doctoral student at Department of Information Technology, Division of Scientific Computing
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I am a PhD student in Scientific Computing, with Gunilla Kreiss as advisor.
I am interested in high-order numerical methods for time-dependent partial difference equations. In particular, I have been working on numerical simulation of wave propagations.
I have developed a high-order finite difference methods for acoustic wave propagations in heterogeneous media. Geometrical features such as curved boundaries and interfaces are resolved by curvilinear transformations. We use finite difference stencils satisfying a summation-by-parts (SBP) property to discretize the equation on the second order form, imposed boundary and interface conditions in a weak sense by penalty terms. The highlight of the developed scheme is that it is provably stable and high-order accurate.
The interior stencil of an SBP operator is the standard central differences. It is known that to satisfy the SBP property, the order of the truncation error at a few grid points near boundaries is reduced by a factor 2. Much work has been done in analyzing the effect of large truncation errors localized near boundaries and interfaces to the overall convergence rate of the numerical scheme. In particular, we are able to analyze a large truncation error located at a corner of a two dimensional domain. Rigorous error estimates are obtained by normal mode analysis.
Recently, I have been working on an energy based discontinuous Galerkin method for an acoustic-elastic coupling problem. The method is energy stable, high-order accurate and very flexible with complex geometry. We are currently building a solver based on C and Fortran, and expect to complete the implementation in the spring of 2017.
I am approaching to the end of my PhD journey, and am looking for postdoc positions right now. An exciting extension of my current work is to extend the high-order finite difference method and the discontinuous Galerkin method for problems with moving geometries. Such a phenomenon occurs in many applications in biomedicine when a solid undergoes rotations and distortions in a fluid. In addition, taming the time step restriction of a standard discontinuous Galerkin method is of great interest.
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