Pipelined Numerical Integration on Reduced Accuracy Architectures for Power System Transient Simulations
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A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a random forcing term, ...
Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...
As historical stone masonry structures are vulnerable and prone to damage in earthquakes, investigating their structural integrity is important to reduce injuries and casualties while preserving their historical value. Stone masonry is a composite material ...
In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...
Ehrenfest dynamics is a useful approximation for ab initio mixed quantum-classical molecular dynamics that can treat electronically nonadiabatic effects. Although a severe approximation to the exact solution of the molecular time-dependent Schrödinger equa ...
Among the single-trajectory Gaussian-based methods for solving the time-dependent Schrödinger equation, the variational Gaussian approximation is the most accurate one. In contrast to Heller’s original thawed Gaussian approximation, it is symplectic, conse ...
The isentropic vortex problem is frequently solved to test the accuracy of numerical methods and verify corresponding code. Unfortunately, its existing solution was derived in the relativistic magnetohydrodynamics by numerically solving an ordinary differe ...
In this thesis we explore uncertainty quantification of forward and inverse problems involving differential equations. Differential equations are widely employed for modeling natural and social phenomena, with applications in engineering, chemistry, meteor ...
The homotopy continuation method has been widely used to compute multiple solutions of nonlinear differential equations, but the computational cost grows exponentially based on the traditional finite difference and finite element discretizations. In this w ...
Many physical and chemical reactions are driven by nonadiabatic processes, which imply the breakdown of the celebrated Born-Oppenheimer approximation. To understand these processes, experimentalists employ spectroscopic techniques. However, the obtained re ...