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Manapy: MPI-Based framework for solving partial differential equations using finite-volume on unstructured-grid

Imad Kissami, Ahmed Ratnani

TL;DR

Manapy presents a MPI-enabled, Python-based finite-volume framework for solving PDEs on unstructured grids, addressing convective-diffusive and Poisson equations with scalable parallel operators. It integrates convective flux discretization via upwind schemes with MUSCL and Barth-Jespersen limiting, diffusive flux via the diamond scheme, and a third-order Runge-Kutta time integration, while offering parallel assembly and solver options through MUMPS and PETSc. The paper demonstrates strong scaling and performance on a high-performance cluster, including a 3D streamer discharge model that couples fluid and electrostatic fields, validating the framework's capability to handle large, multi-physics problems. It emphasizes ease of use and extensibility through Pyccel-generated C/Fortran code, with future directions aimed at parallel adaptive mesh refinement and more sophisticated preconditioning to tackle even larger simulations.

Abstract

Manapy is a parallel, unstructured, finite-volume based solver for the solution of partial differential equations (PDE). The framework is written using Python, it is object-oriented, and is organized in such a way that it is easy to understand and modify. In this paper, we present the parallel implementation and scalability of the differential operators used on a general case of PDE. The performance of massively parallel direct and iterative methods for solving large sparse systems of linear equations in plasma physics is evaluated on a latest high performance computing system, and 3D test cases for plasma physics are presented.

Manapy: MPI-Based framework for solving partial differential equations using finite-volume on unstructured-grid

TL;DR

Manapy presents a MPI-enabled, Python-based finite-volume framework for solving PDEs on unstructured grids, addressing convective-diffusive and Poisson equations with scalable parallel operators. It integrates convective flux discretization via upwind schemes with MUSCL and Barth-Jespersen limiting, diffusive flux via the diamond scheme, and a third-order Runge-Kutta time integration, while offering parallel assembly and solver options through MUMPS and PETSc. The paper demonstrates strong scaling and performance on a high-performance cluster, including a 3D streamer discharge model that couples fluid and electrostatic fields, validating the framework's capability to handle large, multi-physics problems. It emphasizes ease of use and extensibility through Pyccel-generated C/Fortran code, with future directions aimed at parallel adaptive mesh refinement and more sophisticated preconditioning to tackle even larger simulations.

Abstract

Manapy is a parallel, unstructured, finite-volume based solver for the solution of partial differential equations (PDE). The framework is written using Python, it is object-oriented, and is organized in such a way that it is easy to understand and modify. In this paper, we present the parallel implementation and scalability of the differential operators used on a general case of PDE. The performance of massively parallel direct and iterative methods for solving large sparse systems of linear equations in plasma physics is evaluated on a latest high performance computing system, and 3D test cases for plasma physics are presented.
Paper Structure (23 sections, 17 equations, 14 figures, 11 tables, 2 algorithms)

This paper contains 23 sections, 17 equations, 14 figures, 11 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Mathematical Model
  3. Temporal and Spacial discretization of the equation \ref{['eq:1']}
  4. Convective flux discretization
  5. Diffusive flux discretization
  6. Temporal discretization
  7. Discretization of Poisson's equation \ref{['eq:1.1']}
  8. Manapy performance
  9. Working environment
  10. Halo data
  11. Strong scaling for the FV operators implementation
  12. Poisson's equation
  13. Parallel assembly for 3D Matrix
  14. Solving Poisson equation
  15. Representing the 3D streamer model
  16. ...and 8 more sections

Figures (14)

  • Figure 1: Compute the gradient $\nabla u$ ($(u)_x$, $(u)_y$, $(u)_z$) on cell $T_i$
  • Figure 2: An example of a 3D (projected in 2D) mesh (left) and a mesh decomposition into four subdomains (right).
  • Figure 3: General representation of Diamond cell in 3D.
  • Figure 4: Least square interpolation (value on node A)
  • Figure 5: Strong Speedup for the FV operators using grid G1.
  • ...and 9 more figures