# Research Focus

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## Contents

## Efficient Numerical Algorithms

- High-dimensional numerics – Sparse Grids
- Fast iterative solvers – multi-level methods, preconditioners
- Adaptive, octree-based grid generation
- Space-filling curves
- Numerical linear algebra
- Numerical algorithms for image processing

## Parallel & High-Performance Computing

- HW-aware numerical programming
- Parallelisation – MPI, OpenMP, hybrid; load balancing, scalability
- Grid Computing

## Uncertainty Quantification

- Stochastic Collocation / gPC Methods for different simulation applications
- Sparse Grids in Uncertainty Quantification

## Computational Fluid Dynamics

- Discretisation and algorithms on adaptive Cartesian grids
- Fluid-structure interaction

## Fields of Application in Simulation

- Molecular dynamics
- Quantum chemistry
- CFD
- Traffic
- Computational Finance

## Integration of Simulation Tasks

- Problem solving environments
- Octree-based approaches

## Quantum Computing and Computational Physics

- Tensor network methods
- Quantum Monte Carlo
- Neural-network quantum states
- Quantum Boltzmann equations
- Quantum algorithms