Fast Poisson solvers for spectral methods

Fast Poisson Solvers for Graphics Processing Units

Two block cyclic reduction linear system solvers are considered and implemented using the OpenCL framework. The topics of interest include a simplified scalar cyclic reduction tridiagonal system solver and the impact of increasing the radix-number of the algorithm. Both implementations are tested for the Poisson problem in two and three dimensions, using a Nvidia GTX 580 series GPU and double p...

Fast Poisson-based Solvers for Linear and Nonlinear PDEs

Over the last few decades, developing efficient iterative methods for solving discretized partial differential equations (PDEs) has been a topic of intensive research. Though these efforts have yielded many mathematically optimal solvers, such as the multigrid method, the unfortunate reality is that multigrid methods have not been used much in practical applications. This marked gap between the...

Poisson Solvers

Fast Solvers for Models of Fluid Flow with Spectral Elements

Title of dissertation: FAST SOLVERS FOR MODELS OF FLUID FLOW WITH SPECTRAL ELEMENTS P. Aaron Lott, Doctor of Philosophy, 2008 Dissertation directed by: Professor Howard Elman Department of Computer Science Institute for Advanced Computer Studies & Associate Research Professor Anil Deane Institute for Physical Sciences and Technology We introduce a preconditioning technique based on Domain Decom...

Fast finite difference Poisson solvers on heterogeneous architectures

In this paper we propose and evaluate a set of new strategies for the solution of three dimensional separable elliptic problems on CPU-GPU platforms. The numerical solution of the system of linear equations arising when discretizing those operators often represents the most time consuming part of larger simulation codes tackling a variety of physical situations. Incompressible fluid flows, elec...