Exponential, Non-Exponential Splitting and Their Applications for Solving Singular Partial Differential Equations Dr. Tim Sheng, Baylor University Host: JaEun Ku
Abstract: This talk consists of two interactive parts. First, we will pay an attention to
optimized operator splitting strategies, such as the non-exponential ADI and exponential
LOD methods, and explore their modernizations. Then we will focus at interesting issues
involving the constructions and analysis of highly-effective and highly-efficient finite difference
approximations of singular partial differential equations which are crucial to rocket
engine designs. The quenching phenomenon will be revealed. Adaptive splitting approaches
will then be introduced. Mathematical
analysis on solution positivity, monotonicity and stability will be discussed. We will also
present the latest ideas on moving mesh strategies which can be extended for solving many
multiphysics equations with blow-up
singularities from biomathematics, oil pipeline decay detections, cancer treatments,
and laser-materials interactions. Potentials of collaborative investigations will be desirable.
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