Metacomputing for Directly Computable Multiphysics Models

Abstract

The ever-improving advances of computational technologies have forced the user to manage higher resource complexity and motivates the modeling of more complex multiphysics systems than before. Consequently, the time for the user's iterations within the context space characterizing all choices required for a successful computation far exceeds the time required for the runtime software execution to produce acceptable results. This paper presents metacomputing as an approach to address this issue, starting with describing this high-dimensional context space. Then it highlights the abstract process of multiphysics model generation/solution and proposes performing top-down and bottom-up metacomputing. In the top-down approach, metacomputing is used for: Automating the process of generating theories; Raising the semantic dimensionality of these theories in higher dimensional algebraic systems that enable simplification of the equational representation and raising the syntactic dimensionality of equational representation from 1-D equational forms to 2-D and 3-D algebraic solution graphs that reduce solving to path-following. In the bottom-up approach, already existing legacy codes evolving over multiple decades are encapsulated at the bottom layer of a multilayer semantic framework that utilizes Category Theory based operations on specifications to enable the user to spend time only for defining the physics of the relevant problem and not have to deal with the rest of the details involved in deploying and executing the solution of the problem at hand. Consequently, these two metacomputing approaches enable the generation, composition, deployment, and execution of directly computable multiphysics models.