are shown. The second model is two-dimensional and incorporates an enhanced air chemistry formulation. Momentum conservation equations replace the mobility assumption of the first model. Energy conservation equations for neutrals, heavy ions, and electrons are also used. Energy transfer into molecular vibrational modes is accounted for. The purpose for the enhanced model is to include the effects of temperature into the air breakdown, a necessary step if the model is to simulate more than the very earliest stages of breakdown. Therefore, the model also incorporates a temperature-dependent electron avalanche rate. Results from the model's application to breakdown around a conducting ellipsoid placed in an electric field are shown.
Contraction pre-conditioner in finite-difference electromagnetic modelling
NASA Astrophysics Data System (ADS)
Yavich, Nikolay; Zhdanov, Michael S.
2016-09-01
This paper introduces a novel approach to constructing an effective pre-conditioner for finite-difference (FD) electromagnetic modelling in geophysical applications. This approach is based on introducing an FD contraction operator, similar to one developed for integral equation formulation of Maxwell's equation. The properties of the FD contraction operator were established using an FD analogue of the energy equality for the anomalous electromagnetic field. A new pre-conditioner uses a discrete Green's function of a 1-D layered background conductivity. We also developed the formulae for an estimation of the condition number of the system of FD equations pre-conditioned with the introduced FD contraction operator. Based on this estimation, we have established that the condition number is bounded by the maximum conductivity contrast between the background conductivity and actual conductivity. When there are both resistive and conductive anomalies relative to the background, the new pre-conditioner is advantageous over using the 1-D discrete Green's function directly. In our numerical experiments with both resistive and conductive anomalies, for a land geoelectrical model with 1:10 contrast, the method accelerates convergence of an iterative method (BiCGStab) by factors of 2-2.5, and in a marine example with 1:50 contrast, by a factor of 4.6, compared to direct use of the discrete 1-D Green's function as a pre-conditioner.
Assessment of Linear Finite-Difference Poisson-Boltzmann Solvers
Wang, Jun; Luo, Ray
2009-01-01
CPU time and memory usage are two vital issues that any numerical solvers for the Poisson-Boltzmann equation have to face in biomolecular applications. In this study we systematically analyzed the CPU time and memory usage of five commonly used finite-difference solvers with a large and diversified set of biomolecular structures. Our comparative analysis shows that modified incomplete Cholesky conjugate gradient and geometric multigrid are the most efficient in the diversified test set. For the two efficient solvers, our test shows that their CPU times increase approximately linearly with the numbers of grids. Their CPU times also increase almost linearly with the negative logarithm of the convergence criterion at very similar rate. Our comparison further shows that geometric multigrid performs better in the large set of tested biomolecules. However, modified incomplete Cholesky conjugate gradient is superior to geometric multigrid in molecular dynamics simulations of tested molecules. We also investigated other significant components in numerical solutions of the Poisson-Boltzmann equation. It turns out that the time-limiting step is the free boundary condition setup for the linear systems for the selected proteins if the electrostatic focusing is not used. Thus, development of future numerical solvers for the Poisson-Boltzmann equation should balance all aspects of the numerical procedures in realistic biomolecular applications. PMID:20063271
A hybrid finite-difference and analytic element groundwater model.
Haitjema, H M; Feinstein, D T; Hunt, R J; Gusyev, M A
2010-01-01
Regional finite-difference models tend to have large cell sizes, often on the order of 1-2 km on a side. Although the regional flow patterns in deeper formations may be adequately represented by such a model, the intricate surface water and groundwater interactions in the shallower layers are not. Several stream reaches and nearby wells may occur in a single cell, precluding any meaningful modeling of the surface water and groundwater interactions between the individual features. We propose to replace the upper MODFLOW layer or layers, in which the surface water and groundwater interactions occur, by an analytic element model (GFLOW) that does not employ a model grid; instead, it represents wells and surface waters directly by the use of point-sinks and line-sinks. For many practical cases it suffices to provide GFLOW with the vertical leakage rates calculated in the original coarse MODFLOW model in order to obtain a good representation of surface water and groundwater interactions. However, when the combined transmissivities in the deeper (MODFLOW) layers dominate, the accuracy of the GFLOW solution diminishes. For those cases, an iterative coupling procedure, whereby the leakages between the GFLOW and MODFLOW model are updated, appreciably improves the overall solution, albeit at considerable computational cost. The coupled GFLOW-MODFLOW model is applicable to relatively large areas, in many cases to the entire model domain, thus forming an attractive alternative to local grid refinement or inset models. PMID:20132324