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Mathematics > Numerical Analysis

arXiv:2211.16548 (math)
[Submitted on 29 Nov 2022]

Title:Solving High Dimensional Partial Differential Equations Using Tensor Type Discretization and Optimization Process

Authors:Yangfei Liao, Yifan Wang, Hehu Xie
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Abstract:In this paper, we propose a tensor type of discretization and optimization process for solving high dimensional partial differential equations. First, we design the tensor type of trial function for the high dimensional partial differential equations. Based on the tensor structure of the trial functions, we can do the direct numerical integration of the approximate solution without the help of Monte-Carlo method. Then combined with the Ritz or Galerkin method, solving the high dimensional partial differential equation can be transformed to solve a concerned optimization problem. Some numerical tests are provided to validate the proposed numerical methods.
Comments: 9 pages, 4 figures
Subjects: Numerical Analysis (math.NA)
MSC classes: 65N30, 65N25, 65L15, 65B99
Cite as: arXiv:2211.16548 [math.NA]
  (or arXiv:2211.16548v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2211.16548

Submission history

From: Hehu Xie [view email]
[v1] Tue, 29 Nov 2022 19:17:05 UTC (89 KB)
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