Matrix-dependent prolongations and restrictions in a blackbox multigrid solver
Journal of Computational and Applied Mathematics
SIAM Journal on Scientific and Statistical Computing
Matrix computations (3rd ed.)
A Multigrid Method Enhanced by Krylov Subspace Iteration for Discrete Helmholtz Equations
SIAM Journal on Scientific Computing
Separation-of-variables as a preconditioner for an iterative Helmholtz solver
Applied Numerical Mathematics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Preconditioning techniques for the solution of the Helmholtz equation by the finite element method
Mathematics and Computers in Simulation - Special issue: Wave phenomena in physics and engineering: New models, algorithms, and appications
On a class of preconditioners for solving the Helmholtz equation
Applied Numerical Mathematics
A Novel Multigrid Based Preconditioner For Heterogeneous Helmholtz Problems
SIAM Journal on Scientific Computing
Journal of Scientific Computing
SIAM Journal on Scientific Computing
Debunking the 100X GPU vs. CPU myth: an evaluation of throughput computing on CPU and GPU
Proceedings of the 37th annual international symposium on Computer architecture
Algorithm 913: An elegant IDR(s) variant that efficiently exploits biorthogonality properties
ACM Transactions on Mathematical Software (TOMS)
Robust and highly scalable parallel solution of the Helmholtz equation with large wave numbers
Journal of Computational and Applied Mathematics
A generalized Block FSAI preconditioner for nonsymmetric linear systems
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
A Helmholtz equation in two dimensions discretized by a second order finite difference scheme is considered. Krylov methods such as Bi-CGSTAB and IDR(s) have been chosen as solvers. Since the convergence of the Krylov solvers deteriorates with increasing wave number, a shifted Laplace multigrid preconditioner is used to improve the convergence. The implementation of the preconditioned solver on CPU (Central Processing Unit) is compared to an implementation on GPU (Graphics Processing Units or graphics card) using CUDA (Compute Unified Device Architecture). The results show that preconditioned Bi-CGSTAB on GPU as well as preconditioned IDR(s) on GPU is about 30 times faster than on CPU for the same stopping criterion.