Solution of elliptic PDEs by fast Poisson solvers using a local relaxation factor
Journal of Computational Physics
Solving tridiagonal systems on ensemble architectures
SIAM Journal on Scientific and Statistical Computing
Fast Fourier transforms for direct solution of Poisson's equation with staggered boundary conditions
Journal of Computational Physics
Computer simulation using particles
Computer simulation using particles
A Fast Direct Solution of Poisson's Equation Using Fourier Analysis
Journal of the ACM (JACM)
Waveform Relaxation with Fast Direct Methods as Preconditioner
SIAM Journal on Scientific Computing
Automatically tuned collective communications
Proceedings of the 2000 ACM/IEEE conference on Supercomputing
Fast parallel direct solvers for Coarse Grid problems
Journal of Parallel and Distributed Computing
Numerical Linear Algebra for High Performance Computers
Numerical Linear Algebra for High Performance Computers
Parallel Computers Two: Architecture, Programming and Algorithms
Parallel Computers Two: Architecture, Programming and Algorithms
The Convergence of Spectral and Finite Difference Methods for Initial-Boundary Value Problems
SIAM Journal on Scientific Computing
MPI solver for 3D elasticity problems
Mathematics and Computers in Simulation - MODELLING 2001 - Second IMACS conference on mathematical modelling and computational methods in mechanics, physics, biomechanics and geodynamics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Tutorial on Elliptic PDE Solvers and Their Parallelization
Tutorial on Elliptic PDE Solvers and Their Parallelization
Efficient collective communication in distributed heterogeneous systems
Journal of Parallel and Distributed Computing
Approximate Solution Methods in Engineering Mechanics
Approximate Solution Methods in Engineering Mechanics
Numerical treatment of two-dimensional interfaces for acoustic and elastic waves
Journal of Computational Physics
A Fast Spectral Subtractional Solver for Elliptic Equations
Journal of Scientific Computing
Finite Differences And Partial Differential Equations
Finite Differences And Partial Differential Equations
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
An Introduction to Parallel and Vector Scientific Computation (Cambridge Texts in Applied Mathematics)
High-order schemes for acoustic waveform simulation
Applied Numerical Mathematics
An efficient direct parallel spectral-element solver for separable elliptic problems
Journal of Computational Physics
A domain decomposition solver for acoustic scattering by elastic objects in layered media
Journal of Computational Physics
Computational Mathematics and Mathematical Physics
Hi-index | 31.45 |
A high-performance parallel algorithm is proposed for modeling the propagation of acoustic and elastic waves in inhomogeneous media. An initial boundary-value problem is replaced by a series of boundary-value problems for a constant elliptic operator and different right-hand sides via the integral Laguerre transform. It is proposed to solve difference equations by the conjugate gradient method for acoustic equations and by the GMRES(k) method for modeling elastic waves. A preconditioning operator was the Laplace operator that is inverted using the variable separation method. The novelty of the proposed algorithm is using the Dichotomy Algorithm [26], which was designed for solving a series of tridiagonal systems of linear equations, in the context of the preconditioning operator inversion. Via considering analytical solutions, it is shown that modeling wave processes for long instants of time requires high-resolution meshes. The proposed parallel fine-mesh algorithm enabled to solve real application seismic problems in acceptable time and with high accuracy. By solving model problems, it is demonstrated that the considered parallel algorithm possesses high performance and efficiency over a wide range of the number of processors (from 2 to 8192).