Agent-based parallel system for numerical computations

Abstract

The paper describes a way of applying agent paradigm to hp-adaptive Finite Element Method (hp-FEM). We discuss a choice of classical numerical algorithms suitable for incorporating into an agent-based application, along with an efficient way of adopting them into an agent-based application. We define formally a Computing Multi Agent System (C-MAS) for adaptive 1D FEM based on Smart Solid Agent model and describe tasks executed by hp-FEM agents. Finally, we spare a few paragraphs for numerical experiments performed with an application developed accordingly to the described model.Keywords: computing multi-agent systems; adaptive finite element method; distributed computations MotivationAdaptive systems for numerical methods like Finite Element Method or Finite Difference Method grow nowadays to great sizes because of the amount of included components, algorithms and parallelism subroutines combined altogether (typical solutions in this area are still based on low-level communication libraries like PVM or MPI [12]). A usual way of attempting to address complexity issues by applying object-or component-oriented approaches [6,7] works well with simplifying general design, but seems to struggle where parallelism matters, as this is not the aim these paradigms were designed for. This is a point where multi-agent system concept comes in handy. Agent paradigm is a high-level, scalable and relatively simple approach of developing distributed applications (for detailed description, see for example [11]). Its usefulness, for not only artificial intelligence but also numerical computations, has already been proven in existing works [4,5].The aim of this work is to apply the agent approach to hp-FEM. By doing so, we gain an ability to divide and merge computational tasks in runtime, which is crucial to a vast majority of adaptive algorithms. This allows for a more accurate automatic load balancing, which can be delegated to an underlying agent platform [3].Being probably the most advanced adaptive mesh-based algorithm intended for solving PDEs, the hp-FEM is what we focus on in this article. The paper can be treated, however, as a more general proof of concept for agentbased adaptive computational solvers, as the same approach applies to Finite Difference Method and presumably other mesh-based algorithms.

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