Abstract:
This paper provides an overview of Problem Solving Environments (PSEs), which are computer systems designed to solve specific classes of problems without requiring users to have specialized knowledge of underlying hardware or software. The discussion focuses on several PSEs that are used for building other PSEs, such as CECAAD, a foundational project for computer-aided application design. It also describes Coven, a framework for creating PSEs for parallel computers, and the PSEware project, which focuses on symbolic computation, user interfaces, and collaborative technologies. The paper also delves into major issues that PSEs address, with a significant emphasis on Partial Differential Equations (PDEs), which are fundamental to computational science and engineering. It highlights how PSEs like Diffpack and VECFEM are specifically designed as object-oriented frameworks for solving PDEs using Finite Element Analysis (FEA). A key part of the process is mesh generation, which involves transforming a differential equation into a finite-dimensional space by discretizing the domain. The paper describes various mesh generators, including LaGriT and TrueGrid, which are essential for creating the unstructured and structured meshes required for FEA. Furthermore, it covers other critical components like graph partitioning for load balancing on parallel systems and linear solvers such as SuperLU for handling sparse linear systems, all of which are integral to the efficient execution of large-scale FEA problems. The overall purpose is to show how these integrated software tools and technologies facilitate the complex computational tasks necessary for modern scientific and engineering work, including sophisticated simulations that rely heavily on FEA.
