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High-Performance Gradient Evaluation for Complex Soft Materials Using MPI-based DFS Algorithm

Anurag Bhattacharyya

TL;DR

The paper addresses the computational bottleneck of gradient evaluation in topology optimization for soft materials with complex thermo-mechanical behavior. It presents a DFS-based, time-dependent adjoint sensitivity method implemented in a PETSc-based MPI framework to enable large-scale, parallel optimization. SMP-specific residuals and derivatives are derived, and a recursive DFS algorithm computes time-coupled gradients, with validation against finite differences showing high accuracy and negligible discrepancy. The work demonstrates scalable gradient evaluation on HPC resources, enabling practical generative design for physics-integrated simulations of SMPs under complex loading.

Abstract

This article presents a depth-first search (DFS)-based algorithm for evaluating sensitivity gradients in the topology optimization of soft materials exhibiting complex deformation behavior. The algorithm is formulated using a time-dependent adjoint sensitivity approach and is implemented within a PETSc-based C++ MPI framework for efficient parallel computing. It has been found that on a single processor, the sensitivity analysis for these complex materials can take approximately 45 minutes. This necessitates the use of high-performance computing (HPC) to achieve feasible optimization times. This work provides insights into the algorithmic framework and its application to large-scale generative design for physics integrated simulation of soft materials under complex loading conditions.

High-Performance Gradient Evaluation for Complex Soft Materials Using MPI-based DFS Algorithm

TL;DR

The paper addresses the computational bottleneck of gradient evaluation in topology optimization for soft materials with complex thermo-mechanical behavior. It presents a DFS-based, time-dependent adjoint sensitivity method implemented in a PETSc-based MPI framework to enable large-scale, parallel optimization. SMP-specific residuals and derivatives are derived, and a recursive DFS algorithm computes time-coupled gradients, with validation against finite differences showing high accuracy and negligible discrepancy. The work demonstrates scalable gradient evaluation on HPC resources, enabling practical generative design for physics-integrated simulations of SMPs under complex loading.

Abstract

This article presents a depth-first search (DFS)-based algorithm for evaluating sensitivity gradients in the topology optimization of soft materials exhibiting complex deformation behavior. The algorithm is formulated using a time-dependent adjoint sensitivity approach and is implemented within a PETSc-based C++ MPI framework for efficient parallel computing. It has been found that on a single processor, the sensitivity analysis for these complex materials can take approximately 45 minutes. This necessitates the use of high-performance computing (HPC) to achieve feasible optimization times. This work provides insights into the algorithmic framework and its application to large-scale generative design for physics integrated simulation of soft materials under complex loading conditions.

Paper Structure

This paper contains 3 sections, 33 equations, 9 figures, 1 table, 3 algorithms.

Table of Contents

  1. Introduction
  2. Sensitivity Analysis
  3. Derivation of sensitivity analysis

Figures (9)

  • Figure 1: Scaling capability study performed using UIUC campus-cluster
  • Figure 2: Design domain for sensitivity calculations and its verification.
  • Figure 3: Tracking $\frac{\partial \bm{\varepsilon}^{(ir)}_{n}}{\partial \bm{\varepsilon}^{(r)}_{n-1}}$ terms in time
  • Figure 4: Tracking $\frac{\partial \bm{\varepsilon}^{(ig)}_{n}}{\partial \bm{\varepsilon}^{(r)}_{n-1}}$ terms in time
  • Figure 5: Tracking $\frac{\partial \bm{\varepsilon}^{(i)}_{n}}{\partial \bm{\varepsilon}^{(r)}_{n-1}}$ terms in time
  • ...and 4 more figures