Autor/Autorin: Dharmarajah Sohan
Presently pursuing a PhD at Stanford in the areas of mathematical modeling and numerical simulation, Sohan graduated with an undergraduate in Mathematical Physics from Imperial College, London and a Masters in Computational Design and Optimization from the Massachusetts Institute of Technology.
We intend to try to better our understanding of how the combined L-stable ´Trapezoidal Rule with the second order Backward Difference Formula´ (TR-BDF2) integrator and the standard A-stable Trapezoidal integrator perform on systems of coupled non-linear partial differential equations (PDEs). It was originally Professor Klaus-Jurgen Bathe who suggested that further analysis was needed in this area. We draw attention to numerical instabilities that arise due to insufficient numerical damping from the Crank-Nicolson method (which is based on the Trapezoidal rule) and demonstrate how these problems can be rectified with the TR-BDF2 scheme. Several examples are presented, including an advection-diffusion-reaction (ADR) problem and the (chaotic) damped driven pendulum. We also briefly introduce how the ideas of splitting methods can be coupled with the TR-BDF2 scheme and applied to the ADR equation to take advantage of the excellent modern day explicit techniques to solve hyperbolic equations.
We intend to try to better our understanding of how the combined L-stable Trapezoidal Rule with the second order Backward Di erence Formula (TR-BDF2) integrator and the standard A-stable Trapezoidal integrator perform on systems of coupled non-linear partial differential equations (PDEs). It was originally Professor Klaus-Jurgen Bathe who suggested that further analysis was needed in this area. We draw attention to numerical instabilities that arise due to insufficient numerical damping from the Crank-Nicolson method (which is based on the Trapezoidal rule) and demonstrate how these problems can be rectified with the TR-BDF2 scheme. Several examples are presented, including an advection-diffusion-reaction (ADR) problem and the (chaotic) damped driven pendulum. We also brie y introduce how the ideas of splitting methods can be coupled with the TR-BDF2 scheme and applied to the ADR equation to take advantage of the excellent modern day explicit techniques to solve hyperbolic equations.
Über den Autor
Presently pursuing a PhD at Stanford in the areas of mathematical modeling and numerical simulation, Sohan graduated with an undergraduate in Mathematical Physics from Imperial College, London and a Masters in Computational Design and Optimization from the Massachusetts Institute of Technology.
