Parallelized Discrete Exterior Calculus for Three-Dimensional Elliptic Problems
This work provides a new computational tool for steady-state analysis of gradient-driven physical processes, particularly beneficial for materials with heterogeneities that challenge traditional methods like finite elements.
The paper presents the first parallelized discrete exterior calculus (DEC) library for 3D elliptic problems, enabling efficient handling of strong heterogeneities and discontinuities. It demonstrates the method's effectiveness for thermal conductivity evolution in solids with growing crack populations.
A formulation of elliptic boundary value problems is used to develop the first discrete exterior calculus (DEC) library for massively parallel computations with 3D domains. This can be used for steady-state analysis of any physical process driven by the gradient of a scalar quantity, e.g. temperature, concentration, pressure or electric potential, and is easily extendable to transient analysis. In addition to offering this library to the community, we demonstrate one important benefit from the DEC formulation: effortless introduction of strong heterogeneities and discontinuities. These are typical for real materials, but challenging for widely used domain discretization schemes, such as finite elements. Specifically, we demonstrate the efficiency of the method for calculating the evolution of thermal conductivity of a solid with a growing crack population. Future development of the library will deal with transient problems, and more importantly with processes driven by gradients of vector quantities.