Circuit simulation and moving mesh generation

Abstract

The paper outlines two different topics in computational engineering, linear algebra and mesh generation. Many areas of applied mathematics lead to the same fundamental problem in numerical linear algebra. We identify this problem for a network of resistors. Then we discuss the nonlinear problems of circuit simulation, and algorithms for solving them. The generation of a well-spaced mesh is an essential step for partial differential equations (and also for computer graphics). We describe a short, simple, and public code for unstructured meshes. Then we illustrate recent ideas in moving the mesh as the region changes. We want to emphasize the "fundamental problem of applied mathematics" and the new ideas in mesh generation. Our work on linear algebra (the essential subject!) appears on the course page (see http://web.mit.edu/18.06). Video lectures are also available on MIT's OpenCourseWare Website (see http://ocw.mit.edu) under Mathematics.