Dr. Carlson performs research in the areas of numerical modeling of basic transport processes, fundamental analysis of flow through permeable media, and petroleum reservoir characterization. He is particularly interested in the development of function approximations which can be used to depict accurately singular behavior in various numerical models. One very important example of this singular behavior occurs around wells in petroleum reservoirs and ground-water aquifers. Dr. Carlson is also concerned with the development of high-performance numerical models based on the numerical method of lines.