problems

Finite element approximation of parameter dependent eigenvalue problems

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B9 L2 R2322

Eigenvalue problems arising from partial differential equations are used to model several applications in science and engineering, ranging from vibrations of structures, industrial microwaves, photonic crystals, and waveguides, to particle accelerators.

Finite element approximations for variable-order fractional diffusion problems

Prof. Wenyu Lei, University of Electronic Science and Technology of China

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B4 L5 R5209

We propose a finite element scheme for fractional diffusion problems with varying diffusivity and fractional order. A number of challenges are encountered when discretizing such problems. The first is the heterogeneous kernel singularity in the fractional integral operator. The second comes from the dense discrete operator with its quadratic growth in memory footprint and arithmetic operations. To address these challenges, we propose a strategy that decomposes the system matrix into three components. The first is a sparse matrix that handles the singular near-field separately and is computed by adapting singular quadrature techniques available for the homogeneous case to the case of spatially variable order.