Full chronoogical publications list of submitted and published papers is on my google scholar profile

Krylov solvers that hide latencies and avoid communication.

The current generation of iterative methods give a poor performance on modern hardware since communication and synchronization costs dominate over the cost of the floating point operations. We are working on communication avoiding and hiding in iterative Krylov methods and introduced so-called pipelined Krylov methods where the latency associated with dot-products is hidden behind other computations. It offers a much better performance in strong scaling experiments. We are currently also working on high-arithmetic intensity Krylov methods that are build on top of kernels that can be SIMD vectorized.

Bottom-up models in systems biology.

Solvers for Helmholtz and Schrödinger equations

We are developing methods to solve the d-dimensional scattering Helmholtz and Schrödinger equations based on multigrid.

Inverse problems and Tomography

Multiscale Methods for Kinetic Models.

We are developing new numerical lifting operators for problems described by the Boltzmann equation.

Solvers for Nonlinear Schrödinger equations.

Nonlinear Schrödinger equations are used to model a wide range of applications. We have developed efficient solvers that scale optimally.

Numerical Continuation of Resonances.

We have have introduced numerical continuation to track resonances in quantum mechanical systems. Numerical Continuation is frequently used in dynamical systems. The method can track transition betweenresonant and bound state in single channel problems, coupled channel problems with equal and unequal tresholds.

Scattering and breakup of molecular systems.

Scattering in the oscillator representation