Efficient finite cell computations for image-based analyses


Prof. Dr. Ernst Rank
Chair for Computation in Engineering
Technische Universität München

Project Overview

The finite cell method (FCM) is a variant of the finite element method that combines a fictitious domain approach with high-order finite elements [25]. This combination makes FCM suitable for performing accurate numerical analyses on objects with a complex shape, since the computational mesh does not need to conform to the geometry of the original body. The Chair for Computation in Engineering (CiE) at the Technical University Munich centers a major part of its research on the extension of the finite cell method and its application to problems of engineering relevance. This research is realized within the framework of a high-order finite cell code called AdhoC++ that has been in active development at CiE since 2012.

AdhoC++ is a modular code written in C++ that can perform numerical simulations in the field of solid and structural mechanics. It supports both conforming finite element computations as well as non-conforming computations with finite cell discretizations and implements a hybrid parallel programming model (MPI + OpenMP). An integral feature of the code is its ability to handle dynamically changing discretizations in two and three dimensions by means of the multi-level hp-method [17]. The code was successfully ported to modern HPC systems within the scope of the KONWIHR Phase III project entitled The Matrix-Free Finite Cell Method.

The aforementioned KONWIHR project was an important first step towards large-scale finite cell computations. We therefore intent to build upon this work and further push the boundaries of parallel immersed finite element techniques. To this end, the planned project aims to extend the AdhoC++’s capabilities to allow the computation of large-scale industrial examples involving bodies with very complex  geometries and dynamically changing finite cell discretizations. To achieve this goal, we intent to focus on three major aspects i) the adaptation and optimization of the mesh data structures implemented in the previous project to allow for efficient dynamic mesh refinement of hp-refined FCM meshes and ii) improving the performance of the linear system solver and iii) improving the scalability of the parallel I/0. These three tasks are integral in achieving our overall goal of using the large-scale finite cell computations as an analysis tool for problems of engineering relevance.