For more information about this meeting, contact Xiaozhe Hu, Fei Wang, Hope Shaffer, Jinchao Xu, Toan Nguyen.
|Title:||Method of Characteristics for Multiscale Modeling and Simulation (3:30PM-4:30PM)|
|Seminar:||CCMA PDEs and Numerical Methods Seminar Series|
|Speaker:||Scott Miller, Penn State Univeristy|
|The method of characteristics is a technique for solving hyperbolic partial differential equations. By transforming the original equations into characteristic variables, the PDEs are transformed into ODEs which can be integrated along the characteristic directions. Knowledge about the orientation of the characteristic hypersurfaces can be used to construct piecewise solutions by utilizing the range of influence and domain of dependence. The resulting solution process is extremely local in nature and is ‘embarrassingly parallel’. In this talk, we will review the method of characteristics and introduce a special mesh generation procedure that creates causality-obeying spacetime meshes. The spacetime discontinuous Galerkin (SDG) method is used for the field solution on each patch of elements, whereby small patches of elements are solved independently from the rest of the global domain. The SDG method on causal space-time meshes results in a solution procedure with linear computational complexity. The direct discretization of spacetime removes the need for separate temporal integration schemes; rather, the entire spacetime domain solution is represented by finite element basis functions defined on broken Sobolev spaces. SDG methods possess several attractive features, including: high order convergence rates, fixed compact stencil for arbitrary interpolation order, support for fully unstructured and non-conforming meshes, and excellent stability and element-wise conservation properties. SDG methods are a natural choice for transient simulations of dynamic, non-smooth, and complex physics. In this work, we apply the SDG method to several different physical systems: linear elastodynamics, dynamic fracture mechanics, inviscid gas dynamics, and hyperbolic heat conduction. These examples will demonstrate the robustness of SDG for multi-scale and multi-physics applications, including fully nonlinear models and sharp interfaces.
Talk will be 3:30 PM - 4:30 PM|
Room Reservation Information
|Date:||01 / 17 / 2014|
|Time:||03:30pm - 05:00pm|