Proceedings Article10.1145/1645413.1645419
GPU based sparse grid technique for solving multidimensional options pricing PDEs
Abhijeet Gaikwad,Ioane Muni Toke +1 more
- 15 Nov 2009
- pp 6
TL;DR: This paper addresses iterative solutions via preconditioned Krylov subspace based methods, such as Stabilized BiConjugate Gradient and CG Squared, with the main focus on the design of such iterative solvers to harness massive parallelism of general purpose Graphics Processing Units (GPGPU)s.
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Abstract: It has been shown that the sparse grid combination technique can be a practical tool to solve high dimensional PDEs arising in multidimensional option pricing problems in finance. Hierarchical approximation of these problems leads to linear systems that are smaller in size compared to those arising from standard finite element or finite difference discretizations. However, these systems are still excessively demanding in terms of memory for direct methods and challenging to solve by iterative methods. In this paper we address iterative solutions via preconditioned Krylov subspace based methods, such as Stabilized BiConjugate Gradient (BiCGStab) and CG Squared (CGS), with the main focus on the design of such iterative solvers to harness massive parallelism of general purpose Graphics Processing Units (GPGPU)s. We discuss data structures and efficient implementation of iterative solvers. We also present a number of performance results to demonstrate the scalability of these solvers on the NVIDIA's CUDA platform.
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References
•Book
Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods
Richard Barrett
- 01 Jan 1987
TL;DR: In this book, which focuses on the use of iterative methods for solving large sparse systems of linear equations, templates are introduced to meet the needs of both the traditional user and the high-performance specialist.
Multi-level adaptive solutions to boundary-value problems
TL;DR: In this paper, the boundary value problem is discretized on several grids (or finite-element spaces) of widely different mesh sizes, and interactions between these levels enable us to solve the possibly nonlinear system of n discrete equations in 0(n) operations (40n additions and shifts for Poisson problems); and conveniently adapt the discretization (the local mesh size, local order of approximation, etc.) to the evolving solution in a nearly optimal way, obtaining "°°-order" approximations and low n, even when singularities are present.
Linear algebra operators for GPU implementation of numerical algorithms
Jens Krüger,Rüdiger Westermann +1 more
- 01 Jul 2003
TL;DR: This work proposes a stream model for arithmetic operations on vectors and matrices that exploits the intrinsic parallelism and efficient communication on modern GPUs and introduces a framework for the implementation of linear algebra operators on programmable graphics processors (GPUs), thus providing the building blocks for the design of more complex numerical algorithms.
762
Sparse matrix solvers on the GPU
TL;DR: This work shows that high-intensity numerical simulation computations can be performed efficiently on the GPU, which is regarded as a full function streaming system.
496
Optimization of sparse matrix-vector multiplication on emerging multicore platforms
Samuel Williams,Leonid Oliker,Richard Vuduc,John Shalf,Katherine Yelick,James Demmel +5 more
- 10 Nov 2007
TL;DR: In this article, the authors examine sparse matrix-vector multiply (SpMV) kernels across a broad spectrum of multicore designs and present several optimization strategies especially effective for the multicore environment, and demonstrate significant performance improvements compared to existing state-of-the-art serial and parallel SpMV implementations.