Abstract
From engineering analysis and topology optimization to generative design and machine learning, many modern computational design approaches require either large amounts of data or a method to generate that data. This paper addresses key issues with automatically generating such data through automating the construction of Finite Element Method (FEM) simulations from Dirichlet boundary conditions. Most past work on automating FEM assumes prior knowledge of the physics to be run or is limited to a small number of governing equations.
In contrast, we propose three improvements to current methods of automating the FEM: (1) completeness labels that guarantee viability of a simulation under specific conditions, (2) type-based labels for solution fields that robustly generate and identify solution fields, and (3) type-based labels for variational forms of governing equations that map the three components of a simulation set — specifically, boundary conditions, solution fields, and a variational form — to each other to form a viable FEM simulation. We implement these improvements using the FEniCS library as an example case. We show that our improvements increase the percent of viable simulations that are run automatically from a given list of boundary conditions. This paper’s procedures ultimately allow for the automatic — i.e., fully computer-controlled — construction of FEM multi-physics simulations and data collection required to run data-driven models of physics phenomena or automate the exploration of topology optimization under many physics.
A Nitsche Finite Element Approach for Elliptic Problems with Discontinuous Dirichlet Boundary Conditions
