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.

中文翻译：

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三维椭圆问题的并行离散外部演算

椭圆边界值问题的公式用于开发第一个离散外部演算（DEC）库，用于具有3D域的大规模并行计算。它可以用于由标量（例如温度，浓度，压力或电势）的梯度驱动的任何物理过程的稳态分析，并且很容易扩展到瞬态分析。除了向社区提供此库之外，我们还展示了DEC制定的一项重要好处：轻松引入强大的异质性和不连续性。这些对于真实材料来说是典型的，但是对于广泛使用的域离散化方案（例如有限元）则具有挑战性。具体来说，我们证明了该方法的有效性，该方法可用于计算随着裂纹数量增加而产生的固体的导热系数的演变。库的未来开发将处理瞬态问题，更重要的是将处理矢量量梯度驱动的过程。