**Speaker:** Dr. Michael P. Lamoureux, University of Calgary

**Location:** Mathematical Sciences 431

**Date:** Thursday, February 16, 2017

**Time:** 15:00-16:00

**Title:** Grid algebra and finite difference methods

**Abstract:** We are all familiar with linear algebra and methods for representing linear operators as an n by n matrix. Today, we will discuss representing operators on a 2D or 3D grid, or more generally on a directed graph. We develop linear algebraic methods to simplify or factor the operator into a form that is easy to solve using back-substitution. Such techniques are useful in numerical solutions of partial differential equations. We apply the technique to implement an implicit solver for a finite difference algorithm applied to the wave equation in two dimensions.