Advanced topics in computational mathematics and numerical analysis from current problems of interest. May be repeated for credit if different topics are covered.
Sample Offerings:
Because of its Object Orientation, its Platform Independence, and its tight specifications on arithmetic operations, Java is an appealing language for the development of Scientific Simulations. Since Java-based simulations can be distributed in the context of web-based documentation, such Java-based simulations can greatly enhance the dissemination of scientific knowledge and can substantially improve scientific training particularly in the area of understanding complex models. This course focuses on developing Scientific Simulations written in Java and distributed through the World Wide Web. The course is project oriented and involves the development of interactive web-based simulations of scientific topics chosen by the students.
This course, cross-listed as ChE 845, ME 893, and MTHSC 983, is team-taught by Math Sciences and Chemical Engineering faculty. The course presents a systems perspective of fiber and film processes using existing and new models developed by the Center for Advanced Engineering Fibers and Films. Constitutive equations are developed and applied to specific geometries and flow problems encountered in the production of fibers and films. Specific objectives are to develop the governing equations for polymeric fluids, derive various constitutive equations including those based on molecular models, explore analytical and numerical solution of the governing equations for special cases, develop an understanding for the strengths and weaknesses of the models to be discussed, and apply constitutive equations to fiber and film processing geometries.
Topics include classification of partial differential equations, the finite element method in one and higher dimensions, Sobolev spaces, interpolation theory, finite element spaces, and development of error estimates. Related topics are considered as time permits, including application of finite element methods to fluid flow problems which arise in science and engineering.