Search results for "fast direct solver"

A fast Fourier transform based direct solver for the Helmholtz problem

2018

This article is devoted to the efficient numerical solution of the Helmholtz equation in a two‐ or three‐dimensional (2D or 3D) rectangular domain with an absorbing boundary condition (ABC). The Helmholtz problem is discretized by standard bilinear and trilinear finite elements on an orthogonal mesh yielding a separable system of linear equations. The main key to high performance is to employ the fast Fourier transform (FFT) within a fast direct solver to solve the large separable systems. The computational complexity of the proposed FFT‐based direct solver is O(N log N) operations. Numerical results for both 2D and 3D problems are presented confirming the efficiency of the method discussed…

On solving separable block tridiagonal linear systems using a GPU implementation of radix-4 PSCR method

2018

Partial solution variant of the cyclic reduction (PSCR) method is a direct solver that can be applied to certain types of separable block tridiagonal linear systems. Such linear systems arise, e.g., from the Poisson and the Helmholtz equations discretized with bilinear finite-elements. Furthermore, the separability of the linear system entails that the discretization domain has to be rectangular and the discretization mesh orthogonal. A generalized graphics processing unit (GPU) implementation of the PSCR method is presented. The numerical results indicate up to 24-fold speedups when compared to an equivalent CPU implementation that utilizes a single CPU core. Attained floating point perfor…

On GPU-accelerated fast direct solvers and their applications in image denoising

2015