Luke Morris , Andrew Baas , Jesus Arias , Maia Gatlin , Evan Patterson , James P. Fairbanks
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Decapodes: A diagrammatic tool for representing, composing, and computing spatialized partial differential equations
We present Decapodes, a diagrammatic tool for representing, composing, and solving partial differential equations. Decapodes provides an intuitive diagrammatic representation of the relationships between variables in a system of equations, a method for composing systems of partial differential equations using an operad of wiring diagrams, and an algorithm for deriving solvers using hypergraphs and string diagrams. The string diagrams are in turn compiled into executable programs using the techniques of categorical data migration, graph traversal, and the discrete exterior calculus. The generated solvers produce numerical solutions consistent with state-of-the-art open source tools as demonstrated by benchmark comparisons with SU2. These numerical experiments demonstrate the feasibility of this approach to multiphysics simulation and identify areas requiring further development.
期刊介绍:
Computational Science is a rapidly growing multi- and interdisciplinary field that uses advanced computing and data analysis to understand and solve complex problems. It has reached a level of predictive capability that now firmly complements the traditional pillars of experimentation and theory.
The recent advances in experimental techniques such as detectors, on-line sensor networks and high-resolution imaging techniques, have opened up new windows into physical and biological processes at many levels of detail. The resulting data explosion allows for detailed data driven modeling and simulation.
This new discipline in science combines computational thinking, modern computational methods, devices and collateral technologies to address problems far beyond the scope of traditional numerical methods.
Computational science typically unifies three distinct elements:
• Modeling, Algorithms and Simulations (e.g. numerical and non-numerical, discrete and continuous);
• Software developed to solve science (e.g., biological, physical, and social), engineering, medicine, and humanities problems;
• Computer and information science that develops and optimizes the advanced system hardware, software, networking, and data management components (e.g. problem solving environments).