The modeling of the diffusion MRI signal from moving and deforming organs such as the heart is challenging due to significant motion and deformation of the imaged medium during the signal acquisition. Recently, a mathematical formulation of the Bloch-Torre ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2020

MATHICSE Technical Report: A non-intrusive multifidelity method for the reduced order modeling of nonlinear problems

Jan Sickmann Hesthaven, Mariella Kast, Mengwu Guo

We propose a non-intrusive reduced basis (RB) method for parametrized nonlinear partial differential equations (PDEs) that leverages models of different accuracy. The method extracts parameter locations from a collection of low-fidelity (LF) snapshots for ...

MATHICSE2019

A comparative study of earthquake source models in high- order accurate tsunami simulations

Jan Sickmann Hesthaven, Boris Bonev

The discontinuous Galerkin method is used to solve the non-linear spherical shallow water equations with Coriolis force. The numerical method is well-balanced and takes wetting/drying into account. The two fold goal of this work is a comparative study of d ...

2019

Model order reduction for large-scale structures with local nonlinearities

Jan Sickmann Hesthaven, Mengwu Guo, Zhenying Zhang

In solid mechanics, linear structures often exhibit (local) nonlinear behavior when close to failure. For instance, the elastic deformation of a structure becomes plastic after being deformed beyond recovery. To properly assess such problems in a real-life ...

ELSEVIER SCIENCE SA2019

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High-order numerical solvers for conservation laws suer from Gibbs phenomenon close to discontinuities, leading to spurious oscillations and a detrimental effect on the solution accuracy. A possible strategy to reduce it comprises adding a suitable amount ...

MATHICSE2019

MATHICSE Technical Report: Simulation-Based Anomaly Detection and Damage Localization: an Application to Structural Health Monitoring

Jan Sickmann Hesthaven, Caterina Bigoni

We propose a simulation-based decision strategy for the proactive maintenance of complex structures with a particular application to structural health monitoring (SHM). The strategy is based on a data-driven approach which exploits an offine-online decompo ...

MATHICSE2019

Projective multiscale time-integration for electrostatic particle-in-cell methods

Jan Sickmann Hesthaven, Paul Isaac Denis Louis Marie Cazeaux

The simulation of problems in kinetic plasma physics is often challenging due to strongly coupled phenomena across multiple scales. In this work, we propose a wavelet-based coarse-grained numerical scheme, based on the framework of Equation-Free Projective ...

2019

MATHICSE Technical Report: Constraint-Aware Neural Networks for Riemann Problems

Jan Sickmann Hesthaven, Deep Ray

Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be satised to obtain ...

MATHICSE2019

Waves at a fluid-solid interface: Explicit versus implicit formulation of boundary conditions using a discontinuous Galerkin method

Jan Sickmann Hesthaven, Khemraj Shukla

An accurate solution of the wave equation at a fluid-solid interface requires a correct implementation of the boundary condition. Boundary conditions at acousto-elastic interface require continuity of the normal component of particle velocity and traction, ...

2019