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 methods for wave propagation problems.
Together with my advisor Gunilla Kreiss and her former PhD student Kristoffer Virta, we have developed a high-order finite difference method for acoustic wave propagation 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 in the second order form, and impose boundary and interface conditions in a weak sense by penalty terms. Non-conforming interfaces with hanging nodes are handled by an interpolation or a projection technique. 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. This is a joint work with Gunilla Kreiss and Anna Nissen.
Recently, together with Daniel Appelö we 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 Fortran solver to demonstrate the effectiveness and robustness of the developed method.
I have defended my PhD in June 2017. After an exciting teaching period in September in Uppsala, I will be a postdoc in the computational mathematics division at Chalmers University of Technology and University of Gothenburg. I am looking forward to the new challenge.
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