Automating embedded analysis capabilities and managing software complexity in multiphysics simulation part II: application to partial differential equations

TL;DR

This paper details the implementation of a template-based generic programming approach for PDE simulations, enabling automated embedded analysis and managing software complexity, demonstrated through shape optimization and uncertainty quantification.

Contribution

It extends previous work by providing implementation details and solutions for applying generic programming to PDE simulation and analysis.

Findings

Successful shape optimization of a 3D PDE model

Effective uncertainty quantification results

Overcoming software infrastructure challenges

Abstract

A template-based generic programming approach was presented in a previous paper that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded analysis algorithms. In this paper, we describe the implementation details for using the template-based generic programming approach for simulation and analysis of partial differential equations (PDEs). We detail several of the hurdles that we have encountered, and some of the software infrastructure developed to overcome them. We end with a demonstration where we present shape optimization and uncertainty quantification results for a 3D PDE application.