Hybrid Continuum-Discrete Multiscale Models of Solid Tumor Growth March 1, 2010 2:30 p.m. John Lowengrub Abstract We present a hybrid continuum-discrete mathematical multiscale modeling framework for vascular solid tumor growth. A continuum model based on mixture theory is used to describe the volume fractions of the evolution of multiple tumor cell clones, extracellular matrix (ECM), […]
Using Algebraic Multigrid for Numerical Upscaling October 13, 2010 2:30 Panayot S. Vassilevski Abstract We will give an introduction to multigrid methods (or MG) for solving systems of (linear) algebraic equations. We will first give a motivation why the method has the potential to be of optimal order, namely, that it can be viewed as […]
ADI Method for Sylvester Equations January 28, 2011 3:00 p.m. Ren-Cang Li Abstract We are concerned with numerical solutions of large scale Sylvester equations AX XB=C, Lyapunov equations as a special case in particular included, with C having very small rank. For stable Lyapunov equations, Penzl (2000) and Li and White (2002) demonstrated that the […]
Surveillance for Emerging Space-Time Clusters February 17, 2011 3:45 p.m. Renato Assuncao Abstract The interest is on monitoring incoming space-time events to detect an emergent space-time cluster as early as possible. Assume that point process events are continuously recorded in space and time. In a certain unknown moment, a small localized cluster of increased intensity […]
Multilevel Methods for Nonconforming FEM Systems April 25, 2011 4:00 p.m. Svetozar Margenov Abstract The talk is devoted to multilevel preconditioning methods of AMLI type based on block matrix approximate factorization of the stiffness matrix. It is focused on the case of nonconforming finite elements. The theory of the robust AMLI methods for anisotropic Crouzeix-Raviart […]