Convergence of the Combination Technique for Second-Order Elliptic Differential Equations
SIAM Journal on Numerical Analysis
Computing
Linear algebra operators for GPU implementation of numerical algorithms
ACM SIGGRAPH 2003 Papers
Sparse matrix solvers on the GPU: conjugate gradients and multigrid
ACM SIGGRAPH 2003 Papers
Computational Methods for Option Pricing (Frontiers in Applied Mathematics) (Frontiers in Applied Mathematics 30)
LU-GPU: Efficient Algorithms for Solving Dense Linear Systems on Graphics Hardware
SC '05 Proceedings of the 2005 ACM/IEEE conference on Supercomputing
Efficient Hierarchical Approximation of High-Dimensional Option Pricing Problems
SIAM Journal on Scientific Computing
Optimization of sparse matrix-vector multiplication on emerging multicore platforms
Proceedings of the 2007 ACM/IEEE conference on Supercomputing
Benchmarking GPUs to tune dense linear algebra
Proceedings of the 2008 ACM/IEEE conference on Supercomputing
Using GPUs to improve multigrid solver performance on a cluster
International Journal of Computational Science and Engineering
Solving dense linear systems on platforms with multiple hardware accelerators
Proceedings of the 14th ACM SIGPLAN symposium on Principles and practice of parallel programming
Concurrent number cruncher: a GPU implementation of a general sparse linear solver
International Journal of Parallel, Emergent and Distributed Systems
Compact data structure and scalable algorithms for the sparse grid technique
Proceedings of the 16th ACM symposium on Principles and practice of parallel programming
Journal of Computational Physics
Globally scheduled real-time multiprocessor systems with GPUs
Real-Time Systems
Many-core architectures boost the pricing of basket options on adaptive sparse grids
WHPCF '13 Proceedings of the 6th Workshop on High Performance Computational Finance
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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.