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A Stochastic Conservative Field Transfer Method for Black-box Multiscale and Multiphysics Coupling

Abhiyan Paudel, Cameron W. Smith, Jacob S. Merson

Abstract

This paper introduces a new method for performing field transfer operations in black-box coupling, when source discretization information is not available. This approach uses a stochastic approximation of the Galerkin projection which leads to a method that asymptotically provides conservation. Error in the accuracy and conservation has been compared to the mesh intersection method and radial basis functions on a simple domain, as well as on meshes of the LTX fusion reactor. For all cases tested, our new method provides higher accuracy and less conservation error than radial basis functions and can be used for black-box coupling, unlike the mesh-intersection method. Additionally, we demonstrate the implementation and performance of our method on an NVIDIA A100 GPU, showing that the cost is competitive with the mesh intersection method.

A Stochastic Conservative Field Transfer Method for Black-box Multiscale and Multiphysics Coupling

Abstract

This paper introduces a new method for performing field transfer operations in black-box coupling, when source discretization information is not available. This approach uses a stochastic approximation of the Galerkin projection which leads to a method that asymptotically provides conservation. Error in the accuracy and conservation has been compared to the mesh intersection method and radial basis functions on a simple domain, as well as on meshes of the LTX fusion reactor. For all cases tested, our new method provides higher accuracy and less conservation error than radial basis functions and can be used for black-box coupling, unlike the mesh-intersection method. Additionally, we demonstrate the implementation and performance of our method on an NVIDIA A100 GPU, showing that the cost is competitive with the mesh intersection method.
Paper Structure (20 sections, 22 equations, 10 figures)

This paper contains 20 sections, 22 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Conservative Galerkin Projection
  3. Conservative Coupling with Discretization Information
  4. Intersection-Based Galerkin Projection
  5. Common-Refinement/Supermesh Overview
  6. R3D-Based Intersection and GPU Integration
  7. Adjacency-Based Intersection Search
  8. Intersection Integration
  9. Conservative Coupling without Discretization Information
  10. Monte Carlo Approximation of the Galerkin Projection
  11. Sampling Strategies and Integration Error
  12. Numerical Comparison
  13. Convergence Analysis
  14. Continuous (supermesh-based) accuracy error
  15. Continuous (supermesh-based) conservation error
  16. ...and 5 more sections

Figures (10)

  • Figure 1: The supermesh (c) is constructed from geometric intersections of source (a) and target (b) elements.
  • Figure 2: Adjacency-based identification of intersecting source elements for a single target element (red) and its centroid (red dot). Figures (a)–(j) illustrate the progressive expansion of the search front which is expanded from the gray element which is identified through localization of the target element centroid. The dark blue elements represent the expanded set of search elements in each step which constitute the integration regions for the load-vector assembly; light blue elements indicate source elements that are traversed during the search but do not intersect the target element of interest.
  • Figure 3: Intersection integration procedure: geometric clipping, polytope construction, and simplicial decomposition for numerical quadrature.
  • Figure 4: Integral error vs number of samples
  • Figure 5: Representative source and target meshes used in the performance analysis
  • ...and 5 more figures