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Class Project : Parallel Fast Gauss Transform
| Content Provider | Semantic Scholar |
|---|---|
| Author | Wang, Jun |
| Copyright Year | 2015 |
| Abstract | In this report, we present results of 2D Fast Gauss Transform, implemented in the distributed memory parallel setting. We follow the framework of [3], but focus more on the uniform distribution case, and pay more attention to details of parallel implementation. Without using popular distributed memory management packages like PETSc, we write detailed code to manage data communication between processes and demonstrate its efficiency by numerical experiments. Our numerical examples are run on Stampede supercomputer, and a nice weak scalability is observed. (Discrete) Gauss Transform is the computational task of evaluating a discrete sum of the form F (xj) = ∑N k=1Gδ(|xj − yk|)f(yk), k = 1, · · · ,M . We say the function Gδ is of Gaussian type, if it is smooth and decays exponentially in both space and Fourier domain. Here δ is a parameter that controls the decay. Classial kernels of this type include the Gaussian Gδ(|x − y|) = e− |x−y|2 δ , and a polynomial multiplied by Gaussian. Our computational task arises from a variety of disciplines: computational physics, machine learning, computational finance and computer graphics, and potential theory for solving parabolic partial differential equations, just to name a few. Take potential theory as an example. If we want to solve the heat equation in a complex moving domain, we seek solution as a sum of volume and layer potentials. Then by imposing the famous jump relation at the boundary, we reduce it to a second kind Fredholm equation. In the end, everything reduces to the efficient evaluation of heat potentials. A single layer potential, for example, takes the following form: S[σ](x, t) = ∫ t |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://cims.nyu.edu/~stadler/hpc15_projects/presentations/HPC15_WangJ.pdf |
| Alternate Webpage(s) | http://www.cims.nyu.edu/~stadler/hpc15_projects/presentations/HPC15_WangJ.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
