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
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
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.
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
Assessment of linear finite-difference Poisson-Boltzmann solvers.
Wang, Jun; Luo, Ray
2010-06-01
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
Performance of Nonlinear Finite-Difference Poisson-Boltzmann Solvers.
Cai, Qin; Hsieh, Meng-Juei; Wang, Jun; Luo, Ray
2010-01-12
We implemented and optimized seven finite-difference solvers for the full nonlinear Poisson-Boltzmann equation in biomolecular applications, including four relaxation methods, one conjugate gradient method, and two inexact Newton methods. The performance of the seven solvers was extensively evaluated with a large number of nucleic acids and proteins. Worth noting is the inexact Newton method in our analysis. We investigated the role of linear solvers in its performance by incorporating the incomplete Cholesky conjugate gradient and the geometric multigrid into its inner linear loop. We tailored and optimized both linear solvers for faster convergence rate. In addition, we explored strategies to optimize the successive over-relaxation method to reduce its convergence failures without too much sacrifice in its convergence rate. Specifically we attempted to adaptively change the relaxation parameter and to utilize the damping strategy from the inexact Newton method to improve the successive over-relaxation method. Our analysis shows that the nonlinear methods accompanied with a functional-assisted strategy, such as the conjugate gradient method and the inexact Newton method, can guarantee convergence in the tested molecules. Especially the inexact Newton method exhibits impressive performance when it is combined with highly efficient linear solvers that are tailored for its special requirement. PMID:24723843
Asymptotically Correct Finite Difference Schemes for Highly Oscillatory ODEs
Arnold, Anton; Geier, Jens
2010-09-30
We are concerned with the numerical integration of ODE-initial value problems of the form {epsilon}{sup 2{phi}}{sub xx}+a(x){phi} = 0 with given a(x){>=}a{sub 0}>0 in the highly oscillatory regime 0<{epsilon}(appearing as a stationary Schroedinger equation, e.g.). In two steps we derive an accurate finite difference scheme that does not need to resolve each oscillation: With a WKB-ansatz the dominant oscillations are ''transformed out'', yielding a much smoother ODE. For the resulting oscillatory integrals we devise an asymptotic expansion both in {epsilon} and h. The resulting scheme typically has a step size restriction of h = o({radical}({epsilon})). If the phase of the WKB-transformation can be computed explicitly, then the scheme is asymptotically correct with an error bound of the order o({epsilon}{sup 3}h{sup 2}). As an application we present simulations of a 1D-model for ballistic quantum transport in a MOSFET (metal oxide semiconductor field-effect transistor).
NASA Astrophysics Data System (ADS)
Gallego, A.; Moreno-García, P.; Casanova, Cesar F.
2013-06-01
Structural studies to find defects (in particular delaminations) in composite plates have been very prevalent in the Structural Health Monitoring field. The present work develops a new method to detect delaminations in CFRP (Carbon Fiber Reinforced Polymer) plates. In this paper the method is validated with numerical simulations, which come to support its adequacy for use with real acquisition data. This is done firstly through the implementation of a delaminated plate finite element. Using the classical lamination plate theory, delamination is considered in the kinematic equations through jump functions and additional degrees of freedom. The element allows the introduction of nd delaminations through its thickness. Classical QMITC (Quadrilateral Mixed Interpolation Tensorial Components) and DKQ (Discrete Kirchhoff Quadrilateral) elements are used for the membrane and bending FEM (Finite Element Method) formulation. Second, using the vibration modes obtained with the FEM, a damage location technique based on the variational Ritz method and Wavelet Analysis is proposed. The approach has the advantage of requiring only damaged modes and not the healthy ones. Both FEM simulations and Ritz/Wavelet damage detection schemes are applied in an orthotropic CFRP plate with the stacking sequence [0/90]3S. In addition, the influence of delamination thickness position, boundary conditions and added noise (in order to simulate experimental measures) was studied.
NASA Technical Reports Server (NTRS)
Sun, W.; Loeb, N. G.; Tanev, S.; Videen, G.
2004-01-01
The two-dimensional (2-D) finite-difference time domain (FDTD) method is applied to calculate light scattering and absorption by an arbitrarily shaped infinite column embedded in an absorbing dielectric medium. A uniaxial perfectly matched layer (UPML) absorbing boundary condition (ABC) is used to truncate the computational domain. The single-scattering properties of the infinite column embedded in the absorbing medium, including scattering phase functions, extinction and absorption efficiencies, are derived using an area integration of the internal field. An exact solution for light scattering and absorption by a circular cylinder in an absorbing medium is used to examine the accuracy of the 2-D UPML FDTD code. With use of a cell size of 1/120 incident wavelength in the FDTD calculations, the errors in the extinction and absorption efficiencies and asymmetry factors from the 2-D UPML FDTD are generally smaller than approx .1%. The errors in the scattering phase functions are typically smaller than approx .4%. Using the 2-D UPML FDTD technique, light scattering and absorption by long noncircular columns embedded in absorbing media can be accurately solved.
Kociuba, Marek; Kozieł, Slawomir; Chakraborty, Raja
2016-09-01
The ratio of second-to-fourth digit length (2D:4D), which is generally higher in women compared with men, is a putative marker of prenatal testosterone (PT) exposure. Lower 2D:4D is linked with greater physical ability and strength, better sporting performance and a propensity towards jobs demanding greater physical ability. The objectives of this paper were to examine the sexual dimorphism in 2D:4D in both hands 1and compare this dimorphism in the students of military and civil courses at the General Kuściuszko Military Academy of Land Forces in Wrocław. The cross-sectional study compared 59 female and 118 male students from the military courses and 53 females and 64 male students from the civil courses. Besides calculating 2D:4D (2D/4D) for each hand, height and weight were also recorded. Physical fitness and endurance were assessed using Eurofit tests. Handgrip strength was measured using a standardized isometric dynamometer. In almost all physical tests, students in the military cohort showed highly significant greater physical ability and strength (e.g. handgrip strength) when compared with the civil cohort. Male participants had a significantly lower 2D:4D than females for each hand, as well as for the average value for both hands. The sexual dimorphism was, however, a little more pronounced in the right hand than in the left. Both sex and course type were significant predictors of 2D:4D. There were significant interactions between sex and the student type. Among females, but not in males, the military cohort had a significantly lower, i.e. more 'masculine', 2D:4D for the left hand and right hand and average for both hands (t=3.290, p<0.001) than the civil cohort. This was not the case in males. However, the sex difference in 2D:4D was only significant among the civil students, and not among the military cadets. In conclusion, higher PT exposure, as represented by a lower 2D:4D, among the Polish females might be an indicator of relatively increased physical
Park, S.J.; Song, J.H.
1999-07-01
A two-dimensional elastic-plastic finite element analysis is performed for plane stress conditions with 4-node isoparametric elements to investigate the closure behavior under various variable-amplitude loading, i.e., single overloading, Hi-Lo block loading, and narrow- and wide-band random loading. The closure behavior under single overloading and Hi-Lo block loading can be well simulated by applying the concept of the most appropriate mesh size that will provide numerical results consistent with experimental data under constant-amplitude loading. It is found that the crack opening load under random loading may be predicted approximately by replacing the complicated random load history with the appropriate equivalent, simplified variable load history.
NASA Astrophysics Data System (ADS)
Tan, Sirui; Huang, Lianjie
2014-11-01
For modeling scalar-wave propagation in geophysical problems using finite-difference schemes, optimizing the coefficients of the finite-difference operators can reduce numerical dispersion. Most optimized finite-difference schemes for modeling seismic-wave propagation suppress only spatial but not temporal dispersion errors. We develop a novel optimized finite-difference scheme for numerical scalar-wave modeling to control dispersion errors not only in space but also in time. Our optimized scheme is based on a new stencil that contains a few more grid points than the standard stencil. We design an objective function for minimizing relative errors of phase velocities of waves propagating in all directions within a given range of wavenumbers. Dispersion analysis and numerical examples demonstrate that our optimized finite-difference scheme is computationally up to 2.5 times faster than the optimized schemes using the standard stencil to achieve the similar modeling accuracy for a given 2D or 3D problem. Compared with the high-order finite-difference scheme using the same new stencil, our optimized scheme reduces 50 percent of the computational cost to achieve the similar modeling accuracy. This new optimized finite-difference scheme is particularly useful for large-scale 3D scalar-wave modeling and inversion.
Tan, Sirui; Huang, Lianjie
2014-11-01
For modeling scalar-wave propagation in geophysical problems using finite-difference schemes, optimizing the coefficients of the finite-difference operators can reduce numerical dispersion. Most optimized finite-difference schemes for modeling seismic-wave propagation suppress only spatial but not temporal dispersion errors. We develop a novel optimized finite-difference scheme for numerical scalar-wave modeling to control dispersion errors not only in space but also in time. Our optimized scheme is based on a new stencil that contains a few more grid points than the standard stencil. We design an objective function for minimizing relative errors of phase velocities of waves propagating in all directions within a given range of wavenumbers. Dispersion analysis and numerical examples demonstrate that our optimized finite-difference scheme is computationally up to 2.5 times faster than the optimized schemes using the standard stencil to achieve the similar modeling accuracy for a given 2D or 3D problem. Compared with the high-order finite-difference scheme using the same new stencil, our optimized scheme reduces 50 percent of the computational cost to achieve the similar modeling accuracy. This new optimized finite-difference scheme is particularly useful for large-scale 3D scalar-wave modeling and inversion.
Finite-difference-based dynamic modeling of MEMS bridge
NASA Astrophysics Data System (ADS)
Michael, Aron; Yu, Kevin; Kwok, Chee Yee
2005-02-01
In this paper, we present a finite difference based one-dimensional dynamic modeling, which includes electro-thermal coupled with thermo-mechanical behavior of a multi-layered micro-bridge. The electro-thermal model includes the heat transfer from the joule-heated layer to the other layers, and establishes the transient temperature gradient through the thickness of the bridge. The thermal moment and axial load resulting from the transient temperature gradient are used to couple electro-thermal with thermo-mechanical behavior. The dynamic modeling takes into account buckling, and damping effects, asymmetry residual stresses in the layers, and lateral movement at the support ends. The proposed model is applied to a tri-layer micro-bridge of 1000μm length, made of 2μm silicon dioxide sandwiched in between 2μm thick epi-silicon, and 2μm thick poly silicon, with four 400μm long legs, and springs at the four corners the bridge. The beam, and legs are 40μm, and 10μm wide respectively. Results demonstrate the bi-stability of the structure, and a large movement of 40μm between the up and down stable states can easily be obtained. Application of only 21mA electrical current for 15μs to the legs is required to switch buckled-up position to buckled-down position. An additional trapezoidal waveform electrical current of 100mA amplitude for 4μs, and 100μs falling time needs to be applied for the reverse actuation. The switching speed in both cases is less than 500μs.
ERIC Educational Resources Information Center
Kopcha, Theodore J.; Otumfuor, Beryl A.; Wang, Lu
2015-01-01
This study examines the effects of spatial ability, gender differences, and pictorial training on fourth grade students' ability to recall landmark locations from memory. Ninety-six students used Google Earth over a 3-week period to locate landmarks (3-D) and mark their location on a 2-D topographical map. Analysis of covariance on posttest scores…
2D constant-loss taper for mode conversion
NASA Astrophysics Data System (ADS)
Horth, Alexandre; Kashyap, Raman; Quitoriano, Nathaniel J.
2015-03-01
Proposed in this manuscript is a novel taper geometry, the constant-loss taper (CLT). This geometry is derived with 1D slabs of silicon embedded in silicon dioxide using coupled-mode theory (CMT). The efficiency of the CLT is compared to both linear and parabolic tapers using CMT and 2D finite-difference time-domain simulations. It is shown that over a short 2D, 4.45 μm long taper the CLT's mode conversion efficiency is ~90% which is 10% and 18% more efficient than a 2D parabolic or linear taper, respectively.
NASA Astrophysics Data System (ADS)
Tessitore, S.; Fernández-Merodo, J. A.; Herrera, G.; Tomás, R.; Ramondini, M.; Sanabria, M.; Duro, J.; Mulas, J.; Calcaterra, D.
2015-11-01
Subsidence is a hazard that may have natural or anthropogenic origin causing important economic losses. The area of Murcia city (SE Spain) has been affected by subsidence due to groundwater overexploitation since the year 1992. The main observed historical piezometric level declines occurred in the periods 1982-1984, 1992-1995 and 2004-2008 and showed a close correlation with the temporal evolution of ground displacements. Since 2008, the pressure recovery in the aquifer has led to an uplift of the ground surface that has been detected by the extensometers. In the present work an elastic hydro-mechanical finite element code has been used to compute the subsidence time series for 24 geotechnical boreholes, prescribing the measured groundwater table evolution. The achieved results have been compared with the displacements estimated through an advanced DInSAR technique and measured by the extensometers. These spatio-temporal comparisons have showed that, in spite of the limited geomechanical data available, the model has turned out to satisfactorily reproduce the subsidence phenomenon affecting Murcia City. The model will allow the prediction of future induced deformations and the consequences of any piezometric level variation in the study area.
NASA Astrophysics Data System (ADS)
Christlieb, Andrew J.; Rossmanith, James A.; Tang, Qi
2014-07-01
In this work we develop a class of high-order finite difference weighted essentially non-oscillatory (FD-WENO) schemes for solving the ideal magnetohydrodynamic (MHD) equations in 2D and 3D. The philosophy of this work is to use efficient high-order WENO spatial discretizations with high-order strong stability-preserving Runge-Kutta (SSP-RK) time-stepping schemes. Numerical results have shown that with such methods we are able to resolve solution structures that are only visible at much higher grid resolutions with lower-order schemes. The key challenge in applying such methods to ideal MHD is to control divergence errors in the magnetic field. We achieve this by augmenting the base scheme with a novel high-order constrained transport approach that updates the magnetic vector potential. The predicted magnetic field from the base scheme is replaced by a divergence-free magnetic field that is obtained from the curl of this magnetic potential. The non-conservative weakly hyperbolic system that the magnetic vector potential satisfies is solved using a version of FD-WENO developed for Hamilton-Jacobi equations. The resulting numerical method is endowed with several important properties: (1) all quantities, including all components of the magnetic field and magnetic potential, are treated as point values on the same mesh (i.e., there is no mesh staggering); (2) both the spatial and temporal orders of accuracy are fourth-order; (3) no spatial integration or multidimensional reconstructions are needed in any step; and (4) special limiters in the magnetic vector potential update are used to control unphysical oscillations in the magnetic field. Several 2D and 3D numerical examples are presented to verify the order of accuracy on smooth test problems and to show high-resolution on test problems that involve shocks.
NASA Astrophysics Data System (ADS)
Martinez, J.; Belahcen, A.; Detoni, J. G.
2016-01-01
This paper presents a coupled Finite Element Model in order to study the vibrations in induction motors under steady-state. The model utilizes a weak coupling strategy between both magnetic and elastodynamic fields on the structure. Firstly, the problem solves the magnetic vector potential in an axial cut and secondly the former solution is coupled to a three dimensional model of the stator. The coupling is performed using projection based algorithms between the computed magnetic solution and the three-dimensional mesh. The three-dimensional model of the stator includes both end-windings and end-shields in order to give a realistic picture of the motor. The present model is validated using two steps. Firstly, a modal analysis hammer test is used to validate the material characteristic of this complex structure and secondly an array of accelerometer sensors is used in order to study the rotating waves using multi-dimensional spectral techniques. The analysis of the radial vibrations presented in this paper firstly concludes that slot harmonic components are visible when the motor is loaded. Secondly, the multidimensional spectrum presents the most relevant mechanical waves on the stator such as the ones produced by the space harmonics or the saturation of the iron core. The direct retrieval of the wave-number in a multi-dimensional spectrum is able to show the internal current distribution in a non-intrusive way. Experimental results for healthy induction motors are showing mechanical imbalances in a multi-dimensional spectrum in a more straightforward form.
A total variation diminishing finite difference algorithm for sonic boom propagation models
NASA Technical Reports Server (NTRS)
Sparrow, Victor W.
1993-01-01
It is difficult to accurately model the rise phases of sonic boom waveforms with traditional finite difference algorithms because of finite difference phase dispersion. This paper introduces the concept of a total variation diminishing (TVD) finite difference method as a tool for accurately modeling the rise phases of sonic booms. A standard second order finite difference algorithm and its TVD modified counterpart are both applied to the one-way propagation of a square pulse. The TVD method clearly outperforms the non-TVD method, showing great potential as a new computational tool in the analysis of sonic boom propagation.
NASA Technical Reports Server (NTRS)
Ransom, Jonathan B.
2002-01-01
A multifunctional interface method with capabilities for variable-fidelity modeling and multiple method analysis is presented. The methodology provides an effective capability by which domains with diverse idealizations can be modeled independently to exploit the advantages of one approach over another. The multifunctional method is used to couple independently discretized subdomains, and it is used to couple the finite element and the finite difference methods. The method is based on a weighted residual variational method and is presented for two-dimensional scalar-field problems. A verification test problem and a benchmark application are presented, and the computational implications are discussed.
NASA Astrophysics Data System (ADS)
Castaldo, Raffaele; Tizzani, Pietro
2016-04-01
Many numerical models have been developed to simulate the deformation and stress changes associated to the faulting process. This aspect is an important topic in fracture mechanism. In the proposed study, we investigate the impact of the deep fault geometry and tectonic setting on the co-seismic ground deformation pattern associated to different earthquake phenomena. We exploit the impact of the structural-geological data in Finite Element environment through an optimization procedure. In this framework, we model the failure processes in a physical mechanical scenario to evaluate the kinematics associated to the Mw 6.1 L'Aquila 2009 earthquake (Italy), the Mw 5.9 Ferrara and Mw 5.8 Mirandola 2012 earthquake (Italy) and the Mw 8.3 Gorkha 2015 earthquake (Nepal). These seismic events are representative of different tectonic scenario: the normal, the reverse and thrust faulting processes, respectively. In order to simulate the kinematic of the analyzed natural phenomena, we assume, under the plane stress approximation (is defined to be a state of stress in which the normal stress, sz, and the shear stress sxz and syz, directed perpendicular to x-y plane are assumed to be zero), the linear elastic behavior of the involved media. The performed finite element procedure consist of through two stages: (i) compacting under the weight of the rock successions (gravity loading), the deformation model reaches a stable equilibrium; (ii) the co-seismic stage simulates, through a distributed slip along the active fault, the released stresses. To constrain the models solution, we exploit the DInSAR deformation velocity maps retrieved by satellite data acquired by old and new generation sensors, as ENVISAT, RADARSAT-2 and SENTINEL 1A, encompassing the studied earthquakes. More specifically, we first generate 2D several forward mechanical models, then, we compare these with the recorded ground deformation fields, in order to select the best boundaries setting and parameters. Finally
Finite difference elastic wave modeling with an irregular free surface using ADER scheme
NASA Astrophysics Data System (ADS)
Almuhaidib, Abdulaziz M.; Nafi Toksöz, M.
2015-06-01
In numerical modeling of seismic wave propagation in the earth, we encounter two important issues: the free surface and the topography of the surface (i.e. irregularities). In this study, we develop a 2D finite difference solver for the elastic wave equation that combines a 4th- order ADER scheme (Arbitrary high-order accuracy using DERivatives), which is widely used in aeroacoustics, with the characteristic variable method at the free surface boundary. The idea is to treat the free surface boundary explicitly by using ghost values of the solution for points beyond the free surface to impose the physical boundary condition. The method is based on the velocity-stress formulation. The ultimate goal is to develop a numerical solver for the elastic wave equation that is stable, accurate and computationally efficient. The solver treats smooth arbitrary-shaped boundaries as simple plane boundaries. The computational cost added by treating the topography is negligible compared to flat free surface because only a small number of grid points near the boundary need to be computed. In the presence of topography, using 10 grid points per shortest shear-wavelength, the solver yields accurate results. Benchmark numerical tests using several complex models that are solved by our method and other independent accurate methods show an excellent agreement, confirming the validity of the method for modeling elastic waves with an irregular free surface.
NASA Astrophysics Data System (ADS)
Choi, S. J.; Kim, J.; Shin, S.
2014-12-01
In this presentation, a new non-hydrostatic (NH) dynamical core using the spectral element method (SEM) in the horizontal discretization and the finite difference method (FDM) in the vertical discretization will be presented. By using horizontal SEM, which decomposes the physical domain into smaller pieces with a small communication stencil, we can achieve a high level of scalability. Also by using vertical FDM, we provide an easy way for coupling the dynamics and existing physics packages. The Euler equations used here are in a flux form based on the hybrid sigma hydrostatic pressure vertical coordinate, which are similar to those used in the Weather Research and Forecasting (WRF) model. Within these Euler equations, we use a time-split third-order Runge-Kutta (RK3) for the time discretization. In order to establish robustness, firstly the NH dynamical core is verified in a simplified two dimensional (2D) slice framework by conducting widely used standard benchmark tests, and then we verify the global three dimensional (3D) dynamical core on the cubed-sphere grid with several test cases introduced by Dynamical Core Model Intercomparison Project (DCMIP).
NASA Astrophysics Data System (ADS)
Ramadan, Omar
2014-12-01
Systematic split-step finite difference time domain (SS-FDTD) formulations, based on the general Lie-Trotter-Suzuki product formula, are presented for solving the time-dependent Maxwell equations in double-dispersive electromagnetic materials. The proposed formulations provide a unified tool for constructing a family of unconditionally stable algorithms such as the first order split-step FDTD (SS1-FDTD), the second order split-step FDTD (SS2-FDTD), and the second order alternating direction implicit FDTD (ADI-FDTD) schemes. The theoretical stability of the formulations is included and it has been demonstrated that the formulations are unconditionally stable by construction. Furthermore, the dispersion relation of the formulations is derived and it has been found that the proposed formulations are best suited for those applications where a high space resolution is needed. Two-dimensional (2-D) and 3-D numerical examples are included and it has been observed that the SS1-FDTD scheme is computationally more efficient than the ADI-FDTD counterpart, while maintaining approximately the same numerical accuracy. Moreover, the SS2-FDTD scheme allows using larger time step than the SS1-FDTD or ADI-FDTD and therefore necessitates less CPU time, while giving approximately the same numerical accuracy.
NASA Astrophysics Data System (ADS)
Brissaud, Q.; Garcia, R.; Martin, R.; Komatitsch, D.
2015-12-01
The acoustic and gravity waves propagating in the planetary atmospheres have been studied intensively as markers of specific phenomena (tectonic events, explosions) or as contributors to the atmosphere dynamics. To get a better understanding of the physic behind these dynamic processes, both acoustic and gravity waves propagation should be modeled in an attenuating and windy 3D atmosphere from the ground to the upper thermosphere. Thus, In order to provide an efficient numerical tool at the regional or the global scale a high order finite difference time domain (FDTD) approach is proposed that relies on the linearized compressible Navier-Stokes equations (Landau 1959) with non constant physical parameters (density, viscosities and speed of sound) and background velocities (wind). One significant benefit from this code is its versatility. Indeed, it handles both acoustic and gravity waves in the same simulation that enables one to observe correlations between the two. Simulations will also be performed on 2D/3D realistic cases such as tsunamis in a full MSISE-00 atmosphere and gravity-wave generation through atmospheric explosions. Computations are validated by comparison to well-known analytical solutions based on dispersion relations in specific benchmark cases (atmospheric explosion and bottom displacement forcing).
NASA Astrophysics Data System (ADS)
Brissaud, Quentin; Martin, Roland; Garcia, Raphaël F.; Komatitsch, Dimitri
2016-07-01
Acoustic and gravity waves propagating in planetary atmospheres have been studied intensively as markers of specific phenomena such as tectonic events or explosions or as contributors to atmosphere dynamics. To get a better understanding of the physics behind these dynamic processes, both acoustic and gravity waves propagation should be modelled in a 3-D attenuating and windy atmosphere extending from the ground to the upper thermosphere. Thus, in order to provide an efficient numerical tool at the regional or global scale, we introduce a finite difference in the time domain (FDTD) approach that relies on the linearized compressible Navier-Stokes equations with a background flow (wind). One significant benefit of such a method is its versatility because it handles both acoustic and gravity waves in the same simulation, which enables one to observe interactions between them. Simulations can be performed for 2-D or 3-D realistic cases such as tsunamis in a full MSISE-00 atmosphere or gravity-wave generation by atmospheric explosions. We validate the computations by comparing them to analytical solutions based on dispersion relations in specific benchmark cases: an atmospheric explosion, and a ground displacement forcing.
Biffle, J.H.; Blanford, M.L.
1994-05-01
JAC2D is a two-dimensional finite element program designed to solve quasi-static nonlinear mechanics problems. A set of continuum equations describes the nonlinear mechanics involving large rotation and strain. A nonlinear conjugate gradient method is used to solve the equations. The method is implemented in a two-dimensional setting with various methods for accelerating convergence. Sliding interface logic is also implemented. A four-node Lagrangian uniform strain element is used with hourglass stiffness to control the zero-energy modes. This report documents the elastic and isothermal elastic/plastic material model. Other material models, documented elsewhere, are also available. The program is vectorized for efficient performance on Cray computers. Sample problems described are the bending of a thin beam, the rotation of a unit cube, and the pressurization and thermal loading of a hollow sphere.
NASA Astrophysics Data System (ADS)
MacKinnon, Robert J.; Carey, Graham F.
2003-01-01
A new class of positivity-preserving, flux-limited finite-difference and Petrov-Galerkin (PG) finite-element methods are devised for reactive transport problems.The methods are similar to classical TVD flux-limited schemes with the main difference being that the flux-limiter constraint is designed to preserve positivity for problems involving diffusion and reaction. In the finite-element formulation, we also consider the effect of numerical quadrature in the lumped and consistent mass matrix forms on the positivity-preserving property. Analysis of the latter scheme shows that positivity-preserving solutions of the resulting difference equations can only be guaranteed if the flux-limited scheme is both implicit and satisfies an additional lower-bound condition on time-step size. We show that this condition also applies to standard Galerkin linear finite-element approximations to the linear diffusion equation. Numerical experiments are provided to demonstrate the behavior of the methods and confirm the theoretical conditions on time-step size, mesh spacing, and flux limiting for transport problems with and without nonlinear reaction.
NASA Astrophysics Data System (ADS)
Chen, Nai-Dong; Chen, Nai-Fu; Li, Jun; Cao, Cai-Yun; Wang, Jin-Mei
2015-12-01
The accumulating of pharmaceutical chemicals in medicinal plants would greatly be affected by their ages and establishing a fast quality-identification method to evaluate the similarity of medicinal herbs at different cultivated ages is a critical step for assurance of quality and safety in the TCM industry. In this work, tri-step IR macro-fingerprinting and 2D-COS IR spectrum techniques combined with statistical pattern recognition were applied for discrimination and similarity evaluation of different ages of tissue-cultured and wild Dendrobium huoshanense C. Z. Tang et S. J. Cheng as well as Dendrobium henanense J.L.Lu et L.X Gao. Both tissue-cultured and wild D. huoshanense were easily differentiated from D. henanense by FTIR and SD-IR spectra, while it's quite difficult to discriminate different cultivated years of the three investigated Dendrobiums. In 2D-COS IR spectra, 1-5 auto-peaks with different indensity and positions were located in the region 1160-1030 cm-1 of the twelve Dendrobium samples and thus could be used to identify Dendrobium samples at different ages. Principle component analysis (PCA) of synchronous 2D-COS data showed that the twelve samples were effectively identified and evaluated. The results indicated that the tri-step infrared macro-fingerprinting combined with PCA method was suitable to differentiate the cultivated ages of Dendrobiums with species and orgins rapidly and nondestructively.
NASA Astrophysics Data System (ADS)
Shah, Jainil P.; Mann, Steve D.; McKinley, Randolph L.; Tornai, Martin P.
2014-03-01
The 2D scatter-to-primary (SPR) ratios and 3D voxelized difference volumes were characterized for a cone beam breast CT scanner capable of arbitrary (non-traditional) 3D trajectories. The CT system uses a 30x30cm2 flat panel imager with 197 micron pixellation and a rotating tungsten anode x-ray source with 0.3mm focal spot, with an SID of 70cm. Data were acquired for two cylindrical phantoms (12.5cm and 15cm diameter) filled with three different combinations of water and methanol yielding a range of uniform densities. Projections were acquired with two acquisition trajectories: 1) simple-circular azimuthal orbit with fixed tilt; and 2) saddle orbit following a +/-15° sinusoidal trajectory around the object. Projection data were acquired in 2x2 binned mode. Projections were scatter corrected using a beam stop array method, and the 2D SPR was measured on the projections. The scatter corrected and uncorrected data were then reconstructed individually using an iterative ordered subsets convex algorithm, and the 3D difference volumes were calculated as the absolute difference between the two. Results indicate that the 2D SPR is ~7-15% higher on projections with greatest tilt for the saddle orbit, due to the longer x-ray path length through the volume, compared to the 0° tilt projections. Additionally, the 2D SPR increases with object diameter as well as density. The 3D voxelized difference volumes are an estimate of the scatter contribution to the reconstructed attenuation coefficients on a voxel level. They help visualize minor deficiencies and artifacts in the volumes due to correction methods.
Finite difference identification of noisy distributed systems using scanning measurements
NASA Technical Reports Server (NTRS)
Hughes, R. O.
1975-01-01
Most of the present-day literature concerned with identification theory and techniques is directed toward lumped parameter systems, and many comprehensive surveys of the field are available. Relatively little has appeared in the literature concerning distributed identification, and even more noticeable is the scarcity of papers dealing with systems described by the one-dimensional wave equation. Perdeauville and Goodson were perhaps the first researchers with a workable but time consuming method for the identification of coefficients of the wave equation. Fairman and Shen, also considering the wave equation, used the technique of finite differencing to approximate spatial derivatives, and Poisson filter chains to approximate temporal derivatives.
NASA Astrophysics Data System (ADS)
Wu, Yan-Wen; Sun, Su-Qin; Zhou, Qun; Tao, Jia-Xun; Noda, Isao
2008-06-01
As a traditional Chinese medicine (TCM), 'Red Flower Oil' preparation is widely used as a household remedy in China and Southeast Asia. Usually, the preparation is a mixture of several plant essential oils with different volatile features, such as wintergreen oil, turpentine oil and clove oil. The proportions of these plant essential oils in 'Red Flower Oil' vary from different manufacturers. Thus, it is important to develop a simple and rapid evaluation method for quality assurance of the preparations. Fourier transform infrared (FT-IR) was applied and two-dimensional correlation infrared spectroscopy (2D IR) based on the volatile characteristic of samples was used to enhance the resolution of FT-IR spectra. 2D IR technique could, not only easily provide the composition and their volatile sequences in 'Red flower Oil' preparations, but also rapidly discriminate the subtle differences in products from different manufacturers. Therefore, FT-IR combined with volatility-dependent 2D IR correlation analysis provides a very fast and effective method for the quality control of essential oil mixtures in TCM.
NASA Astrophysics Data System (ADS)
Wei, Xiao-Kun; Shao, Wei; Shi, Sheng-Bing; Zhang, Yong; Wang, Bing-Zhong
2015-07-01
An efficient conformal locally one-dimensional finite-difference time-domain (LOD-CFDTD) method is presented for solving two-dimensional (2D) electromagnetic (EM) scattering problems. The formulation for the 2D transverse-electric (TE) case is presented and its stability property and numerical dispersion relationship are theoretically investigated. It is shown that the introduction of irregular grids will not damage the numerical stability. Instead of the staircasing approximation, the conformal scheme is only employed to model the curve boundaries, whereas the standard Yee grids are used for the remaining regions. As the irregular grids account for a very small percentage of the total space grids, the conformal scheme has little effect on the numerical dispersion. Moreover, the proposed method, which requires fewer arithmetic operations than the alternating-direction-implicit (ADI) CFDTD method, leads to a further reduction of the CPU time. With the total-field/scattered-field (TF/SF) boundary and the perfectly matched layer (PML), the radar cross section (RCS) of two 2D structures is calculated. The numerical examples verify the accuracy and efficiency of the proposed method. Project supported by the National Natural Science Foundation of China (Grant Nos. 61331007 and 61471105).
NASA Technical Reports Server (NTRS)
Ryan, Deirdre A.; Luebbers, Raymond J.; Nguyen, Truong X.; Kunz, Karl S.; Steich, David J.
1992-01-01
Prediction of anechoic chamber performance is a difficult problem. Electromagnetic anechoic chambers exist for a wide range of frequencies but are typically very large when measured in wavelengths. Three dimensional finite difference time domain (FDTD) modeling of anechoic chambers is possible with current computers but at frequencies lower than most chamber design frequencies. However, two dimensional FDTD (2D-FTD) modeling enables much greater detail at higher frequencies and offers significant insight into compact anechoic chamber design and performance. A major subsystem of an anechoic chamber for which computational electromagnetic analyses exist is the reflector. First, an analysis of the quiet zone fields of a low frequency anechoic chamber produced by a uniform source and a reflector in two dimensions using the FDTD method is presented. The 2D-FDTD results are compared with results from a three dimensional corrected physical optics calculation and show good agreement. Next, a directional source is substituted for the uniform radiator. Finally, a two dimensional anechoic chamber geometry, including absorbing materials, is considered, and the 2D-FDTD results for these geometries appear reasonable.
The Benard problem: A comparison of finite difference and spectral collocation eigen value solutions
NASA Technical Reports Server (NTRS)
Skarda, J. Raymond Lee; Mccaughan, Frances E.; Fitzmaurice, Nessan
1995-01-01
The application of spectral methods, using a Chebyshev collocation scheme, to solve hydrodynamic stability problems is demonstrated on the Benard problem. Implementation of the Chebyshev collocation formulation is described. The performance of the spectral scheme is compared with that of a 2nd order finite difference scheme. An exact solution to the Marangoni-Benard problem is used to evaluate the performance of both schemes. The error of the spectral scheme is at least seven orders of magnitude smaller than finite difference error for a grid resolution of N = 15 (number of points used). The performance of the spectral formulation far exceeded the performance of the finite difference formulation for this problem. The spectral scheme required only slightly more effort to set up than the 2nd order finite difference scheme. This suggests that the spectral scheme may actually be faster to implement than higher order finite difference schemes.
NASA Technical Reports Server (NTRS)
Panczak, Tim; Ring, Steve; Welch, Mark
1999-01-01
Thermal engineering has long been left out of the concurrent engineering environment dominated by CAD (computer aided design) and FEM (finite element method) software. Current tools attempt to force the thermal design process into an environment primarily created to support structural analysis, which results in inappropriate thermal models. As a result, many thermal engineers either build models "by hand" or use geometric user interfaces that are separate from and have little useful connection, if any, to CAD and FEM systems. This paper describes the development of a new thermal design environment called the Thermal Desktop. This system, while fully integrated into a neutral, low cost CAD system, and which utilizes both FEM and FD methods, does not compromise the needs of the thermal engineer. Rather, the features needed for concurrent thermal analysis are specifically addressed by combining traditional parametric surface based radiation and FD based conduction modeling with CAD and FEM methods. The use of flexible and familiar temperature solvers such as SINDA/FLUINT (Systems Improved Numerical Differencing Analyzer/Fluid Integrator) is retained.
High-order cyclo-difference techniques: An alternative to finite differences
NASA Technical Reports Server (NTRS)
Carpenter, Mark H.; Otto, John C.
1993-01-01
The summation-by-parts energy norm is used to establish a new class of high-order finite-difference techniques referred to here as 'cyclo-difference' techniques. These techniques are constructed cyclically from stable subelements, and require no numerical boundary conditions; when coupled with the simultaneous approximation term (SAT) boundary treatment, they are time asymptotically stable for an arbitrary hyperbolic system. These techniques are similar to spectral element techniques and are ideally suited for parallel implementation, but do not require special collocation points or orthogonal basis functions. The principal focus is on methods of sixth-order formal accuracy or less; however, these methods could be extended in principle to any arbitrary order of accuracy.
Jin, X; Yan, H; Han, C; Zhou, Y; Yi, J
2015-01-01
Objective: To investigate comparatively the percentage gamma passing rate (%GP) of two-dimensional (2D) and three-dimensional (3D) pre-treatment volumetric modulated arc therapy (VMAT) dosimetric verification and their correlation and sensitivity with percentage dosimetric errors (%DE). Methods: %GP of 2D and 3D pre-treatment VMAT quality assurance (QA) with different acceptance criteria was obtained by ArcCHECK® (Sun Nuclear Corporation, Melbourne, FL) for 20 patients with nasopharyngeal cancer (NPC) and 20 patients with oesophageal cancer. %DE were calculated from planned dose–volume histogram (DVH) and patients' predicted DVH calculated by 3DVH® software (Sun Nuclear Corporation). Correlation and sensitivity between %GP and %DE were investigated using Pearson's correlation coefficient (r) and receiver operating characteristics (ROCs). Results: Relatively higher %DE on some DVH-based metrics were observed for both patients with NPC and oesophageal cancer. Except for 2%/2 mm criterion, the average %GPs for all patients undergoing VMAT were acceptable with average rates of 97.11% ± 1.54% and 97.39% ± 1.37% for 2D and 3D 3%/3 mm criteria, respectively. The number of correlations for 3D was higher than that for 2D (21 vs 8). However, the general correlation was still poor for all the analysed metrics (9 out of 26 for 3D 3%/3 mm criterion). The average area under the curve (AUC) of ROCs was 0.66 ± 0.12 and 0.71 ± 0.21 for 2D and 3D evaluations, respectively. Conclusions: There is a lack of correlation between %GP and %DE for both 2D and 3D pre-treatment VMAT dosimetric evaluation. DVH-based dose metrics evaluation obtained from 3DVH will provide more useful analysis. Advances in knowledge: Correlation and sensitivity of %GP with %DE for VMAT QA were studied for the first time. PMID:25494412
NASA Technical Reports Server (NTRS)
Bates, J. R.; Moorthi, S.; Higgins, R. W.
1993-01-01
An adiabatic global multilevel primitive equation model using a two time-level, semi-Lagrangian semi-implicit finite-difference integration scheme is presented. A Lorenz grid is used for vertical discretization and a C grid for the horizontal discretization. The momentum equation is discretized in vector form, thus avoiding problems near the poles. The 3D model equations are reduced by a linear transformation to a set of 2D elliptic equations, whose solution is found by means of an efficient direct solver. The model (with minimal physics) is integrated for 10 days starting from an initialized state derived from real data. A resolution of 16 levels in the vertical is used, with various horizontal resolutions. The model is found to be stable and efficient, and to give realistic output fields. Integrations with time steps of 10 min, 30 min, and 1 h are compared, and the differences are found to be acceptable.
Fei, T.; Larner, K.
1995-11-01
Finite-difference acoustic-wave modeling and reverse-time depth migration based on the full wave equation are general approaches that can take into account arbitrary variations in velocity and density and can handle turning waves as well. However, conventional finite-difference methods for solving the acoustic- or elastic-wave equation suffer from numerical dispersion when too few samples per wavelength are used. The flux-corrected transport (FCT) algorithm, adapted from hydrodynamics, reduces the numerical dispersion in finite-difference wavefield continuation. The flux-correction procedure endeavors to incorporate diffusion into the wavefield continuation process only where needed to suppress the numerical dispersion. Incorporating the flux-correction procedure in conventional finite-difference modeling or reverse-time migration can provide finite-difference solutions with no numerical dispersion even for impulsive sources. The FCT correction, which can be applied to finite-difference approximations of any order in space and time, is an efficient alternative to use for finite-difference approximations of increasing order. Through demonstrations of modeling and migration on both synthetic and field data, the authors show the benefits of the FCT algorithm, as well as its inability to fully recover resolution lost when the spatial sampling becomes too coarse.
NASA Astrophysics Data System (ADS)
Lotsch, Bettina V.
2015-07-01
Graphene's legacy has become an integral part of today's condensed matter science and has equipped a whole generation of scientists with an armory of concepts and techniques that open up new perspectives for the postgraphene area. In particular, the judicious combination of 2D building blocks into vertical heterostructures has recently been identified as a promising route to rationally engineer complex multilayer systems and artificial solids with intriguing properties. The present review highlights recent developments in the rapidly emerging field of 2D nanoarchitectonics from a materials chemistry perspective, with a focus on the types of heterostructures available, their assembly strategies, and their emerging properties. This overview is intended to bridge the gap between two major—yet largely disjunct—developments in 2D heterostructures, which are firmly rooted in solid-state chemistry or physics. Although the underlying types of heterostructures differ with respect to their dimensions, layer alignment, and interfacial quality, there is common ground, and future synergies between the various assembly strategies are to be expected.
Hybrid spectral difference/embedded finite volume method for conservation laws
NASA Astrophysics Data System (ADS)
Choi, Jung J.
2015-08-01
Recently, interests have been increasing towards applying the high-order methods to various engineering applications with complex geometries [30]. As a result, a family of discontinuous high-order methods, such as Discontinuous Galerkin (DG), Spectral Volume (SV) and Spectral Difference (SD) methods, is under active development. These methods provide high-order accurate solutions and are highly parallelizable due to the local solution reconstruction within each element. But, these methods suffer from the Gibbs phenomena when discontinuities are present in the flow fields. Various types of limiters [43-45] and artificial viscosity [46,48] have been employed to overcome this problem. A novel hybrid spectral difference/embedded finite volume method is introduced in order to apply a discontinuous high-order method for large scale engineering applications involving discontinuities in the flows with complex geometries. In the proposed hybrid approach, the finite volume (FV) element, consisting of structured FV subcells, is embedded in the base hexahedral element containing discontinuity, and an FV based high-order shock-capturing scheme is employed to overcome the Gibbs phenomena. Thus, a discontinuity is captured at the resolution of FV subcells within an embedded FV element. In the smooth flow region, the SD element is used in the base hexahedral element. Then, the governing equations are solved by the SD method. The SD method is chosen for its low numerical dissipation and computational efficiency preserving high-order accurate solutions. The coupling between the SD element and the FV element is achieved by the globally conserved mortar method [56]. In this paper, the 5th-order WENO scheme with the characteristic decomposition is employed as the shock-capturing scheme in the embedded FV element, and the 5th-order SD method is used in the smooth flow field. The order of accuracy study and various 1D and 2D test cases are carried out, which involve the discontinuities
NASA Technical Reports Server (NTRS)
Byun, Chansup; Guruswamy, Guru P.
1993-01-01
This paper presents a procedure for computing the aeroelasticity of wing-body configurations on multiple-instruction, multiple-data (MIMD) parallel computers. In this procedure, fluids are modeled using Euler equations discretized by a finite difference method, and structures are modeled using finite element equations. The procedure is designed in such a way that each discipline can be developed and maintained independently by using a domain decomposition approach. A parallel integration scheme is used to compute aeroelastic responses by solving the coupled fluid and structural equations concurrently while keeping modularity of each discipline. The present procedure is validated by computing the aeroelastic response of a wing and comparing with experiment. Aeroelastic computations are illustrated for a High Speed Civil Transport type wing-body configuration.
One-step construction of two different kinds of pores in a 2D covalent organic framework.
Zhou, Tian-You; Xu, Shun-Qi; Wen, Qiang; Pang, Zhong-Fu; Zhao, Xin
2014-11-12
Covalent organic frameworks (COFs) are crystalline porous materials bearing microporous or mesoporous pores. The type and size of pores play crucial roles in regulating the properties of COFs. In this work, a novel COF, which bears two different kinds of ordered pores with controllable sizes: one within microporous range (7.1 Å) and the other in mesoporous range (26.9 Å), has been constructed via one-step synthesis. The structure of the dual-pore COF was confirmed by PXRD investigation, nitrogen adsorption-desorption study, and theoretical calculations. PMID:25360771
Optimization of a finite difference method for nonlinear wave equations
NASA Astrophysics Data System (ADS)
Chen, Miaochao
2013-07-01
Wave equations have important fluid dynamics background, which are extensively used in many fields, such as aviation, meteorology, maritime, water conservancy, etc. This paper is devoted to the explicit difference method for nonlinear wave equations. Firstly, a three-level and explicit difference scheme is derived. It is shown that the explicit difference scheme is uniquely solvable and convergent. Moreover, a numerical experiment is conducted to illustrate the theoretical results of the presented method.
Berry, Robert E.; Muthu, Dhanasekaran; Shokhireva, Tatiana K.; Garrett, Sarah A.; Zhang, Hongjun; Walker, F. Ann
2012-01-01
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
Jin, Meng-ya; Dong, Ling; Luo, Yuan-ming; Yu, Li; Mo, Mei; Hou, Cheng-bo; Li, Zhi-yuan
2015-12-01
This study was designed to use iTRAQ technology coupled with 2D LC-MS/MS to study the comparative proteomics of different processing technology for pilose antler. 1015 proteins were identified with 2D LC combined with MOLDI TOF/TOF mass spectrometry. Comparative analysis with Protein Pilot (Version 4.5) revealed that 87 proteins were changed (P ≤ 0.05, the ratio of > 1.50 or < 0.60 as the threshold selection of difference proteins), of which 24 were up regulated and 33 were down regulated in the traditional frying process (TFP) compared with the fresh pilose antler (P ≤ 0.05). 7 significant different proteins (P ≤ 0.001), most of these significantly changed proteins were found to be involved in calcium ion binding and ATP binding associated with human healthy. Freeze drying with protective agent (FDP) (Trehalose) can improve the content of significantly different proteins (P ≤ 0.001) including Collagen alpha-1 (XII) chain (COL12A1) and Collagen alpha-1 (II) chain (COL2A1). The significant function involves in platelets activating, maintenance of spermatogonium, and disorder expression in tumor cells. The functional annotation by Hierarchical clustering and GO (gene ontology) showed that the main molecule functions of the proteins significantly changed in these processes were involved in binding (52.7%), catalytic (25.3%), structural molecule and transporter (6.6%). PMID:27169289
NASA Astrophysics Data System (ADS)
Provost, B.; Boussu, F.; Coutellier, D.; Vallee, D.; Rondot, F.
2012-08-01
For decades, conventional amour shield is mainly oriented on metallic materials which are today well-known. Since the use of non conventional threats as IEDs, performances of those protections are required to be upgraded. The expected improvements that manufacturers are looking for are mainly oriented to the weight reduction which is the key parameter to reduce the fuel consumption, increase the payload, and offer more manoeuvrability to vehicles [1]. However, the difficulty is to reduce as cautiously as possible the total mass of the protection solution while ensuring the safety of the vehicle. One of the possible solutions is to use new combinations of materials, able to be more efficient against new threats and lighter than the traditional steel armour. It is in this context that the combination between some well-known ballistic alloys and textile composite material appear as a high potential solution for armour plated protection. Indeed, used as a backing, textile composite material present some interesting properties such as a very low density compared with steel and good behaviour in term of ballistic efficiency. This study proposes to test and compare the behaviour and efficiency of three different textile composite backings.
Hu, Yang-Yang; Xiao-Zhang; Zhao, De-Chuan; Guo, Hai-Yang; Fu, Li-Wei; Guo, Lan-Lan; Cui, Xiao-Bing; Huo, Qi-Sheng; Xu, Ji-Qing
2015-09-01
Six new organic-inorganic hybrid compounds based on [XM12O40](4-) (X = heteroatom, M = metal atom), namely [Cu(pic)2][H2XM12O40]·2Hapy·2apy (X = Si, M = W for , X = Ge, M = W for and X = Si, M = Mo for ), [Cu(2,2'-bpy)2][Cu(2,2'-bpy)(H2O)][Cu(pic)2]0.5[XM12O40]·nH2O (X = Si, M = Mo, n = 0.5 for , X = Ge, M = W, n = 1 for ) and [Cu(phen)(H2O)]2[Cu(pic)2][GeW12O40]·2.5H2O () (pic = deprotonated picolinic acid, apy = 2-aminopyridine, 2,2'-bpy = 2,2'-bipyridine, phen = phenanthroline), have been synthesized and characterized by IR, UV-Vis, XRD, cyclic voltammetric measurements and single crystal X-ray diffraction analysis. Single crystal X-ray analysis reveals that compounds are isomorphous and isostructural, in which each is based on [H2XM12O40](2-) and [Cu(pic)2]. Compounds and are also isomorphous and isostructural, of which the structures are more interesting than those of compounds . Both structures are constructed from [XM12O40](4-) and metal mixed-organic-ligand complexes. Compound is also constructed from Keggin ions and metal mixed-organic-ligand complexes, which are, however, thoroughly different from those of compounds and . The photodegradation properties of compounds have been analyzed. Compounds also exhibit rapid absorption properties for RhB (Rhodamine B). Detailed analysis of the photodegradation properties of compounds reveals that the molybdate POM has stronger degradation ability for RhB than the tungstate one. PMID:26223513
NASA Technical Reports Server (NTRS)
Kreider, Kevin L.; Baumeister, Kenneth J.
1996-01-01
An explicit finite difference real time iteration scheme is developed to study harmonic sound propagation in aircraft engine nacelles. To reduce storage requirements for future 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 for a harmonic monochromatic sound field, a parabolic (in time) approximation is introduced to reduce the order of the governing equation. The analysis begins with a harmonic sound source radiating into a quiescent duct. This fully explicit iteration method then calculates stepwise in time to obtain the 'steady state' harmonic solutions of the acoustic field. For stability, applications of conventional impedance boundary conditions requires coupling to explicit hyperbolic difference equations at the boundary. 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.
Finite-difference evolution of a scattered laser pulse in ocean water
NASA Astrophysics Data System (ADS)
Tessendorf, J.; Piotrowski, C.; Kelly, R. L.
1988-01-01
The effects of absorption and scattering on the propagation of a finite-size laser pulse through ocean water are investigated theoretically, applying a finite-difference model based on the time-dependent radiative-transfer equation. The derivation of the finite-difference evolution algorithm is outlined; its FORTRAN numerical implementation is explained; and simulation results for simple test problems are presented in graphs. The method is shown to provide unconditional stability and physically correct propagation velocities in all directions. The need to eliminate or compensate for ray effects is indicated.
A non-linear constrained optimization technique for the mimetic finite difference method
Manzini, Gianmarco; Svyatskiy, Daniil; Bertolazzi, Enrico; Frego, Marco
2014-09-30
This is a strategy for the construction of monotone schemes in the framework of the mimetic finite difference method for the approximation of diffusion problems on unstructured polygonal and polyhedral meshes.
APPLICATION OF A FINITE-DIFFERENCE TECHNIQUE TO THE HUMAN RADIOFREQUENCY DOSIMETRY PROBLEM
A powerful finite difference numerical technique has been applied to the human radiofrequency dosimetry problem. The method possesses inherent advantages over the method of moments approach in that its implementation requires much less computer memory. Consequently, it has the ca...
Techniques for correcting approximate finite difference solutions. [applied to transonic flow
NASA Technical Reports Server (NTRS)
Nixon, D.
1979-01-01
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 given.
Finite-key security analyses on passive decoy-state QKD protocols with different unstable sources.
Song, Ting-Ting; Qin, Su-Juan; Wen, Qiao-Yan; Wang, Yu-Kun; Jia, Heng-Yue
2015-01-01
In quantum communication, passive decoy-state QKD protocols can eliminate many side channels, but the protocols without any finite-key analyses are not suitable for in practice. The finite-key securities of passive decoy-state (PDS) QKD protocols with two different unstable sources, type-II parametric down-convention (PDC) and phase randomized weak coherent pulses (WCPs), are analyzed in our paper. According to the PDS QKD protocols, we establish an optimizing programming respectively and obtain the lower bounds of finite-key rates. Under some reasonable values of quantum setup parameters, the lower bounds of finite-key rates are simulated. The simulation results show that at different transmission distances, the affections of different fluctuations on key rates are different. Moreover, the PDS QKD protocol with an unstable PDC source can resist more intensity fluctuations and more statistical fluctuation. PMID:26471947
Finite-difference scheme for the numerical solution of the Schroedinger equation
NASA Technical Reports Server (NTRS)
Mickens, Ronald E.; Ramadhani, Issa
1992-01-01
A finite-difference scheme for numerical integration of the Schroedinger equation is constructed. Asymptotically (r goes to infinity), the method gives the exact solution correct to terms of order r exp -2.
NASA Astrophysics Data System (ADS)
Lisitsa, Vadim; Tcheverda, Vladimir; Botter, Charlotte
2016-04-01
We present an algorithm for the numerical simulation of seismic wave propagation in models with a complex near surface part and free surface topography. The approach is based on the combination of finite differences with the discontinuous Galerkin method. The discontinuous Galerkin method can be used on polyhedral meshes; thus, it is easy to handle the complex surfaces in the models. However, this approach is computationally intense in comparison with finite differences. Finite differences are computationally efficient, but in general, they require rectangular grids, leading to the stair-step approximation of the interfaces, which causes strong diffraction of the wavefield. In this research we present a hybrid algorithm where the discontinuous Galerkin method is used in a relatively small upper part of the model and finite differences are applied to the main part of the model.
Finite-key security analyses on passive decoy-state QKD protocols with different unstable sources
Song, Ting-Ting; Qin, Su-Juan; Wen, Qiao-Yan; Wang, Yu-Kun; Jia, Heng-Yue
2015-01-01
In quantum communication, passive decoy-state QKD protocols can eliminate many side channels, but the protocols without any finite-key analyses are not suitable for in practice. The finite-key securities of passive decoy-state (PDS) QKD protocols with two different unstable sources, type-II parametric down-convention (PDC) and phase randomized weak coherent pulses (WCPs), are analyzed in our paper. According to the PDS QKD protocols, we establish an optimizing programming respectively and obtain the lower bounds of finite-key rates. Under some reasonable values of quantum setup parameters, the lower bounds of finite-key rates are simulated. The simulation results show that at different transmission distances, the affections of different fluctuations on key rates are different. Moreover, the PDS QKD protocol with an unstable PDC source can resist more intensity fluctuations and more statistical fluctuation. PMID:26471947
NASA Technical Reports Server (NTRS)
Mickens, Ronald E.
1989-01-01
A family of conditionally stable, forward Euler finite difference equations can be constructed for the simplest equation of Schroedinger type, namely u sub t - iu sub xx. Generalization of this result to physically realistic Schroedinger type equations is presented.
NASA Technical Reports Server (NTRS)
Beggs, John H.; Luebbers, Raymond J.; Kunz, Karl S.; Yee, Kane 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 a 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. A 1-D implementation for a surface impedance boundary condition for good conductors in the Finite Difference Time Domain (FDTD) technique.
Exact finite difference schemes for the non-linear unidirectional wave equation
NASA Technical Reports Server (NTRS)
Mickens, R. E.
1985-01-01
Attention is given to the construction of exact finite difference schemes for the nonlinear unidirectional wave equation that describes the nonlinear propagation of a wave motion in the positive x-direction. The schemes constructed for these equations are compared with those obtained by using the usual procedures of numerical analysis. It is noted that the order of the exact finite difference models is equal to the order of the differential equation.
Choas and instabilities in finite difference approximations to nonlinear differential equations
Cloutman, L. D., LLNL
1998-07-01
The numerical solution of time-dependent ordinary and partial differential equations by finite difference techniques is a common task in computational physics and engineering The rate equations for chemical kinetics in combustion modeling are an important example. They not only are nonlinear, but they tend to be stiff, which makes their solution a challenge for transient problems. We show that one must be very careful how such equations are solved In addition to the danger of large time-marching errors, there can be unphysical chaotic solutions that remain numerically stable for a range of time steps that depends on the particular finite difference method used We point out that the solutions of the finite difference equations converge to those of the differential equations only in the limit as the time step approaches zero for stable and consistent finite difference approximations The chaotic behavior observed for finite time steps in some nonlinear difference equations is unrelated to solutions of the differential equations, but is connected with the onset of numerical instabilities of the finite difference equations This behavior suggests that the use of the theory of chaos in nonlinear iterated maps may be useful in stability anlaysis of finite difference approximations to nonlinear differential equations, providing more stringent time step limits than the formal linear stability analysis that tests only for unbounded solutions This observation implies that apparently stable numerical solutions of nonlinear differential equations by finite difference techniques may in fact be contaminated (if not dominated) by nonphysical chaotic parasitic solutions that degrade the accuracy of the numerical solution We demonstrate this phenomenon with some solutions of the logistic equation and a simple two-dimensional computational fluid dynamics example
Tracy, F.T.
1991-09-01
This report describes new advances in the computational modeling of ground water and seepage using the finite element method (FEM) in conjunction with tools and techniques typically used by the aerospace engineers. The unsolved environmental issues regarding our hazardous and toxic waste problems must be resolved, and significant resources must be placed on this effort. Some military bases are contaminated with hazardous waste that has entered the groundwater domain. A groundwater model that takes into account contaminant flow is therefore critical. First, an extension of the technique of generating an orthogonal structured grid (using the Cauchy-Riemann equations) to automatically generate a flow net for two-dimensional (2-D) steady-state seepage problems is presented for various boundary conditions. Second, a complete implementation of a three-dimensional (3-D) seepage package is described where (1) grid generation is accomplished using the EAGLE program, (2) the seepage and groundwater analysis for either confined or unconfined steady-state flow, homogeneous or inhomogeneous media, and isotropic or anisotropic soil is accomplished with no restriction on the FE grid or requirement of an initial guess of the free surface for unconfined flow problems, and (3) scientific visualization is accomplished using the program FAST developed by NASA.
Finite-difference methods for solving loaded parabolic equations
NASA Astrophysics Data System (ADS)
Abdullayev, V. M.; Aida-zade, K. R.
2016-01-01
Loaded partial differential equations are solved numerically. For illustrative purposes, a boundary value problem for a parabolic equation with various point loads is considered. By applying difference approximations, the problems are reduced to systems of algebraic equations of special structure, which are solved using a parametric representation involving solutions of auxiliary linear systems with tridiagonal matrices. Numerical results are presented and analyzed.
Exploring the Effectiveness of Different Approaches to Teaching Finite Mathematics
ERIC Educational Resources Information Center
Smeal, Mary; Walker, Sandra; Carter, Jamye; Simmons-Johnson, Carolyn; Balam, Esenc
2013-01-01
Traditionally, mathematics has been taught using a very direct approach which the teacher explains the procedure to solve a problem and the students use pencil and paper to solve the problem. However, a variety of alternative approaches to mathematics have surfaced from a number of different directions. The purpose of this study was to examine the…
NASA Technical Reports Server (NTRS)
Liu, C.; Liu, Z.
1993-01-01
The high order finite difference and multigrid methods have been successfully applied to direct numerical simulation (DNS) for flow transition in 3D channels and 3D boundary layers with 2D and 3D isolated and distributed roughness in a curvilinear coordinate system. A fourth-order finite difference technique on stretched and staggered grids, a fully-implicit time marching scheme, a semicoarsening multigrid method associated with line distributive relaxation scheme, and a new treatment of the outflow boundary condition, which needs only a very short buffer domain to damp all wave reflection, are developed. These approaches make the multigrid DNS code very accurate and efficient. This makes us not only able to do spatial DNS for the 3D channel and flat plate at low computational costs, but also able to do spatial DNS for transition in the 3D boundary layer with 3D single and multiple roughness elements. Numerical results show good agreement with the linear stability theory, the secondary instability theory, and a number of laboratory experiments.
Otani, Tomoki; Marchetto, Maria C.; Gage, Fred H.; Simons, Benjamin D.; Livesey, Frederick J.
2016-01-01
Summary Variation in cerebral cortex size and complexity is thought to contribute to differences in cognitive ability between humans and other animals. Here we compare cortical progenitor cell output in humans and three nonhuman primates using directed differentiation of pluripotent stem cells (PSCs) in adherent two-dimensional (2D) and organoid three-dimensional (3D) culture systems. Clonal lineage analysis showed that primate cortical progenitors proliferate for a protracted period of time, during which they generate early-born neurons, in contrast to rodents, where this expansion phase largely ceases before neurogenesis begins. The extent of this additional cortical progenitor expansion differs among primates, leading to differences in the number of neurons generated by each progenitor cell. We found that this mechanism for controlling cortical size is regulated cell autonomously in culture, suggesting that primate cerebral cortex size is regulated at least in part at the level of individual cortical progenitor cell clonal output. PMID:27049876
2012-01-05
Code is for a layered electric medium with 2d structure. Includes air-earth interface at node z=2.. The electric ex and ez fields are calculated on edges of elemental grid and magnetic field hy is calculated on the face of the elemental grid. The code allows for a layered earth with 2d structures. Solutions of coupled first order Maxwell's equations are solved in the two dimensional environment using a finite- difference scheme on a staggered spationamore » and temporal grid.« less
Viscous flow simulations in VTOL aerodynamics. [finite difference technique
NASA Technical Reports Server (NTRS)
Bower, W. W.
1978-01-01
The critical issues in viscous flow simulations, such as boundary-layer separation, entrainment, turbulence modeling, and compressibility, are discussed with regard to the ground effects problem for vertical-takeoff-and-landing (VTOL) aircraft. A simulation of the two-dimensional incompressible lift jet in ground proximity is based on solution of the Reynolds-averaged Navier-Stokes equations and a turbulence-model equation which are written in stream function-vorticity form and are solved using Hoffman's augmented-central-difference algorithm. The resulting equations and their shortcomings are discussed when the technique is extended to two-dimensional compressible and three-dimensional incompressible flows.
NASA Technical Reports Server (NTRS)
Baumeister, K. J.; Eversman, W.; Astley, R. J.; White, J. W.
1981-01-01
Sound propagation without flow in a rectangular duct with a converging-diverging area variation was studied experimentally and theoretically. The area variation was of sufficient magnitude to produce large reflections and induce modal scattering. The rms (root-mean-squared) pressure and phase angle on both the flat and curved surface were measured and tabulated. The steady state finite element theory and the transient finite difference theory are in good agreement with the data. It is concluded that numerical finite difference and finite element theories appear ideally suited for handling duct propagation problems which encounter large area variations.
NASA Astrophysics Data System (ADS)
Aravena, J.; Dussaillant, A. R.
2006-12-01
Source control is the fundamental principle behind sustainable management of stormwater. Rain gardens are an infiltration practice that provides volume and water quality control, recharge, and multiple landscape, ecological and economic potential benefits. The fulfillment of these objectives requires understanding their behavior during events as well as long term, and tools for their design. We have developed a model based on Richards equation coupled to a surface water balance, solved with a 2D finite volume Fortran code which allows alternating upper boundary conditions, including ponding, which is not present in available 2D models. Also, it can simulate non homogeneous water input, heterogeneous soil (layered or more complex geometries), and surface irregularities -e.g. terracing-, so as to estimate infiltration and recharge. The algorithm is conservative; being an advantage compared to available finite difference and finite element methods. We will present performance comparisons to known models, to experimental data from a bioretention cell, which receives roof water to its surface depression planted with native species in an organic-rich root zone soil layer (underlain by a high conductivity lower layer that, while providing inter-event storage, percolates water readily), as well as long term simulations for different rain garden configurations. Recharge predictions for different climates show significant increases from natural recharge, and that the optimal area ratio (raingarden vs. contributing impervious area) reduces from 20% (humid) to 5% (dry).
Dynamic Rupture Simulation of Bending Faults With a Finite Difference Approach
NASA Astrophysics Data System (ADS)
Cruz-Atienza, V. M.; Virieux, J.; Operto, S.
2002-12-01
Many questions about physical parameters governing the rupture propagation of earthquakes seem to find their answers within realistic dynamic considerations. Sophisticated constitutive relations based in laboratory experiments have lead to a better understanding of rupture evolution from its very beginning to its arrest. On the other hand, large amount of field observations as well as recent numerical simulations have also demonstrated the importance, in rupture growing, of considering more reasonable geological settings (e.g., bending and step-over fault geometries; heterogeneous surrounding media). So far, despite the development of powerful numerical tools, there still exist some numerical considerations that overstep their possibilities. Authors have solved the dynamic problem by applying the boundary integral equations method (BIEM) in order to explore the influence of fault geometry. This can be possible because of the fact that only the rupture path must be discretized, reducing the impact of numerical discretization. However, the BIEM needs the analytical solution of Green functions that can only be computed for a homogeneous space. Up to date, no interaction with heterogeneous structures can be taken in to account. In contrast, finite difference (FD) approaches have been widely used. In this case, due to the specific discretization of the elastodynamic equations through the entire domain, and the azimuthal anisotropy intrinsic to differential operators, only planar faults have been considered and numerical artefacts have to be carefully checked. In this work, we have used a recently proposed four-order staggered grid finite difference scheme to model in-plane (mode II) dynamic shear fracturing propagation with any pre-established geometry. In contrast with the classical 2-D staggered grid elementary cell in which all the elastic fields are defined in different positions (except the normal stresses), the stencil used here consider the velocity and stress
Mixed finite-difference scheme for free vibration analysis of noncircular cylinders
NASA Technical Reports Server (NTRS)
Noor, A. K.; Stephens, W. B.
1973-01-01
A mixed finite-difference scheme is presented for the free-vibration analysis of simply supported closed noncircular cylindrical shells. The problem is formulated in terms of eight first-order differential equations in the circumferential coordinate which possess a symmetric coefficient matrix and are free of the derivatives of the elastic and geometric characteristics of the shell. In the finite-difference discretization, two interlacing grids are used for the different fundamental unknowns in such a way as to avoid averaging in the difference-quotient expressions used for the first derivative. The resulting finite-difference equations are symmetric. The inverse-power method is used for obtaining the eigenvalues and eigenvectors.
NASA Technical Reports Server (NTRS)
Byun, Chansup; Guruswamy, Guru P.; Kutler, Paul (Technical Monitor)
1994-01-01
In recent years significant advances have been made for parallel computers in both hardware and software. Now parallel computers have become viable tools in computational mechanics. Many application codes developed on conventional computers have been modified to benefit from parallel computers. Significant speedups in some areas have been achieved by parallel computations. For single-discipline use of both fluid dynamics and structural dynamics, computations have been made on wing-body configurations using parallel computers. However, only a limited amount of work has been completed in combining these two disciplines for multidisciplinary applications. The prime reason is the increased level of complication associated with a multidisciplinary approach. In this work, procedures to compute aeroelasticity on parallel computers using direct coupling of fluid and structural equations will be investigated for wing-body configurations. The parallel computer selected for computations is an Intel iPSC/860 computer which is a distributed-memory, multiple-instruction, multiple data (MIMD) computer with 128 processors. In this study, the computational efficiency issues of parallel integration of both fluid and structural equations will be investigated in detail. The fluid and structural domains will be modeled using finite-difference and finite-element approaches, respectively. Results from the parallel computer will be compared with those from the conventional computers using a single processor. This study will provide an efficient computational tool for the aeroelastic analysis of wing-body structures on MIMD type parallel computers.
NASA Astrophysics Data System (ADS)
Reitman, L.; Wolfshtein, M.; Adler, D.
1982-11-01
A finite difference method is developed for solving the non-viscous formulation of a three-dimensional compressible flow problem for turbomachinery impellers. The numerical results and the time efficiency of this method are compared to that provided by a finite element method for this problem. The finite difference method utilizes a numerical, curvilinear, and non-orthogonal coordinate transformation and the ADI scheme. The finite difference method is utilized to solve a test problem of a centrifugal compressor impeller. It is shown that the finite difference method produces results in good agreement with the experimentally determined flow fields and is as accurate as the finite element technique. However, the finite difference method only requires about half the time in order to obtain the solution for this problem as that required by the finite element method.
SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES.
Wan, Xiaohai; Li, Zhilin
2012-06-01
Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size. PMID:22701346
Fei, Tong; Larner, K.
1993-11-01
Finite-difference acoustic-wave modeling and reverse-time depth migration based on the full wave equation are general approaches that can take into account arbitary variations in velocity and density, and can handle turning waves well. However, conventional finite-difference methods for solving the acousticwave equation suffer from numerical dispersion when too few samples per wavelength are used. Here, we present two flux-corrected transport (FCT) algorithms, one based the second-order equation and the other based on first-order wave equations derived from the second-order one. Combining the FCT technique with conventional finite-difference modeling or reverse-time wave extrapolation can ensure finite-difference solutions without numerical dispersion even for shock waves and impulsive sources. Computed two-dimensional migration images show accurate positioning of reflectors with greater than 90-degree dip. Moreover, application to real data shows no indication of numerical dispersion. The FCT correction, which can be applied to finite-difference approximations of any order in space and time, is an efficient alternative to use of approximations of increasing order.
Improving sub-grid scale accuracy of boundary features in regional finite-difference models
Panday, Sorab; Langevin, Christian D.
2012-01-01
As an alternative to grid refinement, the concept of a ghost node, which was developed for nested grid applications, has been extended towards improving sub-grid scale accuracy of flow to conduits, wells, rivers or other boundary features that interact with a finite-difference groundwater flow model. The formulation is presented for correcting the regular finite-difference groundwater flow equations for confined and unconfined cases, with or without Newton Raphson linearization of the nonlinearities, to include the Ghost Node Correction (GNC) for location displacement. The correction may be applied on the right-hand side vector for a symmetric finite-difference Picard implementation, or on the left-hand side matrix for an implicit but asymmetric implementation. The finite-difference matrix connectivity structure may be maintained for an implicit implementation by only selecting contributing nodes that are a part of the finite-difference connectivity. Proof of concept example problems are provided to demonstrate the improved accuracy that may be achieved through sub-grid scale corrections using the GNC schemes.
Abdelall, Eman K A; Kamel, Gehan M
2016-08-01
Two new series of 1,5-diaryl pyrazoles (5a, 5b, 7a, 7b and 10) and 1,5-diaryl pyrazoline (12a and 12b) were prepared as both Cyclooxygenase-2 and 15-lipoxygenase inhibitors. Carrageenan-induced rat paw edema, ulcer index and anti-COX-1/COX-2 and 15-LOX inhibition assays were also included. Cyclization of different pyrazoles was discussed using 2D NMR such as HSQC, HMBC and NOSEY determinations. Compound 5a is more effective with ED50 = 0.98 and 3.98 μM against COX-2 and 15-lipoxygenase respectively, than the references celecoxib (1.54 μM) and meclofenamate sodium (5.64 μM). PMID:27131067
NASA Technical Reports Server (NTRS)
Lee, L. C.
1976-01-01
The cross correlation of the intensity fluctuations between different frequencies and finite bandwidth effects on the intensity correlations based on the Markov approximation were calculated. Results may be applied to quite general turbulence spectra for an extended turbulent medium. Calculations of the cross-correlation function and of finite bandwidth effects are explicitly carried out for both Gaussian and Kolmogorov turbulence spectra. The increases of the correlation scale of intensity fluctuations are different for these two spectra and the difference can be used to determine whether the interstellar turbulent medium has a Gaussian or a Kolmogorov spectrum.
NASA Technical Reports Server (NTRS)
Tam, Christopher K. W.; Webb, Jay C.
1994-01-01
In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The
Relative and Absolute Error Control in a Finite-Difference Method Solution of Poisson's Equation
ERIC Educational Resources Information Center
Prentice, J. S. C.
2012-01-01
An algorithm for error control (absolute and relative) in the five-point finite-difference method applied to Poisson's equation is described. The algorithm is based on discretization of the domain of the problem by means of three rectilinear grids, each of different resolution. We discuss some hardware limitations associated with the algorithm,…
Effects of finite volume on the KL – KS mass difference
Christ, N. H.; Feng, X.; Martinelli, G.; Sachrajda, C. T.
2015-06-24
Phenomena that involve two or more on-shell particles are particularly sensitive to the effects of finite volume and require special treatment when computed using lattice QCD. In this paper we generalize the results of Lüscher and Lellouch and Lüscher, which determine the leading-order effects of finite volume on the two-particle spectrum and two-particle decay amplitudes to determine the finite-volume effects in the second-order mixing of the K⁰ and K⁰⁻ states. We extend the methods of Kim, Sachrajda, and Sharpe to provide a direct, uniform treatment of these three, related, finite-volume corrections. In particular, the leading, finite-volume corrections to the KLmore » – KS mass difference ΔMK and the CP-violating parameter εK are determined, including the potentially large effects which can arise from the near degeneracy of the kaon mass and the energy of a finite-volume, two-pion state.« less
Fast solvers for finite difference approximations for the Stokes and Navier-Stokes equations
Shin, D.
1992-01-01
The authors consider several methods for solving the linear equations arising from finite difference discretizations of the Stokes equations. The pressure equation method presented here for the first time, apparently, and the method, presented by Bramble and Pasciak, are shown to have computational effort that grows slowly with the number of grid points. The methods work with second-order accurate discretizations. Computational results are shown for both the Stokes and incompressible Navier-Stokes at low Reynolds number. The inf-sup conditions resulting from three finite difference approximations of the Stokes equations are proven. These conditions are used to prove that the Schur complement Q[sub h] of the linear system generated by each of these approximations is bounded uniformly away from zero. For the pressure equation method, this guarantees that the conjugate gradient method applied to Q[sub h] converges in a finite number of iterations which is independent of mesh size. The fact that Q[sub h] is bounded below is used to prove convergence estimates for the solutions generated by these finite difference approximations. One of the estimates is for a staggered grid and the estimate of the scheme shows that both the pressure and the velocity parts of the solution are second-order accurate. Iterative methods are compared by the use of the regularized central differencing introduced by Strikwerda. Several finite difference approximations of the Stokes equations by the SOR method are compared and the excellence of the approximations by the regularized central differencing over the other finite difference approximation is mentioned. This difference gives rise to a linear equation with a matrix which is slightly non-symmetric. The convergence of the typical steepest descent method and conjugate gradient method, which is almost as same as the typical conjugate gradient method, applied to slightly non-symmetric positive definite matrices are proven.
Hofmann, R.
1981-11-01
A useful computer simulation method based on the explicit finite difference technique can be used to address transient dynamic situations associated with nuclear reactor design and analysis. This volume is divided into two parts. Part A contains the theoretical background (physical and numerical) and the numerical equations for the STEALTH 1D, 2D, and 3D computer codes. Part B contains input instructions for all three codes. The STEALTH codes are based entirely on the published technology of the Lawrence Livermore National Laboratory, Livermore, California, and Sandia National Laboratories, Albuquerque, New Mexico.
Hofmann, R.
1981-11-01
A useful computer simulation method based on the explicit finite difference technique can be used to address transient dynamic situations associated with nuclear reactor design and analysis. This volume is divided into two parts. Part A contains the theoretical background (physical and numerical) and the numerical equations for the STEALTH 1D, 2D, and 3D computer codes. Part B contains input instructions for all three codes. The STEALTH codes are based entirely on the published technology of the Lawrence Livermore National Laboratory, Livermore, California, and Sandia National Laboratories, Albuquerque, New Mexico.
Numerical solution of a diffusion problem by exponentially fitted finite difference methods.
D'Ambrosio, Raffaele; Paternoster, Beatrice
2014-01-01
This paper is focused on the accurate and efficient solution of partial differential differential equations modelling a diffusion problem by means of exponentially fitted finite difference numerical methods. After constructing and analysing special purpose finite differences for the approximation of second order partial derivatives, we employed them in the numerical solution of a diffusion equation with mixed boundary conditions. Numerical experiments reveal that a special purpose integration, both in space and in time, is more accurate and efficient than that gained by employing a general purpose solver. PMID:26034665
NASA Technical Reports Server (NTRS)
Beggs, John H.; Luebbers, Raymond J.; Kunz, Karl S.; Yee, Kane S.
1991-01-01
Surface impedance boundary conditions are used to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In a finite difference solution, they also can be used to avoid using small cells, made necessary by shorter wavelengths in conducting media, throughout the solution volume. A one dimensional implementation is presented for a surface impedance boundary condition for good conductors in the Finite Difference Time Domain (FDTD) technique. In order to illustrate the FDTD surface impedance boundary condition, a planar air-lossy dielectric interface is considered.
Srivastava, Vineet K.; Awasthi, Mukesh K.; Singh, Sarita
2013-12-15
This article describes a new implicit finite-difference method: an implicit logarithmic finite-difference method (I-LFDM), for the numerical solution of two dimensional time-dependent coupled viscous Burgers’ equation on the uniform grid points. As the Burgers’ equation is nonlinear, the proposed technique leads to a system of nonlinear systems, which is solved by Newton's iterative method at each time step. Computed solutions are compared with the analytical solutions and those already available in the literature and it is clearly shown that the results obtained using the method is precise and reliable for solving Burgers’ equation.
NASA Astrophysics Data System (ADS)
Srivastava, Vineet K.; Awasthi, Mukesh K.; Singh, Sarita
2013-12-01
This article describes a new implicit finite-difference method: an implicit logarithmic finite-difference method (I-LFDM), for the numerical solution of two dimensional time-dependent coupled viscous Burgers' equation on the uniform grid points. As the Burgers' equation is nonlinear, the proposed technique leads to a system of nonlinear systems, which is solved by Newton's iterative method at each time step. Computed solutions are compared with the analytical solutions and those already available in the literature and it is clearly shown that the results obtained using the method is precise and reliable for solving Burgers' equation.
Cédile, Oriane; Popa, Natalia; Pollet-Villard, Frédéric; Garmy, Nicolas; Ibrahim, El Chérif; Boucraut, José
2010-01-01
Background RAE-1 is a ligand of the activating receptor NKG2D expressed by NK cells, NKT, γδT and some CD8+T lymphocytes. RAE-1 is overexpressed in tumor cell lines and its expression is induced after viral infection and genotoxic stress. We have recently demonstrated that RAE-1 is expressed in the adult subventricular zone (SVZ) from C57BL/6 mice. RAE-1 is also expressed in vitro by neural stem/progenitor cells (NSPCs) and plays a non-immune role in cell proliferation. The C57BL/6 mouse genome contains two rae-1 genes, rae-1δ and rae-1ε encoding two different proteins. The goals of this study are first to characterize the in vivo and in vitro expression of each gene and secondly to elucidate the mechanisms underlying their respective expression, which are far from known. Principal Findings We observed that Rae-1δ and Rae-1ε transcripts are differentially expressed according to tissues, pathological conditions and cell lines. Embryonic tissue and the adult SVZ mainly expressed Rae-1δ transcripts. The NSPCs derived from the SVZ also mainly expressed RAE-1δ. The interest of this result is especially related to the observation that RAE-1δ is a weak NKG2D ligand compared to RAE-1ε. On the contrary, cell lines expressed either similar levels of RAE-1δ and RAE-1ε proteins or only RAE-1ε. Since the protein expression correlated with the level of transcripts for each rae-1 gene, we postulated that transcriptional regulation is one of the main processes explaining the difference between RAE-1δ and RAE-1ε expression. We indeed identified two different promoter regions for each gene: one mainly involved in the control of rae-1δ gene expression and the other in the control of rae-1ε expression. Conclusions/Significance RAE-1δ and RAE-1ε differ with respect to their function and the control of their expression. Immune function would be mainly exerted by RAE-1ε and non-immune function by RAE-1δ. PMID:20976056
Vélez, Paula; Izquierdo, Irene; Rosa, Isaac; García, Ángel
2015-01-01
Upon stimulation, platelets release a high number of proteins (the releasate). There are clear indications that these proteins are involved in the pathogenesis of several diseases, such as atherosclerosis. In the present study we compared the platelet releasate following platelet activation with two major endogenous agonists: thrombin and collagen. Proteome analysis was based on 2D-DIGE and LC-MS/MS. Firstly, we showed the primary role of thrombin and collagen receptors in platelet secretion by these agonists; moreover, we demonstrated that GPVI is the primary responsible for collagen-induced platelet activation/aggregation. Proteomic analysis allowed the detection of 122 protein spots differentially regulated between both conditions. After excluding fibrinogen spots, down-regulated in the releasate of thrombin-activated platelets, 84 differences remained. From those, we successfully identified 42, corresponding to 37 open-reading frames. Many of the differences identified correspond to post-translational modifications, primarily, proteolysis induced by thrombin. Among others, we show vitamin K-dependent protein S, an anticoagulant plasma protein, is up-regulated in thrombin samples. Our results could have pathological implications given that platelets might be playing a differential role in various diseases and biological processes through the secretion of different subsets of granule proteins and microvesicles following a predominant activation of certain receptors. PMID:25645904
Finite difference methods for transient signal propagation in stratified dispersive media
NASA Technical Reports Server (NTRS)
Lam, D. H.
1975-01-01
Explicit difference equations are presented for the solution of a signal of arbitrary waveform propagating in an ohmic dielectric, a cold plasma, a Debye model dielectric, and a Lorentz model dielectric. These difference equations are derived from the governing time-dependent integro-differential equations for the electric fields by a finite difference method. A special difference equation is derived for the grid point at the boundary of two different media. Employing this difference equation, transient signal propagation in an inhomogeneous media can be solved provided that the medium is approximated in a step-wise fashion. The solutions are generated simply by marching on in time. It is concluded that while the classical transform methods will remain useful in certain cases, with the development of the finite difference methods described, an extensive class of problems of transient signal propagating in stratified dispersive media can be effectively solved by numerical methods.
A guide to differences between stochastic point-source and stochastic finite-fault simulations
Atkinson, G.M.; Assatourians, K.; Boore, D.M.; Campbell, K.; Motazedian, D.
2009-01-01
Why do stochastic point-source and finite-fault simulation models not agree on the predicted ground motions for moderate earthquakes at large distances? This question was posed by Ken Campbell, who attempted to reproduce the Atkinson and Boore (2006) ground-motion prediction equations for eastern North America using the stochastic point-source program SMSIM (Boore, 2005) in place of the finite-source stochastic program EXSIM (Motazedian and Atkinson, 2005) that was used by Atkinson and Boore (2006) in their model. His comparisons suggested that a higher stress drop is needed in the context of SMSIM to produce an average match, at larger distances, with the model predictions of Atkinson and Boore (2006) based on EXSIM; this is so even for moderate magnitudes, which should be well-represented by a point-source model. Why? The answer to this question is rooted in significant differences between point-source and finite-source stochastic simulation methodologies, specifically as implemented in SMSIM (Boore, 2005) and EXSIM (Motazedian and Atkinson, 2005) to date. Point-source and finite-fault methodologies differ in general in several important ways: (1) the geometry of the source; (2) the definition and application of duration; and (3) the normalization of finite-source subsource summations. Furthermore, the specific implementation of the methods may differ in their details. The purpose of this article is to provide a brief overview of these differences, their origins, and implications. This sets the stage for a more detailed companion article, "Comparing Stochastic Point-Source and Finite-Source Ground-Motion Simulations: SMSIM and EXSIM," in which Boore (2009) provides modifications and improvements in the implementations of both programs that narrow the gap and result in closer agreement. These issues are important because both SMSIM and EXSIM have been widely used in the development of ground-motion prediction equations and in modeling the parameters that control
A FINITE-DIFFERENCE, DISCRETE-WAVENUMBER METHOD FOR CALCULATING RADAR TRACES
A hybrid of the finite-difference method and the discrete-wavenumber method is developed to calculate radar traces. The method is based on a three-dimensional model defined in the Cartesian coordinate system; the electromagnetic properties of the model are symmetric with respect ...
Finite-difference, spectral and Galerkin methods for time-dependent problems
NASA Technical Reports Server (NTRS)
Tadmor, E.
1983-01-01
Finite difference, spectral and Galerkin methods for the approximate solution of time dependent problems are surveyed. A unified discussion on their accuracy, stability and convergence is given. In particular, the dilemma of high accuracy versus stability is studied in some detail.
High Order Finite Difference Methods, Multidimensional Linear Problems and Curvilinear Coordinates
NASA Technical Reports Server (NTRS)
Nordstrom, Jan; Carpenter, Mark H.
1999-01-01
Boundary and interface conditions are derived for high order finite difference methods applied to multidimensional linear problems in curvilinear coordinates. The boundary and interface conditions lead to conservative schemes and strict and strong stability provided that certain metric conditions are met.
Finite difference micromagnetic simulation with self-consistent currents and smooth surfaces
Cerjan, C; Gibbons, M R; Hewett, D W; Parker, G
1999-05-27
A micromagnetic algorithm has been developed using the finite difference method (FDM). Elliptic field equations are solved on the mesh using the efficient Dynamic Alternating Direction Implicit method. Smooth surfaces have been included in the FDM formulation so structures of irregular shape can be modeled. The current distribution and temperature of devices are also calculated. Keywords: Micromagnetic simulation, Magnetic dots, Read heads, Thermal Effects
FWAVE V1.0 a framework for finite difference wave equation modeling
2002-07-01
FWAVE provides a computation framework for the rapid prototyping and efficient use of finite difference wave equation solutions. The user provides single grid Fortran solver components that are integrated using opaque handles to C++ distributed data structures. Permits the scientific researcher to make of clusters and parallel computers by concentrating only on the numerical schemes.
The rate of the electromagnetic energy deposition and the resultant thermoregulatory response of a block model of a squirrel monkey exposed to plane-wave fields at 350 MHz were calculated using a finite-difference procedure. Noninvasive temperature measurements in live squirrel m...
NASA Technical Reports Server (NTRS)
Mickens, R. E.
1984-01-01
Work on the construction of finite difference models of differential equations having zero truncation errors is summarized. Both linear and nonlinear unidirectional wave equations are discussed. Results regarding the construction of zero truncation error schemes for the full wave equation and Burger's equation are also briefly reported.
A FINITE-DIFFERENCE, DISCRETE-WAVENUMBER METHOD FOR CALCULATING RADAR TRACES
A hybrid of the finite-difference method and the discrete-wavenumber method is developed to calculate radar traces. The method is based on a three-dimensional model defined in the Cartesian coordinate system; the electromag-netic properties of the model are symmetric with respect...
NASA Astrophysics Data System (ADS)
Lin, M. C.; Nieter, C.; Stoltz, P. H.; Smithe, D. N.
2009-05-01
This work introduces a conformal finite difference time domain (CFDTD) method to accurately determine the dispersion relation of an A6 relativistic magnetron. The accuracy is measured by comparing with accurate SUPERFISH calculations based on finite element method. The results show that an accuracy of 99.4% can be achieved by using only 10,000 mesh points with Dey-Mittra algorithm. By comparison, a mesh number of 360,000 is needed to preserve 99% accuracy using conventional FDTD method. This suggests one can efficiently and accurately study the hot tests of microwave tubes using CFDTD particle-in-cell method instead of conventional FDTD one.
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1981-01-01
The cutoff mode instability problem associated with a transient finite difference solution to the wave equation is explained. The steady-state impedance boundary condition is found to produce acoustic reflections during the initial transient, which cause finite instabilities in the cutoff modes. The stability problem is resolved by extending the duct length to prevent transient reflections. Numerical calculations are presented at forcing frequencies above, below, and nearly at the cutoff frequency, and exit impedance models are presented for use in the practical design of turbofan inlets.
Spatial parallelism of a 3D finite difference, velocity-stress elastic wave propagation code
Minkoff, S.E.
1999-12-01
Finite difference methods for solving the wave equation more accurately capture the physics of waves propagating through the earth than asymptotic solution methods. Unfortunately, finite difference simulations for 3D elastic wave propagation are expensive. The authors model waves in a 3D isotropic elastic earth. The wave equation solution consists of three velocity components and six stresses. The partial derivatives are discretized using 2nd-order in time and 4th-order in space staggered finite difference operators. Staggered schemes allow one to obtain additional accuracy (via centered finite differences) without requiring additional storage. The serial code is most unique in its ability to model a number of different types of seismic sources. The parallel implementation uses the MPI library, thus allowing for portability between platforms. Spatial parallelism provides a highly efficient strategy for parallelizing finite difference simulations. In this implementation, one can decompose the global problem domain into one-, two-, and three-dimensional processor decompositions with 3D decompositions generally producing the best parallel speedup. Because I/O is handled largely outside of the time-step loop (the most expensive part of the simulation) the authors have opted for straight-forward broadcast and reduce operations to handle I/O. The majority of the communication in the code consists of passing subdomain face information to neighboring processors for use as ghost cells. When this communication is balanced against computation by allocating subdomains of reasonable size, they observe excellent scaled speedup. Allocating subdomains of size 25 x 25 x 25 on each node, they achieve efficiencies of 94% on 128 processors. Numerical examples for both a layered earth model and a homogeneous medium with a high-velocity blocky inclusion illustrate the accuracy of the parallel code.
Spatial Parallelism of a 3D Finite Difference, Velocity-Stress Elastic Wave Propagation Code
MINKOFF,SUSAN E.
1999-12-09
Finite difference methods for solving the wave equation more accurately capture the physics of waves propagating through the earth than asymptotic solution methods. Unfortunately. finite difference simulations for 3D elastic wave propagation are expensive. We model waves in a 3D isotropic elastic earth. The wave equation solution consists of three velocity components and six stresses. The partial derivatives are discretized using 2nd-order in time and 4th-order in space staggered finite difference operators. Staggered schemes allow one to obtain additional accuracy (via centered finite differences) without requiring additional storage. The serial code is most unique in its ability to model a number of different types of seismic sources. The parallel implementation uses the MP1 library, thus allowing for portability between platforms. Spatial parallelism provides a highly efficient strategy for parallelizing finite difference simulations. In this implementation, one can decompose the global problem domain into one-, two-, and three-dimensional processor decompositions with 3D decompositions generally producing the best parallel speed up. Because i/o is handled largely outside of the time-step loop (the most expensive part of the simulation) we have opted for straight-forward broadcast and reduce operations to handle i/o. The majority of the communication in the code consists of passing subdomain face information to neighboring processors for use as ''ghost cells''. When this communication is balanced against computation by allocating subdomains of reasonable size, we observe excellent scaled speed up. Allocating subdomains of size 25 x 25 x 25 on each node, we achieve efficiencies of 94% on 128 processors. Numerical examples for both a layered earth model and a homogeneous medium with a high-velocity blocky inclusion illustrate the accuracy of the parallel code.
An Eigenvalue Analysis of finite-difference approximations for hyperbolic IBVPs
NASA Technical Reports Server (NTRS)
Warming, Robert F.; Beam, Richard M.
1989-01-01
The eigenvalue spectrum associated with a linear finite-difference approximation plays a crucial role in the stability analysis and in the actual computational performance of the discrete approximation. The eigenvalue spectrum associated with the Lax-Wendroff scheme applied to a model hyperbolic equation was investigated. For an initial-boundary-value problem (IBVP) on a finite domain, the eigenvalue or normal mode analysis is analytically intractable. A study of auxiliary problems (Dirichlet and quarter-plane) leads to asymptotic estimates of the eigenvalue spectrum and to an identification of individual modes as either benign or unstable. The asymptotic analysis establishes an intuitive as well as quantitative connection between the algebraic tests in the theory of Gustafsson, Kreiss, and Sundstrom and Lax-Richtmyer L(sub 2) stability on a finite domain.
An eigenvalue analysis of finite-difference approximations for hyperbolic IBVPs
NASA Technical Reports Server (NTRS)
Warming, Robert F.; Beam, Richard M.
1990-01-01
The eigenvalue spectrum associated with a linear finite-difference approximation plays a crucial role in the stability analysis and in the actual computational performance of the discrete approximation. The eigenvalue spectrum associated with the Lax-Wendroff scheme applied to a model hyperbolic equation was investigated. For an initial-boundary-value problem (IBVP) on a finite domain, the eigenvalue or normal mode analysis is analytically intractable. A study of auxiliary problems (Dirichlet and quarter-plane) leads to asymptotic estimates of the eigenvalue spectrum and to an identification of individual modes as either benign or unstable. The asymptotic analysis establishes an intuitive as well as quantitative connection between the algebraic tests in the theory of Gustafsson, Kreiss, and Sundstrom and Lax-Richtmyer L (sub 2) stability on a finite domain.
An improved finite-difference analysis of uncoupled vibrations of tapered cantilever beams
NASA Technical Reports Server (NTRS)
Subrahmanyam, K. B.; Kaza, K. R. V.
1983-01-01
An improved finite difference procedure for determining the natural frequencies and mode shapes of tapered cantilever beams undergoing uncoupled vibrations is presented. Boundary conditions are derived in the form of simple recursive relations involving the second order central differences. Results obtained by using the conventional first order central differences and the present second order central differences are compared, and it is observed that the present second order scheme is more efficient than the conventional approach. An important advantage offered by the present approach is that the results converge to exact values rapidly, and thus the extrapolation of the results is not necessary. Consequently, the basic handicap with the classical finite difference method of solution that requires the Richardson's extrapolation procedure is eliminated. Furthermore, for the cases considered herein, the present approach produces consistent lower bound solutions.
Dickschen, Kristin; Willmann, Stefan; Thelen, Kirstin; Lippert, Jörg; Hempel, Georg; Eissing, Thomas
2012-01-01
Tamoxifen is a first-line endocrine agent in the mechanism-based treatment of estrogen receptor positive (ER+) mammary carcinoma and applied to breast cancer patients all over the world. Endoxifen is a secondary and highly active metabolite of tamoxifen that is formed among others by the polymorphic cytochrome P450 2D6 (CYP2D6). It is widely accepted that CYP2D6 poor metabolizers exert a pronounced decrease in endoxifen steady-state plasma concentrations compared to CYP2D6 extensive metabolizers. Nevertheless, an in-depth understanding of the chain of cause and effect between CYP2D6 genotype, endoxifen steady-state plasma concentration, and subsequent tamoxifen treatment benefit still remains to be evolved. In this study, physiologically based pharmacokinetic (PBPK)-modeling was applied to mechanistically investigate the impact of CYP2D6 phenotype on endoxifen formation in female breast cancer patients undergoing tamoxifen therapy. A PBPK-model of tamoxifen and its pharmacologically important metabolites N-desmethyltamoxifen (NDM-TAM), 4-hydroxytamoxifen (4-OH-TAM), and endoxifen was developed and validated. This model is able to simulate the pharmacokinetics (PK) after single and repeated oral tamoxifen doses in female breast cancer patients in dependence of the CYP2D6 phenotype. A detailed model-based analysis of the mass balance offered support for a recent hypothesis stating a more prominent role for endoxifen formation from 4-OH-TAM. In the future this model provides a good basis to further investigate the linkage of PK, mode of action, and treatment outcome in dependence of factors such as phenotype, ethnicity, or co-treatment with CYP2D6 inhibitors. PMID:22661948
Modeling anisotropic flow and heat transport by using mimetic finite differences
NASA Astrophysics Data System (ADS)
Chen, Tao; Clauser, Christoph; Marquart, Gabriele; Willbrand, Karen; Büsing, Henrik
2016-08-01
Modeling anisotropic flow in porous or fractured rock often assumes that the permeability tensor is diagonal, which means that its principle directions are always aligned with the coordinate axes. However, the permeability of a heterogeneous anisotropic medium usually is a full tensor. For overcoming this shortcoming, we use the mimetic finite difference method (mFD) for discretizing the flow equation in a hydrothermal reservoir simulation code, SHEMAT-Suite, which couples this equation with the heat transport equation. We verify SHEMAT-Suite-mFD against analytical solutions of pumping tests, using both diagonal and full permeability tensors. We compare results from three benchmarks for testing the capability of SHEMAT-Suite-mFD to handle anisotropic flow in porous and fractured media. The benchmarks include coupled flow and heat transport problems, three-dimensional problems and flow through a fractured porous medium with full equivalent permeability tensor. It shows firstly that the mimetic finite difference method can model anisotropic flow both in porous and in fractured media accurately and its results are better than those obtained by the multi-point flux approximation method in highly anisotropic models, secondly that the asymmetric permeability tensor can be included and leads to improved results compared the symmetric permeability tensor in the equivalent fracture models, and thirdly that the method can be easily implemented in existing finite volume or finite difference codes, which has been demonstrated successfully for SHEMAT-Suite.
NASA Astrophysics Data System (ADS)
Yanaga, Daisaku; Kuwabara, Toshihiko; Uema, Naoyuki; Asano, Mineo
2011-08-01
Biaxial tensile tests of 6000 series aluminum alloy sheet with different density cube textures were carried out using cruciform specimens similar to that developed by one of the authors [Kuwabara, T. et al., J. Material Process. Technol., 80/81(1998), 517-523.]. The specimens are loaded under linear stress paths in a servo-controlled biaxial tensile testing machine. Plastic orthotropy remained coaxial with the principal stresses throughout every experiment. Successive contours of plastic work in stress space and the directions of plastic strain rates were precisely measured and compared with those calculated using selected yield functions. The Yld2000-2d yield functions with exponents of 12 and 6 [Barlat, F. et al., Int. J. Plasticity 19 (2003), 1297-1319] are capable of reproducing the general trends of the work contours and the directions of plastic strain rates observed for test materials with high and low cube textures, respectively. Hydraulic bulge tests were also conducted and the variation of thickness strain along the meridian direction of the bulged specimen was compared with that calculated using finite element analysis (FEA) based on the Yld2000-2d yield functions with exponents of 12 and 6. The differences of cube texture cause significant differences in the strain distributions of the bulged specimens, and the FEA results calculated using the Yld2000-2d yield functions show good agreement with the measurement results.
NASA Astrophysics Data System (ADS)
Cole, James B.
2014-09-01
The finite difference time domain (FDTD) algorithm is a popular tool for photonics design and simulations, but it also can yield deep insights into the fundamental nature of light and - more speculatively - into the discretization and connectivity and geometry of space-time. The CFL stability limit in FDTD can be interpreted as a limit on the speed of light. It depends not only on the dimensionality of space-time, but also on its connectivity. Thus the speed of light not only tells us something about the dimensionality of space-time but also about its connectivity. The computational molecule in conventional 2-D FDTD is (х +/- h,y)-(x,+/- y h)-(x-y), where h= triangle x = triangle y . It yields the CFL stability limit ctriangle/h<= t/h 1 √2 . Including diagonal nodes (x+/- h, y +/- h) in the computational molecule changes the connectivity of the space and changes the CFL limit. The FDTD model also predicts precursor signals (which physically exist). The Green's function of the FDTD model, which differs from that of the wave equation, may tell us something about underlying periodicities in space-time. It may be possible to experimentally observe effects of space-time discretization and connectivity in optics experiments.
Silva, F. da; Hacquin, S.
2005-03-01
We present a novel numerical signal injection technique allowing unidirectional injection of a wave in a wave-guiding structure, applicable to 2D finite-difference time-domain electromagnetic codes, both Maxwell and wave-equation. It is particularly suited to continuous wave radar-like simulations. The scheme gives an unidirectional injection of a signal while being transparent to waves propagating in the opposite direction (directional coupling). The reflected or backscattered waves (returned) are separated from the probing waves allowing direct access to the information on amplitude and phase of the returned wave. It also facilitates the signal processing used to extract the phase derivative (or group delay) when simulating radar systems. Although general, the technique is particularly suited to swept frequency sources (frequency modulated) in the context of reflectometry, a fusion plasma diagnostic. The UTS applications presented here are restricted to fusion plasma reflectometry simulations for different physical situations. This method can, nevertheless, also be used in other dispersive media such as dielectrics, being useful, for example, in the simulation of plasma filled waveguides or directional couplers.
NASA Astrophysics Data System (ADS)
MacKinnon, R. J.; Carey, G. F.
1988-03-01
An analysis of material interface discontinuities is developed and applied in finite difference theory to determine mathematically rigorous averaging techniques for material properties. This result is compared with other averaging techniques, particularly harmonic averaging, which is often applied in practice. We also develop a class of formulas of high accuracy for post-processing the difference formula to compute derivatives (fluxes, stresses), and conduct supporting numerical studies.
NASA Technical Reports Server (NTRS)
Chen, G.; Zheng, Q.; Coleman, M.; Weerakoon, S.
1983-01-01
This paper briefly reviews convergent finite difference schemes for hyperbolic initial boundary value problems and their applications to boundary control systems of hyperbolic type which arise in the modelling of vibrations. These difference schemes are combined with the primal and the dual approaches to compute the optimal control in the unconstrained case, as well as the case when the control is subject to inequality constraints. Some of the preliminary numerical results are also presented.
NASA Technical Reports Server (NTRS)
Steger, J. L.; Caradonna, F. X.
1980-01-01
An implicit finite difference procedure is developed to solve the unsteady full potential equation in conservation law form. Computational efficiency is maintained by use of approximate factorization techniques. The numerical algorithm is first order in time and second order in space. A circulation model and difference equations are developed for lifting airfoils in unsteady flow; however, thin airfoil body boundary conditions have been used with stretching functions to simplify the development of the numerical algorithm.
NASA Technical Reports Server (NTRS)
Baumeister, K. J.; Eversman, W.; Astley, R. J.; White, J. W.
1981-01-01
Experimental data are presented for sound propagation in a simulated infinite hard wall duct with a large change in duct cross sectional area. The data are conveniently tabulated for further use. The 'steady' state finite element theory of Astley and Eversman (1981) and the transient finite difference theory of White (1981) are in good agreement with the data for both the axial and transverse pressure profiles and the axial phase angle. Therefore, numerical finite difference and finite element theories appear to be ideally suited for handling duct propagation problems which encounter large axial gradients in acoustic parameters. The measured energy reflection coefficient agrees with the values from the Astley-Eversman modal coupling model.
NASA Astrophysics Data System (ADS)
Ren, B. Y.; Wang, L.; Tzou, H. S.; Yue, H. H.
2010-08-01
Electrical modeling of piezoelectric structronic systems by analog circuits has the disadvantages of huge circuit structure and low precision. However, studies of electrical simulation of segmented distributed piezoelectric structronic plate systems (PSPSs) by using output voltage signals of high-speed digital circuits to evaluate the real-time dynamic displacements are scarce in the literature. Therefore, an equivalent dynamic model based on the finite difference method (FDM) is presented to simulate the actual physical model of the segmented distributed PSPS with simply supported boundary conditions. By means of the FDM, the four-ordered dynamic partial differential equations (PDEs) of the main structure/segmented distributed sensor signals/control moments of the segmented distributed actuator of the PSPS are transformed to finite difference equations. A dynamics matrix model based on the Newmark-β integration method is established. The output voltage signal characteristics of the lower modes (m <= 3, n <= 3) with different finite difference mesh dimensions and different integration time steps are analyzed by digital signal processing (DSP) circuit simulation software. The control effects of segmented distributed actuators with different effective areas are consistent with the results of the analytical model in relevant references. Therefore, the method of digital simulation for vibration analysis of segmented distributed PSPSs presented in this paper can provide a reference for further research into the electrical simulation of PSPSs.
NASA Technical Reports Server (NTRS)
Jameson, A.
1976-01-01
A review is presented of some recently developed numerical methods for the solution of nonlinear equations of mixed type. The methods considered use finite difference approximations to the differential equation. Central difference formulas are employed in the subsonic zone and upwind difference formulas are used in the supersonic zone. The relaxation method for the small disturbance equation is discussed and a description is given of difference schemes for the potential flow equation in quasi-linear form. Attention is also given to difference schemes for the potential flow equation in conservation form, the analysis of relaxation schemes by the time dependent analogy, the accelerated iterative method, and three-dimensional calculations.
Hunt, R.J.; Anderson, M.P.; Kelson, V.A.
1998-01-01
This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.
Projection methods for incompressible flow problems with WENO finite difference schemes
NASA Astrophysics Data System (ADS)
de Frutos, Javier; John, Volker; Novo, Julia
2016-03-01
Weighted essentially non-oscillatory (WENO) finite difference schemes have been recommended in a competitive study of discretizations for scalar evolutionary convection-diffusion equations [20]. This paper explores the applicability of these schemes for the simulation of incompressible flows. To this end, WENO schemes are used in several non-incremental and incremental projection methods for the incompressible Navier-Stokes equations. Velocity and pressure are discretized on the same grid. A pressure stabilization Petrov-Galerkin (PSPG) type of stabilization is introduced in the incremental schemes to account for the violation of the discrete inf-sup condition. Algorithmic aspects of the proposed schemes are discussed. The schemes are studied on several examples with different features. It is shown that the WENO finite difference idea can be transferred to the simulation of incompressible flows. Some shortcomings of the methods, which are due to the splitting in projection schemes, become also obvious.
Finite difference discretization of semiconductor drift-diffusion equations for nanowire solar cells
NASA Astrophysics Data System (ADS)
Deinega, Alexei; John, Sajeev
2012-10-01
We introduce a finite difference discretization of semiconductor drift-diffusion equations using cylindrical partial waves. It can be applied to describe the photo-generated current in radial pn-junction nanowire solar cells. We demonstrate that the cylindrically symmetric (l=0) partial wave accurately describes the electronic response of a square lattice of silicon nanowires at normal incidence. We investigate the accuracy of our discretization scheme by using different mesh resolution along the radial direction r and compare with 3D (x, y, z) discretization. We consider both straight nanowires and nanowires with radius modulation along the vertical axis. The charge carrier generation profile inside each nanowire is calculated using an independent finite-difference time-domain simulation.
NASA Technical Reports Server (NTRS)
Subrahmanyam, K. B.; Kaza, K. R. V.
1985-01-01
Theoretical natural frequencies of the first three modes of torsional vibration of pretwisted, rotating cantilever beams are determined for various thickness and aspect ratios. Conclusions concerning individual and collective effects of warping, pretwist, tension-torsion coupling and tennis racket effect (twist-rotational coupling) terms on the natural frequencies are drawn from numerical results obtained by using a finite difference procedure with first order central differences. The relative importance of structural warping, inertial warping, pretwist, tension-torsion and twist-rotational coupling terms is discussed for various rotational speeds. The accuracy of results obtained by using the finite difference approach is verified by a comparison with the exact solution for specialized simple cases of the equation of motion used in this paper.
MAZE96. Generates 2D Input for DYNA NIKE & TOPAZ
Sanford, L.; Hallquist, J.O.
1992-02-24
MAZE is an interactive program that serves as an input and two-dimensional mesh generator for DYNA2D, NIKE2D, TOPAZ2D, and CHEMICAL TOPAZ2D. MAZE also generates a basic template for ISLAND input. MAZE has been applied to the generation of input data 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.
Generates 2D Input for DYNA NIKE & TOPAZ
1996-07-15
MAZE is an interactive program that serves as an input and two-dimensional mesh generator for DYNA2D, NIKE2D, TOPAZ2D, and CHEMICAL TOPAZ2D. MAZE also generates a basic template for ISLAND input. MAZE has been applied to the generation of input data 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.
NASA Astrophysics Data System (ADS)
Brissaud, Quentin; Martin, Roland; Garcia, Raphaël F.; Komatitsch, Dimitri
2016-04-01
Acoustic and gravity waves propagating in planetary atmospheres have been studied intensively as markers of specific phenomena such as tectonic events or explosions or as contributors to atmosphere dynamics. To get a better understanding of the physics behind these dynamic processes, both acoustic and gravity waves propagation should be modelled in a 3D attenuating and windy atmosphere extending from the ground to the upper thermosphere. Thus, in order to provide an efficient numerical tool at the regional or global scale we introduce a finite difference in the time domain (FDTD) approach that relies on the linearized compressible Navier-Stokes equations with a background flow (wind). One significant benefit of such a method is its versatility because it handles both acoustic and gravity waves in the same simulation, which enables one to observe interactions between them. Simulations can be performed for 2D or 3D realistic cases such as tsunamis in a full MSISE-00 atmosphere or gravity-wave generation by atmospheric explosions. We validate the computations by comparing them to analytical solutions based on dispersion relations in specific benchmark cases: an atmospheric explosion, and a ground displacement forcing.
A finite difference solution for the propagation of sound in near sonic flows
NASA Technical Reports Server (NTRS)
Hariharan, S. I.; Lester, H. C.
1983-01-01
An explicit time/space finite difference procedure is used to model the propagation of sound in a quasi one-dimensional duct containing high Mach number subsonic flow. Nonlinear acoustic equations are derived by perturbing the time-dependent Euler equations about a steady, compressible mean flow. The governing difference relations are based on a fourth-order, two-step (predictor-corrector) MacCormack scheme. The solution algorithm functions by switching on a time harmonic source and allowing the difference equations to iterate to a steady state. The principal effect of the non-linearities was to shift acoustical energy to higher harmonics. With increased source strengths, wave steepening was observed. This phenomenon suggests that the acoustical response may approach a shock behavior at at higher sound pressure level as the throat Mach number aproaches unity. On a peak level basis, good agreement between the nonlinear finite difference and linear finite element solutions was observed, even through a peak sound pressure level of about 150 dB occurred in the throat region. Nonlinear steady state waveform solutions are shown to be in excellent agreement with a nonlinear asymptotic theory.
Higher-order finite-difference formulation of periodic Orbital-free Density Functional Theory
NASA Astrophysics Data System (ADS)
Ghosh, Swarnava; Suryanarayana, Phanish
2016-02-01
We present a real-space formulation and higher-order finite-difference implementation of periodic Orbital-free Density Functional Theory (OF-DFT). Specifically, utilizing a local reformulation of the electrostatic and kernel terms, we develop a generalized framework for performing OF-DFT simulations with different variants of the electronic kinetic energy. In particular, we propose a self-consistent field (SCF) type fixed-point method for calculations involving linear-response kinetic energy functionals. In this framework, evaluation of both the electronic ground-state and forces on the nuclei are amenable to computations that scale linearly with the number of atoms. We develop a parallel implementation of this formulation using the finite-difference discretization. We demonstrate that higher-order finite-differences can achieve relatively large convergence rates with respect to mesh-size in both the energies and forces. Additionally, we establish that the fixed-point iteration converges rapidly, and that it can be further accelerated using extrapolation techniques like Anderson's mixing. We validate the accuracy of the results by comparing the energies and forces with plane-wave methods for selected examples, including the vacancy formation energy in Aluminum. Overall, the suitability of the proposed formulation for scalable high performance computing makes it an attractive choice for large-scale OF-DFT calculations consisting of thousands of atoms.
NASA Astrophysics Data System (ADS)
Cunha, G.; Redonnet, S.
2014-04-01
The present article aims at highlighting the strengths and weaknesses of the so-called spectral-like optimized (explicit central) finite-difference schemes, when the latter are used for numerically approximating spatial derivatives in aeroacoustics evolution problems. With that view, we first remind how differential operators can be approximated using explicit central finite-difference schemes. The possible spectral-like optimization of the latter is then discussed, the advantages and drawbacks of such an optimization being theoretically studied, before they are numerically quantified. For doing so, two popular spectral-like optimized schemes are assessed via a direct comparison against their standard counterparts, such a comparative exercise being conducted for several academic test cases. At the end, general conclusions are drawn, which allows us discussing the way spectral-like optimized schemes shall be preferred (or not) to standard ones, when it comes to simulate real-life aeroacoustics problems.
A mapped finite difference study of noise propagation in nonuniform ducts with mean flow
NASA Technical Reports Server (NTRS)
Raad, Peter E.; White, James W.
1987-01-01
The primary objective of this work is to study noise propagation in acoustically lined variable area ducts with mean fluid flow. The method of study is numerical in nature and involves a body-fitted grid mapping procedure in conjunction with a factored-implicit finite difference technique. The mean fluid flow model used is two-dimensional, inviscid, irrotational, incompressible, and nonheat conducting. Fully-coupled solutions of the linearized gasdynamic equations are obtained for both positive and negative Mach numbers as well as for hard and soft wall conditions. The factored-implicit finite difference technique used did give rise to short wavelength perturbations, but these were dampened by the introduction of higher order artificial dissipation terms into the scheme. Results compared favorably with available numerical and experimental data.
A semi-implicit finite difference model for three-dimensional tidal circulation,
Casulli, V.; Cheng, R.T.
1992-01-01
A semi-implicit finite difference formulation for the numerical solution of three-dimensional tidal circulation is presented. The governing equations are the three-dimensional Reynolds equations in which the pressure is assumed to be hydrostatic. A minimal degree of implicitness has been introduced in the finite difference formula so that in the absence of horizontal viscosity the resulting algorithm is unconditionally stable at a minimal computational cost. When only one vertical layer is specified this method reduces, as a particular case, to a semi-implicit scheme for the solutions of the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm is fast, accurate and mass conservative. This formulation includes the simulation of flooding and drying of tidal flats, and is fully vectorizable for an efficient implementation on modern vector computers.
On One-Dimensional Stretching Functions for Finite-Difference Calculations
NASA Technical Reports Server (NTRS)
Vinokur, M.
1980-01-01
The class of one dimensional stretching function used in finite difference calculations is studied. For solutions containing a highly localized region of rapid variation, simple criteria for a stretching function are derived using a truncation error analysis. These criteria are used to investigate two types of stretching functions. One is an interior stretching function, for which the location and slope of an interior clustering region are specified. The simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine. The other type of function is a two sided stretching function, for which the arbitrary slopes at the two ends of the one dimensional interval are specified. The simplest such general function is found to be one based on the inverse tangent. The general two sided function has many applications in the construction of finite difference grids.
NASA Technical Reports Server (NTRS)
Hannah, S. R.; Palazotto, A. N.
1978-01-01
A new trigonometric approach to the finite difference calculus was applied to the problem of beam buckling as represented by virtual work and equilibrium equations. The trigonometric functions were varied by adjusting a wavelength parameter in the approximating Fourier series. Values of the critical force obtained from the modified approach for beams with a variety of boundary conditions were compared to results using the conventional finite difference method. The trigonometric approach produced significantly more accurate approximations for the critical force than the conventional approach for a relatively wide range in values of the wavelength parameter; and the optimizing value of the wavelength parameter corresponded to the half-wavelength of the buckled mode shape. It was found from a modal analysis that the most accurate solutions are obtained when the approximating function closely represents the actual displacement function and matches the actual boundary conditions.
Analysis of vegetation effect on waves using a vertical 2-D RANS model
Technology Transfer Automated Retrieval System (TEKTRAN)
A vertical two-dimensional (2-D) model has been applied in the simulation of wave propagation through vegetated water bodies. The model is based on an existing model SOLA-VOF which solves the Reynolds-Averaged Navier-Stokes (RANS) equations with the finite difference method on a staggered rectangula...
2005-07-01
Aniso2d is a two-dimensional seismic forward modeling code. The earth is parameterized by an X-Z plane in which the seismic properties Can have monoclinic with x-z plane symmetry. The program uses a user define time-domain wavelet to produce synthetic seismograms anrwhere within the two-dimensional media.
Three-dimensional finite difference time domain modeling of the Earth-ionosphere cavity resonances
NASA Astrophysics Data System (ADS)
Yang, Heng; Pasko, Victor P.
2005-02-01
Comparison of results from a three-dimensional (3-D) finite difference time domain (FDTD) model of Schumann resonances (SR) with a set of classical eigenfrequency and quality factor solutions for laterally uniform spherically symmetric Earth-ionosphere cavity and recent SR observations during solar proton events (SPEs) and X-ray bursts demonstrate the potential and applicability of the FDTD technique for studies of realistic SR problems.
Simulation of realistic rotor blade-vortex interactions using a finite-difference technique
NASA Technical Reports Server (NTRS)
Hassan, Ahmed A.; Charles, Bruce D.
1989-01-01
A numerical finite-difference code has been used to predict helicopter blade loads during realistic self-generated three-dimensional blade-vortex interactions. The velocity field is determined via a nonlinear superposition of the rotor flowfield. Data obtained from a lifting-line helicopter/rotor trim code are used to determine the instantaneous position of the interaction vortex elements with respect to the blade. Data obtained for three rotor advance ratios show a reasonable correlation with wind tunnel data.
Transport and dispersion of pollutants in surface impoundments: a finite difference model
Yeh, G.T.
1980-07-01
A surface impoundment model by finite-difference (SIMFD) has been developed. SIMFD computes the flow rate, velocity field, and the concentration distribution of pollutants in surface impoundments with any number of islands located within the region of interest. Theoretical derivations and numerical algorithm are described in detail. Instructions for the application of SIMFD and listings of the FORTRAN IV source program are provided. Two sample problems are given to illustrate the application and validity of the model.
Finite-difference, time-domain analysis of a folded acoustic transmission line.
Jackson, Charles M
2005-03-01
Recently designed, modern versions of renais sance woodwind instruments such as the recorder and serpent use square cross sections and a folded acoustic transmission line. Conventional microwave techniques would expect that this bend would cause unwanted reflections and impedance discontinuities. This paper analyses the folded acoustic transmission line using finite-difference, time-domain techniques and shows that the discontinuity can be compensated with by the use of a manufacturable method. PMID:15857045
A staggered mesh finite difference scheme for the computation of compressible flows
NASA Technical Reports Server (NTRS)
Sanders, Richard
1992-01-01
A simple high resolution finite difference technique is presented to approximate weak solutions to hyperbolic systems of conservation laws. The method does not rely on Riemann problem solvers and is therefore easy to extend to a wide variety of problems. The overall performance (resolution and CPU requirements) is competitive, with other state-of-the-art techniques offering sharp nonoscillatory shocks and contacts. Theoretical results confirm the reliability of the approach for linear systems and nonlinear scalar equations.
NASA Astrophysics Data System (ADS)
von Sydow, Lina
2013-10-01
The discontinuous Galerkin method for time integration of the Black-Scholes partial differential equation for option pricing problems is studied and compared with more standard time-integrators. In space an adaptive finite difference discretization is employed. The results show that the dG method are in most cases at least comparable to standard time-integrators and in some cases superior to them. Together with adaptive spatial grids the suggested pricing method shows great qualities.
NASA Technical Reports Server (NTRS)
Abramopoulos, Frank
1988-01-01
The conditions under which finite difference schemes for the shallow water equations can conserve both total energy and potential enstrophy are considered. A method of deriving such schemes using operator formalism is developed. Several such schemes are derived for the A-, B- and C-grids. The derived schemes include second-order schemes and pseudo-fourth-order schemes. The simplest B-grid pseudo-fourth-order schemes are presented.
ADI Finite Difference Discretization of the Heston-Hull-White PDE
NASA Astrophysics Data System (ADS)
Haentjens, Tinne; Hout, Karel in't.
2010-09-01
This paper concerns the efficient numerical solution of the time-dependent, three-dimensional Heston-Hull-White PDE for the fair prices of European call options. The numerical solution method described in this paper consists of a finite difference discretization on non-uniform spatial grids followed by an Alternating Direction Implicit scheme for the time discretization and extends the method recently proved effective by In't Hout & Foulon (2010) for the simpler, two-dimensional Heston PDE.
Finite-difference model for 3-D flow in bays and estuaries
Smith, Peter E.; Larock, Bruce E.
1993-01-01
This paper describes a semi-implicit finite-difference model for the numerical solution of three-dimensional flow in bays and estuaries. The model treats the gravity wave and vertical diffusion terms in the governing equations implicitly, and other terms explicitly. The model achieves essentially second-order accurate and stable solutions in strongly nonlinear problems by using a three-time-level leapfrog-trapezoidal scheme for the time integration.
Finite-difference models of ordinary differential equations - Influence of denominator functions
NASA Technical Reports Server (NTRS)
Mickens, Ronald E.; Smith, Arthur
1990-01-01
This paper discusses the influence on the solutions of finite-difference schemes of using a variety of denominator functions in the discrete modeling of the derivative for any ordinary differential equation. The results obtained are a consequence of using a generalized definition of the first derivative. A particular example of the linear decay equation is used to illustrate in detail the various solution possibilities that can occur.
Direct Simulations of Transition and Turbulence Using High-Order Accurate Finite-Difference Schemes
NASA Technical Reports Server (NTRS)
Rai, Man Mohan
1997-01-01
In recent years the techniques of computational fluid dynamics (CFD) have been used to compute flows associated with geometrically complex configurations. However, success in terms of accuracy and reliability has been limited to cases where the effects of turbulence and transition could be modeled in a straightforward manner. Even in simple flows, the accurate computation of skin friction and heat transfer using existing turbulence models has proved to be a difficult task, one that has required extensive fine-tuning of the turbulence models used. In more complex flows (for example, in turbomachinery flows in which vortices and wakes impinge on airfoil surfaces causing periodic transitions from laminar to turbulent flow) the development of a model that accounts for all scales of turbulence and predicts the onset of transition may prove to be impractical. Fortunately, current trends in computing suggest that it may be possible to perform direct simulations of turbulence and transition at moderate Reynolds numbers in some complex cases in the near future. This seminar will focus on direct simulations of transition and turbulence using high-order accurate finite-difference methods. The advantage of the finite-difference approach over spectral methods is that complex geometries can be treated in a straightforward manner. Additionally, finite-difference techniques are the prevailing methods in existing application codes. In this seminar high-order-accurate finite-difference methods for the compressible and incompressible formulations of the unsteady Navier-Stokes equations and their applications to direct simulations of turbulence and transition will be presented.
Properties of finite difference models of non-linear conservative oscillators
NASA Technical Reports Server (NTRS)
Mickens, R. E.
1988-01-01
Finite-difference (FD) approaches to the numerical solution of the differential equations describing the motion of a nonlinear conservative oscillator are investigated analytically. A generalized formulation of the Duffing and modified Duffing equations is derived and analyzed using several FD techniques, and it is concluded that, although it is always possible to contstruct FD models of conservative oscillators which are themselves conservative, caution is required to avoid numerical solutions which do not accurately reflect the properties of the original equation.
NASA Technical Reports Server (NTRS)
Lansing, Faiza S.; Rascoe, Daniel L.
1993-01-01
This paper presents a modified Finite-Difference Time-Domain (FDTD) technique using a generalized conformed orthogonal grid. The use of the Conformed Orthogonal Grid, Finite Difference Time Domain (GFDTD) enables the designer to match all the circuit dimensions, hence eliminating a major source o error in the analysis.
Finite difference time domain analysis of microwave ferrite devices and mobile antenna systems
NASA Astrophysics Data System (ADS)
Yildirim, Bahadir Suleyman
This dissertation presents analysis and design of shielded mobile antenna systems and microwave ferrite devices using a finite-difference time-domain method. Novel shielded antenna structures suitable for cellular communications have been analyzed and designed with emphasize on reducing excessive radiated energy absorbed in user's head and hand, while keeping the antenna performance at its peak in the presence of user. These novel antennas include a magnetically shielded antenna, a dual-resonance shielded antenna and, a shorted and truncated microstrip antenna. The effect of magnetic coating on the performance of a shielded monopole antenna is studied extensively. A parametric study is performed to analyze the dual-resonance phenomenon observed in the dual-resonance shielded antenna, optimize the antenna design within the cellular communications band, and improve the antenna performance. Input impedance, near and far fields of the dual-resonance shielded antenna are calculated using the finite-difference time-domain method. Experimental validation is also presented. In addition, performance of a shorted and truncated microstrip antenna has been investigated over a wide range of substrate parameters and dimensions. Objectives of the research work also include development of a finite-difference time-domain technique to accurately model magnetically anisotropic media, including the effect of non-uniform magnetization within the finite-size ferrite material due to demagnetizing fields. A slow wave thin film isolator and a stripline disc junction circulator are analyzed. An extensive parametric study calculates wide-band frequency-dependent parameters of these devices for various device dimensions and material parameters. Finally, a ferrite-filled stripline configuration is analyzed to study the non- linear behaviour of ferrite by introducing a modified damping factor.
Generating meshes for finite-difference analysis using a solid modeler
NASA Astrophysics Data System (ADS)
Laguna, G. W.; White, W. T.; Cabral, B. K.
1987-09-01
One tool used by the Engineering Research Division of LLNL to help analyze the behavior of electronic systems in hostile environments is 3D finite-difference time-domain (FDTD) computation. FDTD codes solve Maxwell's equations,the differential equations of electromagnetism, on a uniform lattice of points. It is this uniform lattice, or mesh, that distinguishes finite-difference codes from other codes. The simple mesh makes FDTD codes computationally more efficient than other codes, which enables them to run larger problems and to run faster (up to thirty times faster than finite-element codes, for example). Therefore, within the Engineering Department at LLNL, Electronics Engineering (EE) has initiated a project to develop a mesh generator that will provide meshes suitable for FDTD analysis. This report describes the results of the first year of EE's FDTD Mesh Generation Project. During this year a preliminary version of an automated mesh generator was built and used to create a mesh of an object of interest to the High-Power Microwave Program, namely an electrically detonatable land mine. The code was verified by meshing basic solids such as spheres and cylinders. Because of the design of the code, there is no software limitation to the size of meshes that can be accommodated. The algorithm with a mesh space of approximately 500,000 cells has been demonstrated. The mesh generator can detect certain objects with walls that are thinner than the width of a cell. The code has internal graphics for viewing objects as they appear prior to being converted to a finite-difference representation. Additionally, via data files, the code is coupled to two external graphics packages for visually checking the meshes, namely TAURUS on the Cray and a new code, IMAGE, on the Silicon Graphics IRIS workstation.
Generating meshes for finite-difference analysis using a solid modeler
Laguna, G.W.; White, W.T.; Cabral, B.K.
1987-09-01
One tool used by the Engineering Research Division of LLNL to help analyze the behavior of electronic systems in hostile environments is 3D finite-difference time-domain (FDTD) computation. FDTD codes solve Maxwell's equations,the differential equations of electromagnetism, on a uniform lattice of points. It is this uniform lattice, or ''mesh,'' that distinguishes finite-difference codes from other codes. The simple mesh makes FDTD codes computationally more efficient than other codes, which enables them to run larger problems and to run faster (up to thirty times faster than finite-element codes, for example). Therefore, within the Engineering Department at LLNL, Electronics Engineering (EE) has initiated a project to develop a mesh generator that will provide meshes suitable for FDTD analysis. This report describes the results of the first year of EE's FDTD Mesh Generation Project. During this year a preliminary version of an automated mesh generator was built and used to create a mesh of an object of interest to the High-Power Microwave Program, namely an electrically detonatable land mine. The code was verified by meshing basic solids such as spheres and cylinders. Because of the design of the code, there is no software limitation to the size of meshes that can be accommodated. The algorithm with a mesh space of approximately 500,000 cells has been demonstrated. The mesh generator can detect certain objects with walls that are thinner than the width of a cell. The code has internal graphics for viewing objects as they appear prior to being converted to a finite-difference representation. Additionally, via data files, the code is coupled to two external graphics packages for visually checking the meshes, namely TAURUS on the Cray and a new code, IMAGE, on the Silicon Graphics IRIS workstation.
Experiments with explicit filtering for LES using a finite-difference method
NASA Technical Reports Server (NTRS)
Lund, T. S.; Kaltenbach, H. J.
1995-01-01
The equations for large-eddy simulation (LES) are derived formally by applying a spatial filter to the Navier-Stokes equations. The filter width as well as the details of the filter shape are free parameters in LES, and these can be used both to control the effective resolution of the simulation and to establish the relative importance of different portions of the resolved spectrum. An analogous, but less well justified, approach to filtering is more or less universally used in conjunction with LES using finite-difference methods. In this approach, the finite support provided by the computational mesh as well as the wavenumber-dependent truncation errors associated with the finite-difference operators are assumed to define the filter operation. This approach has the advantage that it is also 'automatic' in the sense that no explicit filtering: operations need to be performed. While it is certainly convenient to avoid the explicit filtering operation, there are some practical considerations associated with finite-difference methods that favor the use of an explicit filter. Foremost among these considerations is the issue of truncation error. All finite-difference approximations have an associated truncation error that increases with increasing wavenumber. These errors can be quite severe for the smallest resolved scales, and these errors will interfere with the dynamics of the small eddies if no corrective action is taken. Years of experience at CTR with a second-order finite-difference scheme for high Reynolds number LES has repeatedly indicated that truncation errors must be minimized in order to obtain acceptable simulation results. While the potential advantages of explicit filtering are rather clear, there is a significant cost associated with its implementation. In particular, explicit filtering reduces the effective resolution of the simulation compared with that afforded by the mesh. The resolution requirements for LES are usually set by the need to capture
A mimetic finite difference method for the Stokes problem with elected edge bubbles
Lipnikov, K; Berirao, L
2009-01-01
A new mimetic finite difference method for the Stokes problem is proposed and analyzed. The unstable P{sub 1}-P{sub 0} discretization is stabilized by adding a small number of bubble functions to selected mesh edges. A simple strategy for selecting such edges is proposed and verified with numerical experiments. The discretizations schemes for Stokes and Navier-Stokes equations must satisfy the celebrated inf-sup (or the LBB) stability condition. The stability condition implies a balance between discrete spaces for velocity and pressure. In finite elements, this balance is frequently achieved by adding bubble functions to the velocity space. The goal of this article is to show that the stabilizing edge bubble functions can be added only to a small set of mesh edges. This results in a smaller algebraic system and potentially in a faster calculations. We employ the mimetic finite difference (MFD) discretization technique that works for general polyhedral meshes and can accomodate non-uniform distribution of stabilizing bubbles.
Mimetic finite difference method for the stokes problem on polygonal meshes
Lipnikov, K; Beirao Da Veiga, L; Gyrya, V; Manzini, G
2009-01-01
Various approaches to extend the finite element methods to non-traditional elements (pyramids, polyhedra, etc.) have been developed over the last decade. Building of basis functions for such elements is a challenging task and may require extensive geometry analysis. The mimetic finite difference (MFD) method has many similarities with low-order finite element methods. Both methods try to preserve fundamental properties of physical and mathematical models. The essential difference is that the MFD method uses only the surface representation of discrete unknowns to build stiffness and mass matrices. Since no extension inside the mesh element is required, practical implementation of the MFD method is simple for polygonal meshes that may include degenerate and non-convex elements. In this article, we develop a MFD method for the Stokes problem on arbitrary polygonal meshes. The method is constructed for tensor coefficients, which will allow to apply it to the linear elasticity problem. The numerical experiments show the second-order convergence for the velocity variable and the first-order for the pressure.
Numerical analysis of polarization gratings using the finite-difference time-domain method
Oh, Chulwoo; Escuti, Michael J.
2007-10-15
We report the first full numerical analysis of polarization gratings (PGs), and study their most general properties and limits by using the finite-difference time-domain (FDTD) method. In this way, we avoid limiting assumptions on material properties or grating dimensions (e.g., no paraxial approximations) and provide a more complete understanding of PG diffraction behavior. We identify the fundamental delineation between diffraction regimes (thin versus thick) for anisotropic gratings and determine the conditions for {approx_equal}100% diffraction efficiency in the framework of the coupled-wave {rho} and Q parameters. Diffraction characteristics including the efficiency, spectral response, and polarization sensitivity are investigated for the two primary types of PGs with linear and circular birefringence. The angular response and finite-grating behavior (i.e., pixelation) are also examined. Comparisons with previous analytic approximations, where applicable, show good agreement.
NASA Technical Reports Server (NTRS)
Kishoni, Doron; Taasan, Shlomo
1994-01-01
Solution of the wave equation using techniques such as finite difference or finite element methods can model elastic wave propagation in solids. This requires mapping the physical geometry into a computational domain whose size is governed by the size of the physical domain of interest and by the required resolution. This computational domain, in turn, dictates the computer memory requirements as well as the calculation time. Quite often, the physical region of interest is only a part of the whole physical body, and does not necessarily include all the physical boundaries. Reduction of the calculation domain requires positioning an artificial boundary or region where a physical boundary does not exist. It is important however that such a boundary, or region, will not affect the internal domain, i.e., it should not cause reflections that propagate back into the material. This paper concentrates on the issue of constructing such a boundary region.
NASA Astrophysics Data System (ADS)
Ranjbar-Far, M.; Absi, J.; Mariaux, G.
2012-12-01
A new finite element model is used to investigate catastrophic failures of a thermal barrier coatings system due to crack propagation along the interfaces between the ceramic top-coat, thermally grown oxide, and bond-coat layers, as well as between the lamellas structure of the ceramic layer. The thermo-mechanical model is designed to take into account a non-homogenous temperature distribution and the effects of the residual stresses generated during the coating process. Crack propagation is simulated using the contact tool "Debond" present in the ABAQUS finite element code. Simulations are performed with a geometry corresponding to similar or dissimilar amplitudes of asperity, and for different thicknesses of the oxide layer. The numerical results have shown that crack evolution depends crucially on the ratio of the loading rate caused by growth and swelling of the oxide layer and also on the interface roughness obtained during the spraying of coatings.
Greg Flach, Frank Smith
2011-12-31
Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j0) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assigns an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations.
2011-12-31
Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j0) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assignsmore » an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations.« less
NASA Astrophysics Data System (ADS)
Kumar, Vivek; Raghurama Rao, S. V.
2008-04-01
Non-standard finite difference methods (NSFDM) introduced by Mickens [ Non-standard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994] are interesting alternatives to the traditional finite difference and finite volume methods. When applied to linear hyperbolic conservation laws, these methods reproduce exact solutions. In this paper, the NSFDM is first extended to hyperbolic systems of conservation laws, by a novel utilization of the decoupled equations using characteristic variables. In the second part of this paper, the NSFDM is studied for its efficacy in application to nonlinear scalar hyperbolic conservation laws. The original NSFDMs introduced by Mickens (1994) were not in conservation form, which is an important feature in capturing discontinuities at the right locations. Mickens [Construction and analysis of a non-standard finite difference scheme for the Burgers-Fisher equations, Journal of Sound and Vibration 257 (4) (2002) 791-797] recently introduced a NSFDM in conservative form. This method captures the shock waves exactly, without any numerical dissipation. In this paper, this algorithm is tested for the case of expansion waves with sonic points and is found to generate unphysical expansion shocks. As a remedy to this defect, we use the strategy of composite schemes [R. Liska, B. Wendroff, Composite schemes for conservation laws, SIAM Journal of Numerical Analysis 35 (6) (1998) 2250-2271] in which the accurate NSFDM is used as the basic scheme and localized relaxation NSFDM is used as the supporting scheme which acts like a filter. Relaxation schemes introduced by Jin and Xin [The relaxation schemes for systems of conservation laws in arbitrary space dimensions, Communications in Pure and Applied Mathematics 48 (1995) 235-276] are based on relaxation systems which replace the nonlinear hyperbolic conservation laws by a semi-linear system with a stiff relaxation term. The relaxation parameter ( λ) is chosen locally
Application of finite difference techniques to noise propagation in jet engine ducts
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1973-01-01
A finite difference formulation is presented for wave propagation in a rectangular two-dimensional duct without steady flow. The difference technique, which should be useful in the study of acoustically treated inlet and exhausts ducts used in turbofan engines, can readily handle acoustical flow field complications such as axial variations in wall impedance and cross section area. In the numerical analysis, the continuous acoustic field is lumped into a series of grid points in which the pressure and velocity at each grid point are separated into real and imaginary terms. An example calculation is also presented for the sound attenuation in a two-dimensional straight soft-walled suppressor.
Application of finite difference techniques to noise propagation in jet engine ducts
NASA Technical Reports Server (NTRS)
Baumeister, K. J.
1973-01-01
A finite difference formulation is presented for wave propagation in a rectangular two-dimensional duct without steady flow. The difference technique, which should be used in the study of acoustically treated inlet and exhausts ducts used in turbofan engines, can readily handle acoustical flow field complications such as axial variations in wall impedance and cross-section area. In the numerical analysis, the continuous acoustic field is lumped into a series of grid points in which the pressure and velocity at each grid point are separated into real and imaginary terms. An example calculation is also presented for the sound attenuation in a two-dimensional straight soft-walled suppressor.
Flux vector splitting of the inviscid equations with application to finite difference methods
NASA Technical Reports Server (NTRS)
Steger, J. L.; Warming, R. F.
1979-01-01
The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.
Harbaugh, Arlen W.
1992-01-01
The U.S. Geological Survey's Modular Ground-Water Flow Model assumes that model nodes are in the center of cells and that transmissivity is constant within a cell. Based on these assumptions, the model calculates coefficients, called conductance, that are multiplied by head difference to determine flow between cells. Although these are common assumptions in finite-difference models, other assumptions are possible. A new option to the model program reads conductance as input data rather than calculating it. This optional lows the user to calculate conductance outside of the model. The user thus has the flexibility to define conductance using any desired assumptions. For a water-table condition, horizontal conductance must change as water level varies. To handle this situation, the new option reads conductance divided by thickness (CDT) as input data. The model calculates saturated thickness and multiplies it by CDT to obtain conductance. Thus, the user is still free from the assumptions of centered nodes and constant transmissivity in cells. The model option is written in FORTRAN77 and is fully compatible with the existing model. This report documents the new model option; it includes a description of the concepts, detailed input instructions, and a listing of the code.
NASA Astrophysics Data System (ADS)
Chae, Dongho; Constantin, Peter; Wu, Jiahong
2014-09-01
We give an example of a well posed, finite energy, 2D incompressible active scalar equation with the same scaling as the surface quasi-geostrophic equation and prove that it can produce finite time singularities. In spite of its simplicity, this seems to be the first such example. Further, we construct explicit solutions of the 2D Boussinesq equations whose gradients grow exponentially in time for all time. In addition, we introduce a variant of the 2D Boussinesq equations which is perhaps a more faithful companion of the 3D axisymmetric Euler equations than the usual 2D Boussinesq equations.
NASA Technical Reports Server (NTRS)
Noor, A. K.; Stephens, W. B.
1973-01-01
Several finite difference schemes are applied to the stress and free vibration analysis of homogeneous isotropic and layered orthotropic shells of revolution. The study is based on a form of the Sanders-Budiansky first-approximation linear shell theory modified such that the effects of shear deformation and rotary inertia are included. A Fourier approach is used in which all the shell stress resultants and displacements are expanded in a Fourier series in the circumferential direction, and the governing equations reduce to ordinary differential equations in the meridional direction. While primary attention is given to finite difference schemes used in conjunction with first order differential equation formulation, comparison is made with finite difference schemes used with other formulations. These finite difference discretization models are compared with respect to simplicity of application, convergence characteristics, and computational efficiency. Numerical studies are presented for the effects of variations in shell geometry and lamination parameters on the accuracy and convergence of the solutions obtained by the different finite difference schemes. On the basis of the present study it is shown that the mixed finite difference scheme based on the first order differential equation formulation and two interlacing grids for the different fundamental unknowns combines a number of advantages over other finite difference schemes previously reported in the literature.
TOPAZ2D heat transfer code users manual and thermal property data base
Shapiro, A.B.; Edwards, A.L.
1990-05-01
TOPAZ2D is a two dimensional implicit finite element computer code for heat transfer analysis. This user's manual provides information on the structure of a TOPAZ2D input file. Also included is a material thermal property data base. This manual is supplemented with The TOPAZ2D Theoretical Manual and the TOPAZ2D Verification Manual. TOPAZ2D has been implemented on the CRAY, SUN, and VAX computers. TOPAZ2D can be used to solve for the steady state or transient temperature field on two dimensional planar or axisymmetric geometries. Material properties may be temperature dependent and either isotropic or orthotropic. A variety of time and temperature dependent boundary conditions can be specified including temperature, flux, convection, and radiation. Time or temperature dependent internal heat generation can be defined locally be element or globally by material. TOPAZ2D can solve problems of diffuse and specular band radiation in an enclosure coupled with conduction in material surrounding the enclosure. Additional features include thermally controlled reactive chemical mixtures, thermal contact resistance across an interface, bulk fluid flow, phase change, and energy balances. Thermal stresses can be calculated using the solid mechanics code NIKE2D which reads the temperature state data calculated by TOPAZ2D. A three dimensional version of the code, TOPAZ3D is available. The material thermal property data base, Chapter 4, included in this manual was originally published in 1969 by Art Edwards for use with his TRUMP finite difference heat transfer code. The format of the data has been altered to be compatible with TOPAZ2D. Bob Bailey is responsible for adding the high explosive thermal property data.
An overlapped grid method for multigrid, finite volume/difference flow solvers: MaGGiE
NASA Technical Reports Server (NTRS)
Baysal, Oktay; Lessard, Victor R.
1990-01-01
The objective is to develop a domain decomposition method via overlapping/embedding the component grids, which is to be used by upwind, multi-grid, finite volume solution algorithms. A computer code, given the name MaGGiE (Multi-Geometry Grid Embedder) is developed to meet this objective. MaGGiE takes independently generated component grids as input, and automatically constructs the composite mesh and interpolation data, which can be used by the finite volume solution methods with or without multigrid convergence acceleration. Six demonstrative examples showing various aspects of the overlap technique are presented and discussed. These cases are used for developing the procedure for overlapping grids of different topologies, and to evaluate the grid connection and interpolation data for finite volume calculations on a composite mesh. Time fluxes are transferred between mesh interfaces using a trilinear interpolation procedure. Conservation losses are minimal at the interfaces using this method. The multi-grid solution algorithm, using the coaser grid connections, improves the convergence time history as compared to the solution on composite mesh without multi-gridding.
Evaluation of a thin-slot formalism for finite-difference time-domain electromagnetics codes
Turner, C.D.; Bacon, L.D.
1987-03-01
A thin-slot formalism for use with finite-difference time-domain (FDTD) electromagnetics codes has been evaluated in both two and three dimensions. This formalism allows narrow slots to be modeled in the wall of a scatterer without reducing the space grid size to the gap width. In two dimensions, the evaluation involves the calculation of the total fields near two infinitesimally thin coplanar strips separated by a gap. A method-of-moments (MoM) solution of the same problem is used as a benchmark for comparison. Results in two dimensions show that up to 10% error can be expected in total electric and magnetic fields both near (lambda/40) and far (1 lambda) from the slot. In three dimensions, the evaluation is similar. The finite-length slot is placed in a finite plate and an MoM surface patch solution is used for the benchmark. These results, although less extensive than those in two dimensions, show that slightly larger errors can be expected. Considering the approximations made near the slot in incorporating the formalism, the results are very promising. Possibilities also exist for applying this formalism to walls of arbitrary thickness and to other types of slots, such as overlapping joints. 11 refs., 25 figs., 6 tabs.
NASA Astrophysics Data System (ADS)
Yu, Peicheng; Xu, Xinlu; Tableman, Adam; Decyk, Viktor K.; Tsung, Frank S.; Fiuza, Frederico; Davidson, Asher; Vieira, Jorge; Fonseca, Ricardo A.; Lu, Wei; Silva, Luis O.; Mori, Warren B.
2015-12-01
A hybrid Maxwell solver for fully relativistic and electromagnetic (EM) particle-in-cell (PIC) codes is described. In this solver, the EM fields are solved in k space by performing an FFT in one direction, while using finite difference operators in the other direction(s). This solver eliminates the numerical Cerenkov radiation for particles moving in the preferred direction. Moreover, the numerical Cerenkov instability (NCI) induced by the relativistically drifting plasma and beam can be eliminated using this hybrid solver by applying strategies that are similar to those recently developed for pure FFT solvers. A current correction is applied for the charge conserving current deposit to ensure that Gauss's Law is satisfied. A theoretical analysis of the dispersion properties in vacuum and in a drifting plasma for the hybrid solver is presented, and compared with PIC simulations with good agreement obtained. This hybrid solver is applied to both 2D and 3D Cartesian and quasi-3D (in which the fields and current are decomposed into azimuthal harmonics) geometries. Illustrative results for laser wakefield accelerator simulation in a Lorentz boosted frame using the hybrid solver in the 2D Cartesian geometry are presented, and compared against results from 2D UPIC-EMMA simulation which uses a pure spectral Maxwell solver, and from OSIRIS 2D lab frame simulation using the standard Yee solver. Very good agreement is obtained which demonstrates the feasibility of using the hybrid solver for high fidelity simulation of relativistically drifting plasma with no evidence of the numerical Cerenkov instability.
WFR-2D: an analytical model for PWAS-generated 2D ultrasonic guided wave propagation
NASA Astrophysics Data System (ADS)
Shen, Yanfeng; Giurgiutiu, Victor
2014-03-01
This paper presents WaveFormRevealer 2-D (WFR-2D), an analytical predictive tool for the simulation of 2-D ultrasonic guided wave propagation and interaction with damage. The design of structural health monitoring (SHM) systems and self-aware smart structures requires the exploration of a wide range of parameters to achieve best detection and quantification of certain types of damage. Such need for parameter exploration on sensor dimension, location, guided wave characteristics (mode type, frequency, wavelength, etc.) can be best satisfied with analytical models which are fast and efficient. The analytical model was constructed based on the exact 2-D Lamb wave solution using Bessel and Hankel functions. Damage effects were inserted in the model by considering the damage as a secondary wave source with complex-valued directivity scattering coefficients containing both amplitude and phase information from wave-damage interaction. The analytical procedure was coded with MATLAB, and a predictive simulation tool called WaveFormRevealer 2-D was developed. The wave-damage interaction coefficients (WDICs) were extracted from harmonic analysis of local finite element model (FEM) with artificial non-reflective boundaries (NRB). The WFR-2D analytical simulation results were compared and verified with full scale multiphysics finite element models and experiments with scanning laser vibrometer. First, Lamb wave propagation in a pristine aluminum plate was simulated with WFR-2D, compared with finite element results, and verified by experiments. Then, an inhomogeneity was machined into the plate to represent damage. Analytical modeling was carried out, and verified by finite element simulation and experiments. This paper finishes with conclusions and suggestions for future work.
Lee, D. W.; Joo, H. G.
2013-07-01
The methods and performance of a three-dimensional S{sub n} transport code employing the Discontinuous Finite Element Method (DFEM) and the Coarse Mesh Finite Difference (CMFD) formulation are presented. The mesh generator GMSH and a post processing visualization tool Visit are combined with the code for flexible geometry processing and versatile visualization. The CMFD method for DFEM Sn applications is formulated and the performance of the CMFD acceleration of eigenvalue calculations is demonstrated for a simple set of neutron transport problems. (authors)
A parallel splitting wavelet method for 2D conservation laws
NASA Astrophysics Data System (ADS)
Schmidt, Alex A.; Kozakevicius, Alice J.; Jakobsson, Stefan
2016-06-01
The current work presents a parallel formulation using the MPI protocol for an adaptive high order finite difference scheme to solve 2D conservation laws. Adaptivity is achieved at each time iteration by the application of an interpolating wavelet transform in each space dimension. High order approximations for the numerical fluxes are computed by ENO and WENO schemes. Since time evolution is made by a TVD Runge-Kutta space splitting scheme, the problem is naturally suitable for parallelization. Numerical simulations and speedup results are presented for Euler equations in gas dynamics problems.
A modular three-dimensional finite-difference ground-water flow model
McDonald, M.G.; Harbaugh, A.W.
1984-01-01
This report presents a finite-difference model and its associated modular computer program. The model simulates flow in three dimensions. The report includes detailed explanations of physical and mathematical concepts on which the model is based and an explanation of how those concepts were incorporated in the modular structure of the computer program. The modular structure consists of a Main Program and a series of highly independent subroutines called 'modules.' The modules are grouped into 'packages.' Each package deals with a specific feature of the hydrologic system which is to be simulated, such as flow from rivers or flow into drains, or with a specific method of solving linear equations which describe the flow system, such as the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The division of the program into modules permits the user to examine specific hydrologic features of the model independently. This also facilitates development of additional capabilities because new modules or packages can be added to the program without modifying the existing modules or packages. The input and output systems of the computer program are also designed to permit maximum flexibility. Ground-water flow within the aquifer is simulated using a block-centered finite-difference approach. Layers can be simulated as confined, unconfined, or a combination of confined and unconfined. Flow from external stresses, such as flow to wells, areal recharge, evapotranspiration, flow to drains, and flow through riverbeds, can also be simulated. The finite-difference equations can be solved using either the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The program is written in FORTRAN '66 and will run without modification on most computers which have a FORTRAN '66 compiler. It will also run, without modification, with most extended FORTRAN '77 compilers and with minor modifications on standard FORTRAN '77 compilers. Documentation presented in this report
A modular three-dimensional finite-difference ground-water flow model
McDonald, Michael G.; Harbaugh, Arlen W.
1988-01-01
This report presents a finite-difference model and its associated modular computer program. The model simulates flow in three dimensions. The report includes detailed explanations of physical and mathematical concepts on which the model is based and an explanation of how those concepts are incorporated in the modular structure of the computer program. The modular structure consists of a Main Program and a series of highly independent subroutines called 'modules.' The modules are grouped into 'packages.' Each package deals with a specific feature of the hydrologic system which is to be simulated, such as flow from rivers or flow into drains, or with a specific method of solving linear equations which describe the flow system, such as the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The division of the program into modules permits the user to examine specific hydrologic features of the model independently. This also facilita development of additional capabilities because new packages can be added to the program without modifying the existing packages. The input and output systems of the computer program are also designed to permit maximum flexibility. Ground-water flow within the aquifer is simulated using a block-centered finite-difference approach. Layers can be simulated as confined, unconfined, or a combination of confined and unconfined. Flow associated with external stresses, such as wells, areal recharge, evapotranspiration, drains, and streams, can also be simulated. The finite-difference equations can be solved using either the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The program is written in FORTRAN 77 and will run without modification on most computers that have a FORTRAN 77 compiler. For each program ,module, this report includes a narrative description, a flow chart, a list of variables, and a module listing.
A Modular Three-Dimensional Finite-Difference Ground-Water Flow Model
McDonald, Michael G.; Harbaugh, Arlen W.; Guo, Weixing, (translator); Lu, Guoping
1988-01-01
This report presents a finite-difference model and its associated modular computer program. The model simulates flow in three dimensions. The report includes detailed explanations of physical and mathematical concepts on which the model is based and an explanation of how those concepts are incorporated in the modular structure of the computer program. The modular structure consists of a Main Program and a series of highly independent subroutines called 'modules.' The modules are grouped into 'packages.' Each package deals with a specific feature of the hydrologic system which is to be simulated, such as flow from rivers or flow into drains, or with a specific method of solving linear equations which describe the flow system, such as the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The division of the program into modules permits the user to examine specific hydrologic features of the model independently. This also facilita development of additional capabilities because new packages can be added to the program without modifying the existing packages. The input and output systems of the computer program are also designed to permit maximum flexibility. Ground-water flow within the aquifer is simulated using a block-centered finite-difference approach. Layers can be simulated as confined, unconfined, or a combination of confined and unconfined. Flow associated with external stresses, such as wells, areal recharge, evapotranspiration, drains, and streams, can also be simulated. The finite-difference equations can be solved using either the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The program is written in FORTRAN 77 and will run without modification on most computers that have a FORTRAN 77 compiler. For each program ,module, this report includes a narrative description, a flow chart, a list of variables, and a module listing.
Transient analysis of printed lines using finite-difference time-domain method
Ahmed, Shahid
2012-03-29
Comprehensive studies of ultra-wideband pulses and electromagnetic coupling on printed coupled lines have been performed using full-wave 3D finite-difference time-domain analysis. Effects of unequal phase velocities of coupled modes, coupling between line traces, and the frequency dispersion on the waveform fidelity and crosstalk have been investigated in detail. To discriminate the contributions of different mechanisms into pulse evolution, single and coupled microstrip lines without (ϵ_{r} = 1) and with (ϵ_{r} > 1) dielectric substrates have been examined. To consistently compare the performance of the coupled lines with substrates of different permittivities and transients of different characteristic times, a generic metric similar to the electrical wavelength has been introduced. The features of pulse propagation on coupled lines with layered and pedestal substrates and on the irregular traces have been explored. Finally, physical interpretations of the simulation results are discussed in the paper.
Computing interaural differences through finite element modeling of idealized human heads
Cai, Tingli; Rakerd, Brad; Hartmann, William M.
2015-01-01
Acoustical interaural differences were computed for a succession of idealized shapes approximating the human head-related anatomy: sphere, ellipsoid, and ellipsoid with neck and torso. Calculations were done as a function of frequency (100–2500 Hz) and for source azimuths from 10 to 90 degrees using finite element models. The computations were compared to free-field measurements made with a manikin. Compared to a spherical head, the ellipsoid produced greater large-scale variation with frequency in both interaural time differences and interaural level differences, resulting in better agreement with the measurements. Adding a torso, represented either as a large plate or as a rectangular box below the neck, further improved the agreement by adding smaller-scale frequency variation. The comparisons permitted conjectures about the relationship between details of interaural differences and gross features of the human anatomy, such as the height of the head, and length of the neck. PMID:26428792
Nonlinear Comparison of High-Order and Optimized Finite-Difference Schemes
NASA Technical Reports Server (NTRS)
Hixon, R.
1998-01-01
The effect of reducing the formal order of accuracy of a finite-difference scheme in order to optimize its high-frequency performance is investigated using the I-D nonlinear unsteady inviscid Burgers'equation. It is found that the benefits of optimization do carry over into nonlinear applications. Both explicit and compact schemes are compared to Tam and Webb's explicit 7-point Dispersion Relation Preserving scheme as well as a Spectral-like compact scheme derived following Lele's work. Results are given for the absolute and L2 errors as a function of time.
One-dimensional transient finite difference model of an operational salinity gradient solar pond
NASA Technical Reports Server (NTRS)
Hicks, Michael C.; Golding, Peter
1992-01-01
This paper describes the modeling approach used to simulate the transient behavior of a salinity gradient solar pond. A system of finite difference equations are used to generate the time dependent temperature and salinity profiles within the pond. The stability of the pond, as determined by the capacity of the resulting salinity profile to suppress thermal convection within the primary gradient region of the pond, is continually monitored and when necessary adjustments are made to the thickness of the gradient zone. Results of the model are then compared to measurements taken during two representative seasonal periods at the University of Texas at El Paso's (UTEP's) research solar pond.
Finite Differences and Collocation Methods for the Solution of the Two Dimensional Heat Equation
NASA Technical Reports Server (NTRS)
Kouatchou, Jules
1999-01-01
In this paper we combine finite difference approximations (for spatial derivatives) and collocation techniques (for the time component) to numerically solve the two dimensional heat equation. We employ respectively a second-order and a fourth-order schemes for the spatial derivatives and the discretization method gives rise to a linear system of equations. We show that the matrix of the system is non-singular. Numerical experiments carried out on serial computers, show the unconditional stability of the proposed method and the high accuracy achieved by the fourth-order scheme.
A staggered mesh finite difference scheme for the computation of hypersonic Euler flows
NASA Technical Reports Server (NTRS)
Sanders, Richard
1991-01-01
A shock capturing finite difference method for systems of hyperbolic conservation laws is presented which avoids the need to solve Riemann problems while being competitive in performance with other current methods. A staggered spatial mesh is employed, so that complicated nonlinear waves generated at cell interfaces are averaged over cell interiors at the next time level. The full method combines to form a conservative version of the modified method of characteristics. The advantages of the method are discussed, and numerical results are presented for the two-dimensional double ellipse problem.
Finite-Difference Time-Domain solution of Maxwell's equations for the dispersive ionosphere
NASA Astrophysics Data System (ADS)
Nickisch, L. J.; Franke, P. M.
1992-10-01
The Finite-Difference Time-Domain (FDTD) technique is a conceptually simple, yet powerful, method for obtaining numerical solutions to electromagnetic propagation problems. However, the application of FDTD methods to problems in ionospheric radiowave propagation is complicated by the dispersive nature of the ionospheric plasma. In the time domain, the electric displacement is the convolution of the dielectric tensor with the electric field, and thus requires information from the entire signal history. This difficulty can be avoided by returning to the dynamical equations from which the dielectric tensor is derived. By integrating these differential equations simultaneously with the Maxwell equations, temporal dispersion is fully incorporated.
Rotordynamic coefficients for labyrinth seals calculated by means of a finite difference technique
NASA Technical Reports Server (NTRS)
Nordmann, R.; Weiser, P.
1989-01-01
The compressible, turbulent, time dependent and three dimensional flow in a labyrinth seal can be described by the Navier-Stokes equations in conjunction with a turbulence model. Additionally, equations for mass and energy conservation and an equation of state are required. To solve these equations, a perturbation analysis is performed yielding zeroth order equations for centric shaft position and first order equations describing the flow field for small motions around the seal center. For numerical solution a finite difference method is applied to the zeroth and first order equations resulting in leakage and dynamic seal coefficients respectively.
NASA Astrophysics Data System (ADS)
Yamamoto, Kaho; Iwai, Yosuke; Uchida, Yoshiaki; Nishiyama, Norikazu
2016-08-01
We numerically analyzed the light propagation in cholesteric liquid crystalline (CLC) droplet array by the finite-difference time-domain (FDTD) method. The FDTD method successfully reproduced the experimental light path observed in the complicated photonic structure of the CLC droplet array more accurately than the analysis of CLC droplets by geometric optics with Bragg condition, and this method help us understand the polarization of the propagating light waves. The FDTD method holds great promise for the design of various photonic devices composed of curved photonic materials like CLC droplets and microcapsules.
The electromagnetic modeling of thin apertures using the finite-difference time-domain technique
NASA Technical Reports Server (NTRS)
Demarest, Kenneth R.
1987-01-01
A technique which computes transient electromagnetic responses of narrow apertures in complex conducting scatterers was implemented as an extension of previously developed Finite-Difference Time-Domain (FDTD) computer codes. Although these apertures are narrow with respect to the wavelengths contained within the power spectrum of excitation, this technique does not require significantly more computer resources to attain the increased resolution at the apertures. In the report, an analytical technique which utilizes Babinet's principle to model the apertures is developed, and an FDTD computer code which utilizes this technique is described.
NASA Technical Reports Server (NTRS)
Tadghighi, Hormoz; Hassan, Ahmed A.; Charles, Bruce
1990-01-01
The present numerical finite-difference scheme for helicopter blade-load prediction during realistic, self-generated three-dimensional blade-vortex interactions (BVI) derives the velocity field through a nonlinear superposition of the rotor flow-field yielded by the full potential rotor flow solver RFS2 for BVI, on the one hand, over the rotational vortex flow field computed with the Biot-Savart law. Despite the accurate prediction of the acoustic waveforms, peak amplitudes are found to have been persistently underpredicted. The inclusion of BVI noise source in the acoustic analysis significantly improved the perceived noise level-corrected tone prediction.
A fully nonlinear, mixed spectral and finite difference model for thermally driven, rotating flows
NASA Technical Reports Server (NTRS)
Miller, Timothy L.; Lu, Huei-Iin; Butler, Karen A.
1992-01-01
Finite difference in time and the meridional plane, in conjunction with a spectral technique in the azimuthal direction, are used to approximate the Navier-Stokes equations in a model that can simulate a variety of thermally driven rotating flows in cylindrical and spherical geometries. Axisymmetric flow, linearized waves relative to a fixed or changing axisymmetric flow, nonlinear waves without wave-wave interaction, and fully nonlinear 3D flow, can in this way be calculated. A reexamination is conducted of the steady baroclinic wave case previously treated by Williams (1971) and Quon (1976).
Finite difference methods with non-uniform meshes for nonlinear fractional differential equations
NASA Astrophysics Data System (ADS)
Li, Changpin; Yi, Qian; Chen, An
2016-07-01
In this article, finite difference methods with non-uniform meshes for solving nonlinear fractional differential equations are presented, where the non-equidistant stepsize is non-decreasing. The rectangle formula and trapezoid formula are proposed based on the non-uniform meshes. Combining the above two methods, we then establish the predictor-corrector scheme. The error and stability analysis are carefully investigated. At last, numerical examples are carried out to verify the theoretical analysis. Besides, the comparisons between non-uniform and uniform meshes are given, where the non-uniform meshes show the better performance when dealing with the less smooth problems.
NASA Technical Reports Server (NTRS)
Steger, J. L.
1978-01-01
Although the Navier-Stokes equations describe most flows of interest in aerodynamics, the inviscid conservation law equations may be used for small regions with viscous forces. Thus, Euler equations and several time-accurate finite difference procedures, explicit and implicit, are discussed. Although implicit techniques require more computational work, they permit larger time steps to be taken without instability. It is noted that the Jacobian matrices for Euler equations in conservation-law form have certain eigenvalue-eigenvector properties which may be used to construct conservative-form coefficient matrices. This reduces the computation time of several implicit and semiimplicit schemes. Extensions of the basic approach to other areas are suggested.
WONDY V: a one-dimensional finite-difference wave-propagation code
Kipp, M.E.; Lawrence, R.J.
1982-06-01
WONDY V solves the finite difference analogs to the Lagrangian equations of motion in one spatial dimension (planar, cylindrical, or spherical). Simulations of explosive detonation, energy deposition, plate impact, and dynamic fracture are possible, using a variety of existing material models. In addition, WONDY has proven to be a powerful tool in the evaluation of new constitutive models. A preprocessor is available to allocate storage arrays commensurate with problem size, and automatic rezoning may be employed to improve resolution. This document provides a description of the equations solved, available material models, operating instructions, and sample problems.
A multigrid algorithm for the cell-centered finite difference scheme
NASA Technical Reports Server (NTRS)
Ewing, Richard E.; Shen, Jian
1993-01-01
In this article, we discuss a non-variational V-cycle multigrid algorithm based on the cell-centered finite difference scheme for solving a second-order elliptic problem with discontinuous coefficients. Due to the poor approximation property of piecewise constant spaces and the non-variational nature of our scheme, one step of symmetric linear smoothing in our V-cycle multigrid scheme may fail to be a contraction. Again, because of the simple structure of the piecewise constant spaces, prolongation and restriction are trivial; we save significant computation time with very promising computational results.
An adaptive-mesh finite-difference solution method for the Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Luchini, Paolo
1987-02-01
An adjustable variable-spacing grid is presented which permits the addition or deletion of single points during iterative solutions of the Navier-Stokes equations by finite difference methods. The grid is designed for application to two-dimensional steady-flow problems which can be described by partial differential equations whose second derivatives are constrained to the Laplacian operator. An explicit Navier-Stokes equations solution technique defined for use with the grid incorporates a hybrid form of the convective terms. Three methods are developed for automatic modifications of the mesh during calculations.
Ramirez-Granados, J C; Paez, G; Strojnik, M
2012-06-01
We develop a technique to analyze pulsed thermography videos in order to detect and reconstruct subsurface defects in homogeneous and layered objects. The technique is based on the analysis of the thermal response of an object to a heat pulse. This thermal response is compared to the predictions of a finite-difference model that is systematically and progressively adjusted to minimize a cost function. With this minimization process, we obtain a depth and a thickness function that allow us to determine the three-dimensional shape, size, depth, thickness, and location of internal defects. The detected defects are reliably reconstructed with graphics of easy interpretation. PMID:22695546
A finite-difference program for stresses in anisotropic, layered plates in bending
NASA Technical Reports Server (NTRS)
Salamon, N. J.
1975-01-01
The interlaminar stresses induced in a layered laminate that is bent into a cylindrical surface are studied. The laminate is modeled as a continuum, and the resulting elasticity equations are solved using the finite difference method. The report sets forth the mathematical framework, presents some preliminary results, and provides a listing and explanation of the computer program. Significant among the results are apparent symmetry relationships that will reduce the numerical size of certain problems and an interlaminar stress behavior having a sharp rise at the free edges.
NASA Technical Reports Server (NTRS)
Osher, S.
1984-01-01
The construction of a reliable, shock capturing finite difference method to solve the Euler equations for inviscid, supersonic flow past fighter and missile type configurations is highly desirable. The numerical method must have a firm theoretical foundation and must be robust and efficient. It should be able to treat subsonic pockets in a predominantly supersonic flow. The method must also be easily applicable to the complex topologies of the aerodynamic configuration under consideration. The ongoing approach to this task is described and for steady supersonic flows is presented. This scheme is the basic numerical method. Results of work obtained during previous years are presented.
NASA Technical Reports Server (NTRS)
Van Dalsem, W. R.; Steger, J. L.
1983-01-01
A new, fast, direct-inverse, finite-difference boundary-layer code has been developed and coupled with a full-potential transonic airfoil analysis code via new inviscid-viscous interaction algorithms. The resulting code has been used to calculate transonic separated flows. The results are in good agreement with Navier-Stokes calculations and experimental data. Solutions are obtained in considerably less computer time than Navier-Stokes solutions of equal resolution. Because efficient inviscid and viscous algorithms are used, it is expected this code will also compare favorably with other codes of its type as they become available.
A 3-dimensional finite-difference method for calculating the dynamic coefficients of seals
NASA Technical Reports Server (NTRS)
Dietzen, F. J.; Nordmann, R.
1989-01-01
A method to calculate the dynamic coefficients of seals with arbitrary geometry is presented. The Navier-Stokes equations are used in conjunction with the k-e turbulence model to describe the turbulent flow. These equations are solved by a full 3-dimensional finite-difference procedure instead of the normally used perturbation analysis. The time dependence of the equations is introduced by working with a coordinate system rotating with the precession frequency of the shaft. The results of this theory are compared with coefficients calculated by a perturbation analysis and with experimental results.
Ceotto, Michele; Zhuang, Yu; Hase, William L
2013-02-01
This paper shows how a compact finite difference Hessian approximation scheme can be proficiently implemented into semiclassical initial value representation molecular dynamics. Effects of the approximation on the monodromy matrix calculation are tested by propagating initial sampling distributions to determine power spectra for analytic potential energy surfaces and for "on the fly" carbon dioxide direct dynamics. With the approximation scheme the computational cost is significantly reduced, making ab initio direct semiclassical dynamics computationally more feasible and, at the same time, properly reproducing important quantum effects inherent in the monodromy matrix and the pre-exponential factor of the semiclassical propagator. PMID:23406107
Memory cost of absorbing conditions for the finite-difference time-domain method.
Chobeau, Pierre; Savioja, Lauri
2016-07-01
Three absorbing layers are investigated using standard rectilinear finite-difference schemes. The perfectly matched layer (PML) is compared with basic lossy layers terminated by two types of absorbing boundary conditions, all simulated using equivalent memory consumption. Lossy layers present the advantage of being scalar schemes, whereas the PML relies on a staggered scheme where both velocity and pressure are split. Although the PML gives the lowest reflection magnitudes over all frequencies and incidence angles, the most efficient lossy layer gives reflection magnitudes of the same order as the PML from mid- to high-frequency and for restricted incidence angles. PMID:27475200
NASA Technical Reports Server (NTRS)
Liu, C.; Liu, Z.
1993-01-01
The fourth-order finite-difference scheme with fully implicit time-marching presently used to computationally study the spatial instability of planar Poiseuille flow incorporates a novel treatment for outflow boundary conditions that renders the buffer area as short as one wavelength. A semicoarsening multigrid method accelerates convergence for the implicit scheme at each time step; a line-distributive relaxation is developed as a robust fast solver that is efficient for anisotropic grids. Computational cost is no greater than that of explicit schemes, and excellent agreement with linear theory is obtained.
Computation of wing-vortex interaction in transonic flow using implicit finite difference algorithm
NASA Technical Reports Server (NTRS)
Srinivasan, G.; Steger, J. L.
1981-01-01
An implicit delta form finite difference algorithm for Euler equations in conservation law form was used in preliminary calculations of three dimensional wing vortex interaction. Both steady and unsteady transonic flow wing vortex interactions are computed. The computations themselves are meant to guide upcoming wind tunnel experiments of the same flow field. Various modifications to the numerical method that are intended to improve computational efficiency are also described and tested in both two and three dimensions. Combination of these methods can reduce the overall computational time by a factor of 4.
NASA Technical Reports Server (NTRS)
Bridgeman, J. O.; Steger, J. L.; Caradonna, F. X.
1982-01-01
An implicit, approximate-factorization, finite-difference algorithm has been developed for the computation of unsteady, inviscid transonic flows in two and three dimensions. The computer program solves the full-potential equation in generalized coordinates in conservation-law form in order to properly capture shock-wave position and speed. A body-fitted coordinate system is employed for the simple and accurate treatment of boundary conditions on the body surface. The time-accurate algorithm is modified to a conventional ADI relaxation scheme for steady-state computations. Results from two- and three-dimensional steady and two-dimensional unsteady calculations are compared with existing methods.
NASA Technical Reports Server (NTRS)
Anderson, O. L.
1974-01-01
A finite-difference procedure for computing the turbulent, swirling, compressible flow in axisymmetric ducts is described. Arbitrary distributions of heat and mass transfer at the boundaries can be treated, and the effects of struts, inlet guide vanes, and flow straightening vanes can be calculated. The calculation procedure is programmed in FORTRAN 4 and has operated successfully on the UNIVAC 1108, IBM 360, and CDC 6600 computers. The analysis which forms the basis of the procedure, a detailed description of the computer program, and the input/output formats are presented. The results of sample calculations performed with the computer program are compared with experimental data.
Phase-field-based lattice Boltzmann finite-difference model for simulating thermocapillary flows.
Liu, Haihu; Valocchi, Albert J; Zhang, Yonghao; Kang, Qinjun
2013-01-01
A phase-field-based hybrid model that combines the lattice Boltzmann method with the finite difference method is proposed for simulating immiscible thermocapillary flows with variable fluid-property ratios. Using a phase field methodology, an interfacial force formula is analytically derived to model the interfacial tension force and the Marangoni stress. We present an improved lattice Boltzmann equation (LBE) method to capture the interface between different phases and solve the pressure and velocity fields, which can recover the correct Cahn-Hilliard equation (CHE) and Navier-Stokes equations. The LBE method allows not only use of variable mobility in the CHE, but also simulation of multiphase flows with high density ratio because a stable discretization scheme is used for calculating the derivative terms in forcing terms. An additional convection-diffusion equation is solved by the finite difference method for spatial discretization and the Runge-Kutta method for time marching to obtain the temperature field, which is coupled to the interfacial tension through an equation of state. The model is first validated against analytical solutions for the thermocapillary driven convection in two superimposed fluids at negligibly small Reynolds and Marangoni numbers. It is then used to simulate thermocapillary migration of a three-dimensional deformable droplet and bubble at various Marangoni numbers and density ratios, and satisfactory agreement is obtained between numerical results and theoretical predictions. PMID:23410429
Ground motion simulations in Marmara (Turkey) region from 3D finite difference method
NASA Astrophysics Data System (ADS)
Aochi, Hideo; Ulrich, Thomas; Douglas, John
2016-04-01
In the framework of the European project MARSite (2012-2016), one of the main contributions from our research team was to provide ground-motion simulations for the Marmara region from various earthquake source scenarios. We adopted a 3D finite difference code, taking into account the 3D structure around the Sea of Marmara (including the bathymetry) and the sea layer. We simulated two moderate earthquakes (about Mw4.5) and found that the 3D structure improves significantly the waveforms compared to the 1D layer model. Simulations were carried out for different earthquakes (moderate point sources and large finite sources) in order to provide shake maps (Aochi and Ulrich, BSSA, 2015), to study the variability of ground-motion parameters (Douglas & Aochi, BSSA, 2016) as well as to provide synthetic seismograms for the blind inversion tests (Diao et al., GJI, 2016). The results are also planned to be integrated in broadband ground-motion simulations, tsunamis generation and simulations of triggered landslides (in progress by different partners). The simulations are freely shared among the partners via the internet and the visualization of the results is diffused on the project's homepage. All these simulations should be seen as a reference for this region, as they are based on the latest knowledge that obtained during the MARSite project, although their refinement and validation of the model parameters and the simulations are a continuing research task relying on continuing observations. The numerical code used, the models and the simulations are available on demand.
McLeod, R.; Hawkins, R.J.; Kallman, J.S.
1991-04-01
Interest has recently grown in applying microwave modeling techniques to optical circuit modeling. One of the simplest, yet most powerful, microwave simulation techniques is the finite-difference time-domain algorithm (FDTD). In this technique, the differential form of the time-domain Maxwell's equations are discretized and all derivatives are approximated as differences. Minor algebraic manipulations on the resulting equations produces a set of update equations that produce fields at a given time step from fields at the previous time step. The FDTD algorithm, then, is quite simple. Source fields are launched into the discrete grid by some means. The FDTD equations advance these fields in time. At the boundaries of the grid, special update equations called radiation conditions are applied that approximate a continuing, infinite space. Because virtually no assumptions are made in the development of the FDTD method, the algorithm is able to represent a wide-range of physical effects. Waves can propagate in any direction, multiple reflections within structures can cause resonances, multiple modes of various polarizations can be launched, each of which may generate within the device an infinite spectrum of bound and radiation modes. The ability to model these types of general physical effects is what makes the FDTD method interesting to the field of optics. In this paper, we discuss the application of the finite-difference time-domain technique to integrated optics. Animations will be shown of the simulations of a TE coupler, TM grating, and a TE integrated detector. 3 refs., 1 fig.
On the Definition of Surface Potentials for Finite-Difference Operators
NASA Technical Reports Server (NTRS)
Tsynkov, S. V.; Bushnell, Dennis M. (Technical Monitor)
2001-01-01
For a class of linear constant-coefficient finite-difference operators of the second order, we introduce the concepts similar to those of conventional single- and double-layer potentials for differential operators. The discrete potentials are defined completely independently of any notion related to the approximation of the continuous potentials on the grid. We rather use all approach based on differentiating, and then inverting the differentiation of a function with surface discontinuity of a particular kind, which is the most general way of introducing surface potentials in the theory of distributions. The resulting finite-difference "surface" potentials appear to be solutions of the corresponding continuous potentials. Primarily, this pertains to the possibility of representing a given solution to the homogeneous equation on the domain as a variety of surface potentials, with the density defined on the domain's boundary. At the same time the discrete surface potentials can be interpreted as one specific realization of the generalized potentials of Calderon's type, and consequently, their approximation properties can be studied independently in the framework of the difference potentials method by Ryaben'kii. The motivation for introducing and analyzing the discrete surface potentials was provided by the problems of active shielding and control of sound, in which the aforementioned source terms that drive the potentials are interpreted as the acoustic control sources that cancel out the unwanted noise on a predetermined region of interest.
NASA Technical Reports Server (NTRS)
Mccoy, M. J.
1980-01-01
Various finite difference techniques used to solve Laplace's equation are compared. Curvilinear coordinate systems are used on two dimensional regions with irregular boundaries, specifically, regions around circles and airfoils. Truncation errors are analyzed for three different finite difference methods. The false boundary method and two point and three point extrapolation schemes, used when having the Neumann boundary condition are considered and the effects of spacing and nonorthogonality in the coordinate systems are studied.
Static & Dynamic Response of 2D Solids
1996-07-15
NIKE2D is an implicit finite-element code for analyzing the finite deformation, static and dynamic response of two-dimensional, axisymmetric, plane strain, and plane stress solids. The code is fully vectorized and available on several computing platforms. A number of material models are incorporated to simulate a wide range of material behavior including elasto-placicity, anisotropy, creep, thermal effects, and rate dependence. Slideline algorithms model gaps and sliding along material interfaces, including interface friction, penetration and single surfacemore » contact. Interactive-graphics and rezoning is included for analyses with large mesh distortions. In addition to quasi-Newton and arc-length procedures, adaptive algorithms can be defined to solve the implicit equations using the solution language ISLAND. Each of these capabilities and more make NIKE2D a robust analysis tool.« less
An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation
NASA Astrophysics Data System (ADS)
Li, Xiao; Qiao, ZhongHua; Zhang, Hui
2016-09-01
In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional. For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.
Mason, W.E.
1983-03-01
A set of finite element codes for the solution of nonlinear, two-dimensional (TACO2D) and three-dimensional (TACO3D) heat transfer problems. Performs linear and nonlinear analyses of both transient and steady state heat transfer problems. Has the capability to handle time or temperature dependent material properties. Materials may be either isotropic or orthotropic. A variety of time and temperature dependent boundary conditions and loadings are available including temperature, flux, convection, radiation, and internal heat generation.
NASA Astrophysics Data System (ADS)
Kobus, J.; Moncrieff, D.; Wilson, S.
2001-12-01
A comparison is made of the accuracy by which the electric dipole polarizability αzz and hyperpolarizability βzzz can be calculated by using the finite basis set approach (the algebraic approximation) and finite difference method in calculations employing the Hartree-Fock model. The numerical and algebraic methods were tested on the ground states of H2, LiH, BH and FH molecules at their respective experimental equilibrium geometries. For the FH molecule at its experimental equilibrium geometry, a sequence of distributed universal even-tempered basis sets have been used to explore the convergence pattern of the total energy, dipole moment and polarizabilities. The comparison of finite difference and finite basis set methods is extended to geometries for which the nuclear separation, RFH, lies in the range 1.5-2.2 b. The methods give consistent results to within 1% or better. In the case of the FH molecule the dependence of truncation errors of the total energy, dipole moment and polarizabilities on the geometry have been studied and are shown to be negligible.
NASA Astrophysics Data System (ADS)
Kang, K.-T.; Kim, K.-Y.; Jung, H.-J.; Lee, H.-Y.; Chun, H.-J.; Lee, H.-M.; Moon, S.-H.; Kim, H.-J.
2010-03-01
The aim of this study is to evaluate the biomechanical changes after Spinous Process Osteotomy (SPO) with different amounts of facetectomy of the lumbar spine and to compare the models with SPO and intact models using finite element models. Intact spine models and one decompression models (L3-4) with SPO were developed. SPO models included three different amounts of facetectomy (25%, 50%, and 75%). After validation of the models, finite element analyses were performed to investigate the ranges of motion and disc stresses at each corresponding level among three SPO models and intact lumbar spine models. The ranges of motion in the SPO models were increased more than the intact models. According to increase of amounts of facetectomy, ranges of motion were also increased. Similar to range of motion, the von Mises stress of disc in the SPO models was higher than that of intact models. Moreover, with the increase of amount of facetectomy, the disc stress increased at each segments under various moments. The decompression procedures using spinous process osteotomy has been reported to provide better postoperative stability compared to the conventional laminectomy. However, facetectomy over 50 % is likely to attenuate this advantage.
NASA Astrophysics Data System (ADS)
Kang, K.-T.; Kim, K.-Y.; Jung, H.-J.; Lee, H.-Y.; Chun, H.-J.; Lee, H.-M.; Moon, S.-H.; Kim, H.-J.
2009-12-01
The aim of this study is to evaluate the biomechanical changes after Spinous Process Osteotomy (SPO) with different amounts of facetectomy of the lumbar spine and to compare the models with SPO and intact models using finite element models. Intact spine models and one decompression models (L3-4) with SPO were developed. SPO models included three different amounts of facetectomy (25%, 50%, and 75%). After validation of the models, finite element analyses were performed to investigate the ranges of motion and disc stresses at each corresponding level among three SPO models and intact lumbar spine models. The ranges of motion in the SPO models were increased more than the intact models. According to increase of amounts of facetectomy, ranges of motion were also increased. Similar to range of motion, the von Mises stress of disc in the SPO models was higher than that of intact models. Moreover, with the increase of amount of facetectomy, the disc stress increased at each segments under various moments. The decompression procedures using spinous process osteotomy has been reported to provide better postoperative stability compared to the conventional laminectomy. However, facetectomy over 50 % is likely to attenuate this advantage.
Feldberg, S.W.
1991-01-01
Commencing in the early 60s the application of explicit finite difference (EFD) methods to the analysis of electrochemical problems paralleled the development and availability of fast, main-frame, digital computers. The appeal of the EFD method has been its simplicity of principle and of application. EFD algorithms, however, are notoriously inefficient for solving certain types of stiff problems (e.g., problems involving a wide dynamic range of time constants). In this presentation the author discusses the principles and some applications of a fast quasi-explicit finite difference (FQEFD) method in which the computational speed is enhanced, by many orders of magnitude in some cases, without compromising the user friendliness which has popularized the EFD method. The method is designed to treat electrochemical responses to a discontinuous (e.g, chronoamperometric) perturbation and utilizes the DuFort-Frankel algorithm (1) with exponentially expanding space (2) and exponentially expanding time grids. (A previously published version of the FQEFD method (3,4) was designed to treat electrochemical responses to a continuous (e.g., cyclic voltammetric) perturbation and utilizes the DuFort-Frankel (3) algorithm in conjunction with an exponentially expanding space grid and a uniform time grid. The development of the basic FQEFD equations was presented there). The protocol for introducing the expanding time grid is straightforward and is discussed. 7 refs., 1 fig. 1 tab.
NASA Astrophysics Data System (ADS)
Wu, Kailiang; Tang, Huazhong
2015-10-01
The paper develops high-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamical (RHD) equations, built on the local Lax-Friedrichs splitting, the WENO reconstruction, the physical-constraints-preserving flux limiter, and the high-order strong stability preserving time discretization. They are extensions of the positivity-preserving finite difference WENO schemes for the non-relativistic Euler equations [20]. However, developing physical-constraints-preserving methods for the RHD system becomes much more difficult than the non-relativistic case because of the strongly coupling between the RHD equations, no explicit formulas of the primitive variables and the flux vectors with respect to the conservative vector, and one more physical constraint for the fluid velocity in addition to the positivity of the rest-mass density and the pressure. The key is to prove the convexity and other properties of the admissible state set and discover a concave function with respect to the conservative vector instead of the pressure which is an important ingredient to enforce the positivity-preserving property for the non-relativistic case. Several one- and two-dimensional numerical examples are used to demonstrate accuracy, robustness, and effectiveness of the proposed physical-constraints-preserving schemes in solving RHD problems with large Lorentz factor, or strong discontinuities, or low rest-mass density or pressure etc.
A moving mesh finite difference method for equilibrium radiation diffusion equations
Yang, Xiaobo; Huang, Weizhang; Qiu, Jianxian
2015-10-01
An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.
A coarse-mesh nodal method-diffusive-mesh finite difference method
Joo, H.; Nichols, W.R.
1994-05-01
Modern nodal methods have been successfully used for conventional light water reactor core analyses where the homogenized, node average cross sections (XSs) and the flux discontinuity factors (DFs) based on equivalence theory can reliably predict core behavior. For other types of cores and other geometries characterized by tightly-coupled, heterogeneous core configurations, the intranodal flux shapes obtained from a homogenized nodal problem may not accurately portray steep flux gradients near fuel assembly interfaces or various reactivity control elements. This may require extreme values of DFs (either very large, very small, or even negative) to achieve a desired solution accuracy. Extreme values of DFs, however, can disrupt the convergence of the iterative methods used to solve for the node average fluxes, and can lead to a difficulty in interpolating adjacent DF values. Several attempts to remedy the problem have been made, but nothing has been satisfactory. A new coarse-mesh nodal scheme called the Diffusive-Mesh Finite Difference (DMFD) technique, as contrasted with the coarse-mesh finite difference (CMFD) technique, has been developed to resolve this problem. This new technique and the development of a few-group, multidimensional kinetics computer program are described in this paper.
A moving mesh finite difference method for equilibrium radiation diffusion equations
NASA Astrophysics Data System (ADS)
Yang, Xiaobo; Huang, Weizhang; Qiu, Jianxian
2015-10-01
An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor-corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.
NASA Astrophysics Data System (ADS)
Zehner, Björn; Hellwig, Olaf; Linke, Maik; Görz, Ines; Buske, Stefan
2016-01-01
3D geological underground models are often presented by vector data, such as triangulated networks representing boundaries of geological bodies and geological structures. Since models are to be used for numerical simulations based on the finite difference method, they have to be converted into a representation discretizing the full volume of the model into hexahedral cells. Often the simulations require a high grid resolution and are done using parallel computing. The storage of such a high-resolution raster model would require a large amount of storage space and it is difficult to create such a model using the standard geomodelling packages. Since the raster representation is only required for the calculation, but not for the geometry description, we present an algorithm and concept for rasterizing geological models on the fly for the use in finite difference codes that are parallelized by domain decomposition. As a proof of concept we implemented a rasterizer library and integrated it into seismic simulation software that is run as parallel code on a UNIX cluster using the Message Passing Interface. We can thus run the simulation with realistic and complicated surface-based geological models that are created using 3D geomodelling software, instead of using a simplified representation of the geological subsurface using mathematical functions or geometric primitives. We tested this set-up using an example model that we provide along with the implemented library.
Kudryavtsev, Oleg
2013-01-01
In the paper, we consider the problem of pricing options in wide classes of Lévy processes. We propose a general approach to the numerical methods based on a finite difference approximation for the generalized Black-Scholes equation. The goal of the paper is to incorporate the Wiener-Hopf factorization into finite difference methods for pricing options in Lévy models with jumps. The method is applicable for pricing barrier and American options. The pricing problem is reduced to the sequence of linear algebraic systems with a dense Toeplitz matrix; then the Wiener-Hopf factorization method is applied. We give an important probabilistic interpretation based on the infinitely divisible distributions theory to the Laurent operators in the correspondent factorization identity. Notice that our algorithm has the same complexity as the ones which use the explicit-implicit scheme, with a tridiagonal matrix. However, our method is more accurate. We support the advantage of the new method in terms of accuracy and convergence by using numerical experiments. PMID:24489518
2013-01-01
In the paper, we consider the problem of pricing options in wide classes of Lévy processes. We propose a general approach to the numerical methods based on a finite difference approximation for the generalized Black-Scholes equation. The goal of the paper is to incorporate the Wiener-Hopf factorization into finite difference methods for pricing options in Lévy models with jumps. The method is applicable for pricing barrier and American options. The pricing problem is reduced to the sequence of linear algebraic systems with a dense Toeplitz matrix; then the Wiener-Hopf factorization method is applied. We give an important probabilistic interpretation based on the infinitely divisible distributions theory to the Laurent operators in the correspondent factorization identity. Notice that our algorithm has the same complexity as the ones which use the explicit-implicit scheme, with a tridiagonal matrix. However, our method is more accurate. We support the advantage of the new method in terms of accuracy and convergence by using numerical experiments. PMID:24489518
Modeling of tension-modulated strings using finite difference and digital waveguide techniques
NASA Astrophysics Data System (ADS)
Pakarinen, Jyri
2005-09-01
Tension modulation is a nonlinear phenomenon where large-amplitude string vibrations cause the tension of the string to vary. This results in an initial pitch glide and energy coupling between modes, causing for example the generation of missing harmonics. The presentation discusses two methods for numerical simulation of the tension modulation nonlinearity from the sound synthesis point of view. The tension modulation is assumed to propagate instantaneously along the string. In the digital waveguide approach, spatially distributed fractional delay filters are used in modulating the string length during run time. Energy-preserving techniques can be used in implementing the fractional delays. In the finite difference approach, time-domain interpolation is used to artificially modulate the wave propagation velocity. The generation of missing harmonics is implemented in the finite difference model by creating an additional excitation point at the string termination. In the waveguide model, the same effect can be obtained by using suitable approximations in the string elongation calculation. Synthesis results for both techniques are presented. Also, a brief comparison of the models with a discussion on stability issues is provided. [This research has been funded by the Academy of Finland (Project No. 104934), S3TK graduate school, and Tekniikan edistamissaatio.
Converged accelerated finite difference scheme for the multigroup neutron diffusion equation
Terranova, N.; Mostacci, D.; Ganapol, B. D.
2013-07-01
Computer codes involving neutron transport theory for nuclear engineering applications always require verification to assess improvement. Generally, analytical and semi-analytical benchmarks are desirable, since they are capable of high precision solutions to provide accurate standards of comparison. However, these benchmarks often involve relatively simple problems, usually assuming a certain degree of abstract modeling. In the present work, we show how semi-analytical equivalent benchmarks can be numerically generated using convergence acceleration. Specifically, we investigate the error behavior of a 1D spatial finite difference scheme for the multigroup (MG) steady-state neutron diffusion equation in plane geometry. Since solutions depending on subsequent discretization can be envisioned as terms of an infinite sequence converging to the true solution, extrapolation methods can accelerate an iterative process to obtain the limit before numerical instability sets in. The obtained results have been compared to the analytical solution to the 1D multigroup diffusion equation when available, using FORTRAN as the computational language. Finally, a slowing down problem has been solved using a cascading source update, showing how a finite difference scheme performs for ultra-fine groups (104 groups) in a reasonable computational time using convergence acceleration. (authors)
Hurrell, Andrew M
2008-06-01
The interaction of an incident sound wave with an acoustically impenetrable two-layer barrier is considered. Of particular interest is the presence of several acoustic wave components in the shadow region of this barrier. A finite difference model capable of simulating this geometry is validated by comparison to the analytical solution for an idealized, hard-soft barrier. A panel comprising a high air-content closed cell foam backed with an elastic (metal) back plate is then examined. The insertion loss of this panel was found to exceed the dynamic range of the measurement system and was thus acoustically impenetrable. Experimental results from such a panel are shown to contain artifacts not present in the diffraction solution, when acoustic waves are incident upon the soft surface. A finite difference analysis of this experimental configuration replicates the presence of the additional field components. Furthermore, the simulated results allow the additional components to be identified as arising from the S(0) and A(0) Lamb modes traveling in the elastic plate. These Lamb mode artifacts are not found to be present in the shadow region when the acoustic waves are incident upon the elastic surface. PMID:18537372
Accuracy issues in the finite difference time domain simulation of photomask scattering
NASA Astrophysics Data System (ADS)
Pistor, Thomas V.
2001-09-01
As the use of electromagnetic simulation in lithography increases, accuracy issues are uncovered and must be addressed. A proper understanding of these issues can allow the lithographer to avoid pitfalls in electromagnetic simulation and to know what can and can not be accurately simulated. This paper addresses the important accuracy issues related to the simulation of photomask scattering using the Finite Difference Time Domain (FDTD) method. Errors related to discretization and periodic boundary conditions are discussed. Discretization-related issues arise when derivatives are replaced by finite differences and when integrals are replaced by summations. These approximations can lead to mask features that do not have exact dimensions. The effects of discretization error on phase wells and thin films are shown. The reflectivity of certain thin film layers is seen to be very sensitive to the layer thickness. Simulation experiments and theory are used to determine how fine a discretization is necessary and various discretization schemes that help minimize error are presented. Boundary-condition-related errors arise from the use of periodic boundary conditions when simulating isolated mask features. The effects of periodic boundary conditions are assessed through the use of simulation experiments. All errors are associated with an ever-present trade-off between accuracy and computational resources. However, choosing the cell size wisely can, in many cases, minimize error without significantly increasing computation resource requirements.
Real-space finite difference scheme for the von Neumann equation with the Dirac Hamiltonian
NASA Astrophysics Data System (ADS)
Schreilechner, Magdalena; Pötz, Walter
2016-07-01
A finite difference scheme for the numerical treatment of the von Neumann equation for the (2+1)D Dirac Hamiltonian is presented. It is based on a sequential left-right (ket-bra) application of a staggered space-time scheme for the pure-state Dirac equation and offers a numerical treatment of the general mixed-state dynamics of an isolated quantum system within the von Neumann equation. Thereby this direct scheme inherits all the favorable features of the finite-difference scheme for the pure-state Dirac equation, such as the single-cone energy-momentum dispersion, convergence conditions, and scaling behavior. A conserved functional is identified. Moreover this scheme is shown to conserve both Hermiticity and positivity. Numerical tests comprise a numerical analysis of stability, as well as the simulation of a mixed-state time-evolution of Gaussian wave functions, illustrating Zitterbewegung and transverse current oscillations. Imaginary-potential absorbing boundary conditions and parameters which pertain to topological insulator surface states were used in the numerical simulations.
Development of an advanced finite-difference atmospheric general circulation model
Randall, D.A.
1992-03-01
We have proposed to provide and further develop an advanced finite-difference climate model for use in CHAMMP. The model includes advanced parameterizations of cumulus convection, boundary-layer processes, cloud formation, and land-surface vegetation, as well as parameterizations of radiative transfer and gravity wave drag. Postprocessing codes and a user's guide will also be provided. This research is being conducted in collaboration with Professors C.R. Mechoso and A. Arakawa at the University of California at Los Angeles (UCLA). The following research tasks are being carried out in support of CHAMMP: (1) Provide to CHAMMP a base-line finite-difference model and postprocessing codes for further development by the CHAMMP Science Team; (2) Provide to CHAMMP improved model physics to be developed in the course of our research project; (3) Provide to CHAMMP improved computational methods for use in the model; and, (4) Investigate the performance of current and to-be-developed physical parameterizations and computational methods at very high resolution.
ATLAS: A real-space finite-difference implementation of orbital-free density functional theory
NASA Astrophysics Data System (ADS)
Mi, Wenhui; Shao, Xuecheng; Su, Chuanxun; Zhou, Yuanyuan; Zhang, Shoutao; Li, Quan; Wang, Hui; Zhang, Lijun; Miao, Maosheng; Wang, Yanchao; Ma, Yanming
2016-03-01
Orbital-free density functional theory (OF-DFT) is a promising method for large-scale quantum mechanics simulation as it provides a good balance of accuracy and computational cost. Its applicability to large-scale simulations has been aided by progress in constructing kinetic energy functionals and local pseudopotentials. However, the widespread adoption of OF-DFT requires further improvement in its efficiency and robustly implemented software. Here we develop a real-space finite-difference (FD) method for the numerical solution of OF-DFT in periodic systems. Instead of the traditional self-consistent method, a powerful scheme for energy minimization is introduced to solve the Euler-Lagrange equation. Our approach engages both the real-space finite-difference method and a direct energy-minimization scheme for the OF-DFT calculations. The method is coded into the ATLAS software package and benchmarked using periodic systems of solid Mg, Al, and Al3Mg. The test results show that our implementation can achieve high accuracy, efficiency, and numerical stability for large-scale simulations.
2015-01-01
PURPOSE The objective of this study was to evaluate the influence of various cement types on the stress distribution in monolithic zirconia crowns under maximum bite force using the finite element analysis. MATERIALS AND METHODS The models of the prepared #46 crown (deep chamfer margin) were scanned and solid models composed of the monolithic zirconia crown, cement layer, and prepared tooth were produced using the computer-aided design technology and were subsequently translated into 3-dimensional finite element models. Four models were prepared according to different cement types (zinc phosphate, polycarboxylate, glass ionomer, and resin). A load of 700 N was applied vertically on the crowns (8 loading points). Maximum principal stress was determined. RESULTS Zinc phosphate cement had a greater stress concentration in the cement layer, while polycarboxylate cement had a greater stress concentration on the distal surface of the monolithic zirconia crown and abutment tooth. Resin cement and glass ionomer cement showed similar patterns, but resin cement showed a lower stress distribution on the lingual and mesial surface of the cement layer. CONCLUSION The test results indicate that the use of different luting agents that have various elastic moduli has an impact on the stress distribution of the monolithic zirconia crowns, cement layers, and abutment tooth. Resin cement is recommended for the luting agent of the monolithic zirconia crowns. PMID:26816578
Parallelized implicit propagators for the finite-difference Schrödinger equation
NASA Astrophysics Data System (ADS)
Parker, Jonathan; Taylor, K. T.
1995-08-01
We describe the application of block Gauss-Seidel and block Jacobi iterative methods to the design of implicit propagators for finite-difference models of the time-dependent Schrödinger equation. The block-wise iterative methods discussed here are mixed direct-iterative methods for solving simultaneous equations, in the sense that direct methods (e.g. LU decomposition) are used to invert certain block sub-matrices, and iterative methods are used to complete the solution. We describe parallel variants of the basic algorithm that are well suited to the medium- to coarse-grained parallelism of work-station clusters, and MIMD supercomputers, and we show that under a wide range of conditions, fine-grained parallelism of the computation can be achieved. Numerical tests are conducted on a typical one-electron atom Hamiltonian. The methods converge robustly to machine precision (15 significant figures), in some cases in as few as 6 or 7 iterations. The rate of convergence is nearly independent of the finite-difference grid-point separations.
NASA Technical Reports Server (NTRS)
Stein, M.; Housner, J. D.
1978-01-01
A numerical analysis developed for the buckling of rectangular orthotropic layered panels under combined shear and compression is described. This analysis uses a central finite difference procedure based on trigonometric functions instead of using the conventional finite differences which are based on polynomial functions. Inasmuch as the buckle mode shape is usually trigonometric in nature, the analysis using trigonometric finite differences can be made to exhibit a much faster convergence rate than that using conventional differences. Also, the trigonometric finite difference procedure leads to difference equations having the same form as conventional finite differences; thereby allowing available conventional finite difference formulations to be converted readily to trigonometric form. For two-dimensional problems, the procedure introduces two numerical parameters into the analysis. Engineering approaches for the selection of these parameters are presented and the analysis procedure is demonstrated by application to several isotropic and orthotropic panel buckling problems. Among these problems is the shear buckling of stiffened isotropic and filamentary composite panels in which the stiffener is broken. Results indicate that a break may degrade the effect of the stiffener to the extent that the panel will not carry much more load than if the stiffener were absent.
NASA Astrophysics Data System (ADS)
Appadu, A. R.
2016-06-01
An unconditionally positive definite scheme has been derived in [1] to approximate a linear advection-diffusion-reaction equation which models exponential travelling waves and the coefficients of advective, diffusive and reactive terms have been chosen as one. The scheme has been baptised as Unconditionally Positive Finite Difference (UPFD). In this work, we use the UPFD scheme to solve the advection-diffusion-reaction problem in [1] and we also extend our study to three other important regimes involved in this model. The temporal step size is varied while fixing the spatial step size. We compute some errors namely; L1 error, dispersion, dissipation errors. We also study the variation of the modulus of the exact amplification factor, modulus of amplification factor of the scheme and relative phase error, all vs the phase angle for the four different regimes.
NASA Astrophysics Data System (ADS)
Vasyliv, Yaroslav; Alexeev, Alexander
2015-11-01
In the meshfree family of methods, partial differential equations are solved on unstructured grids where a search radius establishes an implicit nodal connectivity used to determine whether to include or exclude neighboring nodes in the constructed approximation. Smoothed Particle Hydrodynamics (SPH) is widely attributed to be the eldest of the meshfree methods dating back to an astrophysics paper published in 1977 by Gingold and Monaghan. However, beating them by five years was Jensen when he published Finite Differences for Arbitrary Grids (FIDAG) in 1972. Ultimately this work and others were generalized by Liszka and Orkisz in 1979 as a weighted least squares formulation solving for the Taylor coefficients and is now commonly known as General Finite Differences (GFD). Shortly after in 1981, Lancaster and Salkauskas introduced the Moving Least Squares (MLS) approximation for surface reconstruction using a weighted least squares formulation where the unknown coefficients are treated as functions varying from node to node in the support domain. Here we examine important differences, similarities and limitations of each method by solving the 2D Poisson equation on unstructured grids. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1148903.
NASA Technical Reports Server (NTRS)
Handschuh, Robert F.
1987-01-01
An exponential finite difference algorithm, as first presented by Bhattacharya for one-dimensianal steady-state, heat conduction in Cartesian coordinates, has been extended. The finite difference algorithm developed was used to solve the diffusion equation in one-dimensional cylindrical coordinates and applied to two- and three-dimensional problems in Cartesian coordinates. The method was also used to solve nonlinear partial differential equations in one (Burger's equation) and two (Boundary Layer equations) dimensional Cartesian coordinates. Predicted results were compared to exact solutions where available, or to results obtained by other numerical methods. It was found that the exponential finite difference method produced results that were more accurate than those obtained by other numerical methods, especially during the initial transient portion of the solution. Other applications made using the exponential finite difference technique included unsteady one-dimensional heat transfer with temperature varying thermal conductivity and the development of the temperature field in a laminar Couette flow.
NASA Astrophysics Data System (ADS)
Deng, Xiaogang; Mao, Meiliang; Tu, Guohua; Liu, Huayong; Zhang, Hanxin
2011-02-01
The geometric conservation law (GCL) includes the volume conservation law (VCL) and the surface conservation law (SCL). Though the VCL is widely discussed for time-depending grids, in the cases of stationary grids the SCL also works as a very important role for high-order accurate numerical simulations. The SCL is usually not satisfied on discretized grid meshes because of discretization errors, and the violation of the SCL can lead to numerical instabilities especially when high-order schemes are applied. In order to fulfill the SCL in high-order finite difference schemes, a conservative metric method (CMM) is presented. This method is achieved by computing grid metric derivatives through a conservative form with the same scheme applied for fluxes. The CMM is proven to be a sufficient condition for the SCL, and can ensure the SCL for interior schemes as well as boundary and near boundary schemes. Though the first-level difference operators δ3 have no effects on the SCL, no extra errors can be introduced as δ3 = δ2. The generally used high-order finite difference schemes are categorized as central schemes (CS) and upwind schemes (UPW) based on the difference operator δ1 which are used to solve the governing equations. The CMM can be applied to CS and is difficult to be satisfied by UPW. Thus, it is critical to select the difference operator δ1 to reduce the SCL-related errors. Numerical tests based on WCNS-E-5 show that the SCL plays a very important role in ensuring free-stream conservation, suppressing numerical oscillations, and enhancing the robustness of the high-order scheme in complex grids.
2d PDE Linear Symmetric Matrix Solver
1983-10-01
ICCG2 (Incomplete Cholesky factorized Conjugate Gradient algorithm for 2d symmetric problems) was developed to solve a linear symmetric matrix system arising from a 9-point discretization of two-dimensional elliptic and parabolic partial differential equations found in plasma physics applications, such as resistive MHD, spatial diffusive transport, and phase space transport (Fokker-Planck equation) problems. These problems share the common feature of being stiff and requiring implicit solution techniques. When these parabolic or elliptic PDE''s are discretized withmore » finite-difference or finite-element methods,the resulting matrix system is frequently of block-tridiagonal form. To use ICCG2, the discretization of the two-dimensional partial differential equation and its boundary conditions must result in a block-tridiagonal supermatrix composed of elementary tridiagonal matrices. The incomplete Cholesky conjugate gradient algorithm is used to solve the linear symmetric matrix equation. Loops are arranged to vectorize on the Cray1 with the CFT compiler, wherever possible. Recursive loops, which cannot be vectorized, are written for optimum scalar speed. For matrices lacking symmetry, ILUCG2 should be used. Similar methods in three dimensions are available in ICCG3 and ILUCG3. A general source containing extensions and macros, which must be processed by a pre-compiler to obtain the standard FORTRAN source, is provided along with the standard FORTRAN source because it is believed to be more readable. The pre-compiler is not included, but pre-compilation may be performed by a text editor as described in the UCRL-88746 Preprint.« less
2d PDE Linear Asymmetric Matrix Solver
1983-10-01
ILUCG2 (Incomplete LU factorized Conjugate Gradient algorithm for 2d problems) was developed to solve a linear asymmetric matrix system arising from a 9-point discretization of two-dimensional elliptic and parabolic partial differential equations found in plasma physics applications, such as plasma diffusion, equilibria, and phase space transport (Fokker-Planck equation) problems. These equations share the common feature of being stiff and requiring implicit solution techniques. When these parabolic or elliptic PDE''s are discretized with finite-difference or finite-elementmore » methods, the resulting matrix system is frequently of block-tridiagonal form. To use ILUCG2, the discretization of the two-dimensional partial differential equation and its boundary conditions must result in a block-tridiagonal supermatrix composed of elementary tridiagonal matrices. A generalization of the incomplete Cholesky conjugate gradient algorithm is used to solve the matrix equation. Loops are arranged to vectorize on the Cray1 with the CFT compiler, wherever possible. Recursive loops, which cannot be vectorized, are written for optimum scalar speed. For problems having a symmetric matrix ICCG2 should be used since it runs up to four times faster and uses approximately 30% less storage. Similar methods in three dimensions are available in ICCG3 and ILUCG3. A general source, containing extensions and macros, which must be processed by a pre-compiler to obtain the standard FORTRAN source, is provided along with the standard FORTRAN source because it is believed to be more readable. The pre-compiler is not included, but pre-compilation may be performed by a text editor as described in the UCRL-88746 Preprint.« less
NASA Technical Reports Server (NTRS)
Nordstrom, Jan; Carpenter, Mark H.
1998-01-01
Boundary and interface conditions for high order finite difference methods applied to the constant coefficient Euler and Navier-Stokes equations are derived. The boundary conditions lead to strict and strong stability. The interface conditions are stable and conservative even if the finite difference operators and mesh sizes vary from domain to domain. Numerical experiments show that the new conditions also lead to good results for the corresponding nonlinear problems.
Improved finite-difference computation of the van der Waals force: One-dimensional case
Pinto, Fabrizio
2009-10-15
We present an improved demonstration of the calculation of Casimir forces in one-dimensional systems based on the recently proposed numerical imaginary frequency Green's function computation approach. The dispersion force on two thick lossy dielectric slabs separated by an empty gap and placed within a perfectly conducting cavity is obtained from the Green's function of the modified Helmholtz equation by means of an ordinary finite-difference method. In order to demonstrate the possibility to develop algorithms to explore complex geometries in two and three dimensions to higher order in the mesh spacing, we generalize existing classical electromagnetism algebraic methods to generate the difference equations for dielectric boundaries not coinciding with any grid points. Diagnostic tests are presented to monitor the accuracy of our implementation of the method and follow-up applications in higher dimensions are introduced.
Finite Difference Time Domain Electromagnetic Scattering from Frequency-Dependent Lossy Materials
NASA Technical Reports Server (NTRS)
Luebbers, Raymond J.; Beggs, John H.
1991-01-01
During this effort the tasks specified in the Statement of Work have been successfully completed. The extension of Finite Difference Time Domain (FDTD) to more complicated materials has been made. A three-dimensional FDTD code capable of modeling interactions with both dispersive dielectric and magnetic materials has been written, validated, and documented. This code is efficient and is capable of modeling interesting targets using a modest computer work station platform. However, in addition to the tasks in the Statement of Work, a significant number of other FDTD extensions and calculations have been made. RCS results for two different plate geometries have been reported. The FDTD method has been extended to computing far zone time domain results in two dimensions. Finally, the capability to model nonlinear materials has been incorporated into FDTD and validated. The FDTD computer codes developed have been supplied, along with documentation, and preprints describing the other FDTD advances have been included with this report as attachments.
Computationally efficient finite-difference modal method for the solution of Maxwell's equations.
Semenikhin, Igor; Zanuccoli, Mauro
2013-12-01
In this work, a new implementation of the finite-difference (FD) modal method (FDMM) based on an iterative approach to calculate the eigenvalues and corresponding eigenfunctions of the Helmholtz equation is presented. Two relevant enhancements that significantly increase the speed and accuracy of the method are introduced. First of all, the solution of the complete eigenvalue problem is avoided in favor of finding only the meaningful part of eigenmodes by using iterative methods. Second, a multigrid algorithm and Richardson extrapolation are implemented. Simultaneous use of these techniques leads to an enhancement in terms of accuracy, which allows a simple method such as the FDMM with a typical three-point difference scheme to be significantly competitive with an analytical modal method. PMID:24323014
NASA Technical Reports Server (NTRS)
Lansing, F. L.
1976-01-01
A numerical procedure was established using the finite-difference technique in the determination of the time-varying temperature distribution of a tubular solar collector under changing solar radiancy and ambient temperature. Three types of spatial discretization processes were considered and compared for their accuracy of computations and for selection of the shortest computer time and cost. The stability criteria of this technique was analyzed in detail to give the critical time increment to ensure stable computations. The results of the numerical analysis were in good agreement with the analytical solution previously reported. The numerical method proved to be a powerful tool in the investigation of the collector sensitivity to two different flow patterns and several flow control mechanisms.
Samak, M. Mosleh E. Abu; Bakar, A. Ashrif A.; Kashif, Muhammad; Zan, Mohd Saiful Dzulkifly
2016-01-01
This paper discusses numerical analysis methods for different geometrical features that have limited interval values for typically used sensor wavelengths. Compared with existing Finite Difference Time Domain (FDTD) methods, the alternating direction implicit (ADI)-FDTD method reduces the number of sub-steps by a factor of two to three, which represents a 33% time savings in each single run. The local one-dimensional (LOD)-FDTD method has similar numerical equation properties, which should be calculated as in the previous method. Generally, a small number of arithmetic processes, which result in a shorter simulation time, are desired. The alternating direction implicit technique can be considered a significant step forward for improving the efficiency of unconditionally stable FDTD schemes. This comparative study shows that the local one-dimensional method had minimum relative error ranges of less than 40% for analytical frequencies above 42.85 GHz, and the same accuracy was generated by both methods.
NASA Astrophysics Data System (ADS)
Arias-Ramirez, Walter; Olson, Britton; Wolf, William; Lawrence Livermore National Laboratory Team; University of Campinas Team
2015-11-01
The suitability of a continuing forcing immersed boundary method (IBM) combined with a high-order finite difference method is examined on several acoustic scattering problems. A suite of two-dimensional numerical simulations of canonical cases are conducted with the aim of analyzing the error behavior associated with the IBM, through wave reflection, wave diffraction, and the shock-boundary layer interaction phenomena. The compressible Navier-Stokes equations are solved using the Miranda code developed at Lawrence Livermore National Laboratory. Comparison of analytical solution against numerical results is shown for different flow parameters. Preliminary results indicate that the continuing forcing approach has the largest error in wave reflection compared to analytical solution. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract No. DE-AC52-07NA27344.
Exact finite-size corrections for the spanning-tree model under different boundary conditions
NASA Astrophysics Data System (ADS)
Izmailian, N. Sh.; Kenna, R.
2015-02-01
We express the partition functions of the spanning tree on finite square lattices under five different sets of boundary conditions in terms of a principal partition function with twisted-boundary conditions. Based on these expressions, we derive the exact asymptotic expansions of the logarithm of the partition function for each case. We have also established several groups of identities relating spanning-tree partition functions for the different boundary conditions. We also explain an apparent discrepancy between logarithmic correction terms in the free energy for a two-dimensional spanning-tree model with periodic and free-boundary conditions and conformal field theory predictions. We have obtained corner free energy for the spanning tree under free-boundary conditions in full agreement with conformal field theory predictions.
Seismic effects of viscous Biot-coupling: Finite difference simulations on micro-scale
NASA Astrophysics Data System (ADS)
Saenger, E. H.; Shapiro, S. A.; Keehm, Y.
2005-07-01
This paper is concerned with numerical considerations of viscous fluid effects on wave propagation in porous media. We apply a displacement-stress rotated staggered finite-difference (FD) grid technique to solve the elastodynamic wave equation. An accurate approximation of a Newtonian fluid is implemented in this technique by using a generalized Maxwell body. With this approach we consider the velocity predictions of the Biot theory for elastic waves in different digital rock samples. To distinguish between the low and the high frequency range we estimate the effective permeabilities by a flow simulation. Our numerical results indicate that the viscous Biot-coupling is visible in the numerical experiments. Moreover, the influences of other solid-fluid interactions (e.g., Squirt flow) are also discussed.
NASA Astrophysics Data System (ADS)
Jang, Jihyeon; Hong, Song-You
2016-04-01
The spectral method is generally assumed to provide better numerical accuracy than the finite difference method. However, the majority of regional models use finite discretization methods due to the difficulty of specifying time-dependent lateral boundary conditions in spectral models. This study evaluates the behavior of nonhydrostatic dynamics with a spectral discretization. To this end, Juang's nonhydrostatic dynamical core for the National Centers for Environmental Prediction (NCEP) regional spectral model has been implemented into the Regional Model Program (RMP) of the Global/Regional Integrated Model system (GRIMs). The behavior of the nonhydrostatic RMP is validated, and compared with that of the hydrostatic core in 2-D idealized experiments: the mountain wave, rising thermal bubble, and density current experiments. The nonhydrostatic effect in the RMP is further validated in comparison with the results from the Weather Research and Forecasting (WRF) model, which uses a finite difference method. The analyses of the experimental results from the RMP generally follow the characteristics found in previous studies without any discernible difference. For example, in both the RMP and the WRF model, the eastward-tilted propagation of mountain waves is very similar in the nonhydrostatic core experiments. Both nonhydrostatic models also efficiently reproduce the motion and deformation of the warm and cold bubbles, but the RMP results contain more small-scale noise. In a 1-km real-case simulation testbed, the lee waves that originate over the eastern flank of the Korean peninsula travel further eastward in the WRF model than in the RMP. It is found that differences of small-scale wave characteristics between the RMP and WRF model are mainly from the numerical techniques used, such as the accuracy of the advection scheme and the magnitude of the numerical diffusion, rather than from discrepancies in the spatial discretization.
NASA Astrophysics Data System (ADS)
Borisov, Dmitry; Singh, Satish C.; Fuji, Nobuaki
2015-09-01
Seismic full waveform inversion is an objective method to estimate elastic properties of the subsurface and is an important area of research, particularly in seismic exploration community. It is a data-fitting approach, where the difference between observed and synthetic data is minimized iteratively. Due to a very high computational cost, the practical implementation of waveform inversion has so far been restricted to a 2-D geometry with different levels of physics incorporated in it (e.g. elasticity/viscoelasticity) or to a 3-D geometry but using an acoustic approximation. However, the earth is three-dimensional, elastic and heterogeneous and therefore a full 3-D elastic inversion is required in order to obtain more accurate and valuable models of the subsurface. Despite the recent increase in computing power, the application of 3-D elastic full waveform inversion to real-scale problems remains quite challenging on the current computer architecture. Here, we present an efficient method to perform 3-D elastic full waveform inversion for time-lapse seismic data using a finite-difference injection method. In this method, the wavefield is computed in the whole model and is stored on a surface above a finite volume where the model is perturbed and localized inversion is performed. Comparison of the final results using the 3-D finite-difference injection method and conventional 3-D inversion performed within the whole volume shows that our new method provides significant reductions in computational time and memory requirements without any notable loss in accuracy. Our approach shows a big potential for efficient reservoir monitoring in real time-lapse experiments.
Transfer-matrix approach for finite-difference time-domain simulation of periodic structures.
Deinega, Alexei; Belousov, Sergei; Valuev, Ilya
2013-11-01
Optical properties of periodic structures can be calculated using the transfer-matrix approach, which establishes a relation between amplitudes of the wave incident on a structure with transmitted or reflected waves. The transfer matrix can be used to obtain transmittance and reflectance spectra of finite periodic structures as well as eigenmodes of infinite structures. Traditionally, calculation of the transfer matrix is performed in the frequency domain and involves linear algebra. In this work, we present a technique for calculation of the transfer matrix using the finite-difference time-domain (FDTD) method and show the way of its implementation in FDTD code. To illustrate the performance of our technique we calculate the transmittance spectra for opal photonic crystal slabs consisting of multiple layers of spherical scatterers. Our technique can be used for photonic band structure calculations. It can also be combined with existing FDTD methods for the analysis of periodic structures at an oblique incidence, as well as for modeling point sources in a periodic environment. PMID:24329377
Reddy, Jaggari Chandrakanth; Srikakula, Naveen Kumar; Juturu, Rajesh Kumar Reddy; Paidi, Shameen Kumar; Tedlapu, Satyendra Kumar; Mannava, Padmakanth; Khatoon, Rukhaiya
2016-01-01
Introduction Retention and esthetics are believed to play a crucial role in deciding the success of removable partial dentures. Aim To compare retention of acetal resin and cobalt–chromium clasps. Materials and Methods A finite element model was designed with an edentulous space between mandibular right second premolar and second molar. Occlusal rests were placed on distal fossa of the second premolar and mesial fossa of second molar. An undercut depth of 0.01inch was created on the mesiobuccal surface of the premolar and distobuccal surface of second molar. Three dimensional finite element model of clasp assembly was designed and assigned with the properties of two different materials namely acetal resin and cobalt–chromium in successive steps. A horizontal bar was constructed between the occlusal rests of the prosthesis. Later, variable amount of dislodging force, in increasing order, was applied at the centre of the horizontal bar and the force at which the clasp arm gets dislodged was noted with respect to each of the material. The obtained values were noted and then subsequently analyzed. Results The amount of force required to dislodge acetal resin and cobalt–chromium clasps was found to be 0.02N and 2N respectively. Conclusion The results obtained suggested that acetal resin clasp exhibited less retentive force than cobalt–chromium clasps. PMID:27437346