Multiscale problems are some of the greatest challenges in computational mathematics today. In all branches of the engineering sciences we encounter problems with features on several different scales. A typical example is computer simulation involving a heterogeneous medium where material data, such as the module of elasticity, conductivity, or permeability, vary in space. Simulation of porous edium flow is a typical example of a multiscale problem. There are numerous applications of porous media flow including ground water flow, oil reservoir simulation, and CO2 sequestration. The permeability in the ground varies over several different scales.
Mathematically this kind of problems transforms into coupled systems of non-linear partial differential equations with multiscale features in the coefficients. Such problems are in general very hard to solve within a reasonable tolerance on a single global mesh on a single processor.
Parallel methods that are designed to handle these problems, multiscale methods, are needed in order to compute approximate solutions. Reliable solutions can only be achieved by control of the error in the method. The goal of this project is to implement and analyze multiscale methods that are used in industrial codes and study how efficient and reliable they are.