• Corpus ID: 12211125

GPU Acceleration of Solving Parabolic Partial Differential Equations Using Difference Equations

@inproceedings{Foster2011GPUAO,
  title={GPU Acceleration of Solving Parabolic Partial Differential Equations Using Difference Equations},
  author={David L. Foster},
  year={2011}
}
Parabolic partial differential equations are often used to model systems involving heat transfer, acoustics, and electrostatics. The need for more complex models with increasing precision drives greater computational demands from processors. Since solving these types of equations is inherently parallel, GPU computing offers an attractive solution for drastically decreasing time to completion, power usage, and increasing the computation per dollar. However, since GPU computing involves a much… 
3 Citations
Fast GPU algorithms for implementing the red-black Gauss-Seidel method for Solving Partial Differential Equations
TLDR
The red-black Gauss-Seidel method is employed, in this paper, to solve the 2D steady state heat conduction problem on two different GPUs with an overall speedup of 484 relative to the CPU sequential implementation.
Graphics processing unit acceleration of the red/black SOR method
TLDR
The results prove that the global memory cache added on recent GPU architectures assist achieving high performance without requiring to employ the special memory types provided by the GPU (i.e. shared, texture or constant memory).
High-performance Implementation of Parallel Semi-Implicit Method for Pressure Linked Equations Solver on CPU+GPU Platform
  • Qianting Xu, Ruitian Li, Minghai Xu
  • Computer Science
    International Journal of Heat and Mass Transfer
  • 2022
TLDR
A new GPU implement of red-black SOR, the mono-color floating-point scheme, was developed in this paper to remove the suspension and improve computing performance and the numerical results of iteration of discrete equations in SIMPLE showed that the new scheme can get 60–70% performance improvement compared with the traditional implementation.

References

SHOWING 1-6 OF 6 REFERENCES
Cyclic Reduction Tridiagonal Solvers on GPUs Applied to Mixed-Precision Multigrid
TLDR
This paper demonstrates that mixed precision schemes constitute a significant performance gain over native double precision and presents a new implementation of cyclic reduction for the parallel solution of tridiagonal systems and employs this scheme as a line relaxation smoother in a GPU-based multigrid solver.
Programming Massively Parallel Processors. A Hands-on Approach
  • Jie Cheng
  • Computer Science
    Scalable Comput. Pract. Exp.
  • 2010
TLDR
This comprehensive test/reference provides a foundation for the understanding and implementation of parallel programming skills which are needed to achieve breakthrough results by developing parallel applications that perform well on certain classes of Graphic Processor Units (GPUs).
CUDA by Example: An Introduction to General-Purpose GPU Programming
  • Jie Cheng
  • Computer Science
    Scalable Comput. Pract. Exp.
  • 2010
TLDR
This book is designed for readers who are interested in studying how to develop general parallel applications on graphics processing unit (GPU) by using CUDA C, a programming language which combines industry standard programming C language and some more features which can exploit CUDA architecture.
High performance finite difference PDE solvers on GPUs
Tesla C2050/C2070 GPU Computing Processor Overview
  • Tesla C2050/C2070 GPU Computing Processor Overview
  • 2010