Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed

Composing Scalable Nonlinear Algebraic Solvers

Most efficient linear solvers use composable algorithmic components, with the most common model being the combination of a Krylov accelerator and one or more preconditioners. A similar set of concepts may be used for nonlinear algebraic systems, where nonlinear composition of different nonlinear solvers may significantly improve the time to solution. We describe the basic concepts of nonlinear composition and preconditioning and present a number of solvers applicable to nonlinear partial differential equations. We have developed a software framework in order to easily explore the possible combinations of solvers. We show that the performance gains from using composed solvers can be substantial compared with gains from standard Newton-Krylov methods.Comment: 29 pages, 14 figures, 13 table

Model Coupling between the Weather Research and Forecasting Model and the DPRI Large Eddy Simulator for Urban Flows on GPU-accelerated Multicore Systems

In this report we present a novel approach to model coupling for shared-memory multicore systems hosting OpenCL-compliant accelerators, which we call The Glasgow Model Coupling Framework (GMCF). We discuss the implementation of a prototype of GMCF and its application to coupling the Weather Research and Forecasting Model and an OpenCL-accelerated version of the Large Eddy Simulator for Urban Flows (LES) developed at DPRI. The first stage of this work concerned the OpenCL port of the LES. The methodology used for the OpenCL port is a combination of automated analysis and code generation and rule-based manual parallelization. For the evaluation, the non-OpenCL LES code was compiled using gfortran, fort and pgfortran}, in each case with auto-parallelization and auto-vectorization. The OpenCL-accelerated version of the LES achieves a 7 times speed-up on a NVIDIA GeForce GTX 480 GPGPU, compared to the fastest possible compilation of the original code running on a 12-core Intel Xeon E5-2640. In the second stage of this work, we built the Glasgow Model Coupling Framework and successfully used it to couple an OpenMP-parallelized WRF instance with an OpenCL LES instance which runs the LES code on the GPGPI. The system requires only very minimal changes to the original code. The report discusses the rationale, aims, approach and implementation details of this work.Comment: This work was conducted during a research visit at the Disaster Prevention Research Institute of Kyoto University, supported by an EPSRC Overseas Travel Grant, EP/L026201/