Parallelized discrete exterior calculus for three-dimensional elliptic problems

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. Program summary Program Title: ParaGEMS CPC Library link to program files: https://doi .org /10 .17632 /t8rpkc7xnx .1 Developer's repository link: https://bitbucket .org /pieterboom /paragems/ Licensing provisions: BSD 2-clause Programming language: Fortran 90 External routines/libraries: BLAS/LAPACK, MPI, PETSc [1], hypre ParaSails [2,3] Nature of problem: Large scale simulation of 3D elliptic boundary value problems in discrete media with heterogeneous or discontinuous properties. Solution method: ParaGEMS is a library implementing discrete exterior calculus (DEC) for distributed memory architectures. It is distributed with mini-applications for solving 3D elliptic boundary value problems, which describe a number of physical laws (Fourier's law, Fick's law, Darcy's law and Ohm's law), in discrete media with heterogeneous or discontinuous properties. Additional comments including restrictions and unusual features: ParaGEMS requires meshes generated in the default format used by Triangle [4] and TetGen [5]. References [1] S. Balay et al., PETSc Web page, https://www.mcs .anl .gov /petsc, 2019. [2] R.D. Falgout, U.M. Yang, in: P.M.A. Sloot, A.G. Hoekstra, C.J.K. Tan, J.J. Dongarra (Eds.), Computational Science - ICCS 2002, Springer Berlin Heidelberg, Berlin, Heidelberg, 2002, pp. 632-641. [3] E. Chow, SIAM J. Sci. Comput. 21 (5) (2000) 1804-1822. [4] J.R. Shewchuk, in: M.C. Lin, D. Manocha (Eds.), Applied Computational Geometry: Towards Geometric Engineering, in: Lecture Notes in Computer Science, vol. 1148, Springer-Verlag, 1996, pp. 203-222, from the First ACM Workshop on Applied Computational Geometry.[5] H. Si, ACM Trans. Math. Softw. 41 (2) (2015) 11, https://doi .org /10 .1145 /2629697. (c) 2022 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).