Publications related to Simulation and Optimization of Partial Differential-Algebraic Equations with a Separation of Time Scales

MATHICSE technical Report : Stabilized explicit multirate methods for stiff differential equations

Stabilized Runge–Kutta (aka Chebyshev) methods are especially efficient for the numerical solution of large systems of stiff differential equations because they are fully explicit; hence, they are inherently parallel and easily accommodate nonlinearity. Fo ...

MATHICSE2020

Dynamical System Modeling of Self-Regulated Systems Undergoing Multiple Excitations: First Order Differential Equation Approach

Julien Gilles Edgar Gateau

This article proposes a dynamical system modeling approach for the analysis of longitudinal data of self-regulated homeostatic systems experiencing multiple excitations. It focuses on the evolution of a signal (e.g., heart rate) before, during, and after e ...

ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD2020

On the stability of blowup solutions for the critical corotational wave-map problem

Joachim Krieger, Shuang Miao

We show that the finite time blow up solutions for the co-rotational Wave Maps problem constructed in [7,15] are stable under suitably small perturbations within the co-rotational class, provided the scaling parameter

λ(t)=t−1−ν

is sufficiently close to ...

2020

Hybrid high-resolution RBF-ENO method

Jan Sickmann Hesthaven, Fabian Mönkeberg

Essentially nonoscillatory (ENO) and weighted ENO (WENO) methods on equidistant Cartesian grids are widely used to solve partial differential equations with discontinuous solutions. The RBF-ENO method is highly flexible in terms of geometry, but its stenci ...

2020

Optimal lower bounds on hitting probabilities for stochastic heat equations in spatial dimension k >= 1

Robert Dalang, Fei Pu

We establish a sharp estimate on the negative moments of the smallest eigenvalue of the Malliavin matrix gamma z of Z := (u(s, y), u(t , x) - u(s, y)), where u is the solution to a system of d non-linear stochastic heat equations in spatial dimension k >= ...

UNIV WASHINGTON, DEPT MATHEMATICS2020

Meta-concrete by means of discrete element method

Sacha Zenon Wattel

The basis of the discrete element method is to model masses interacting with each other through different forces and constraints. On each mass, the second law of Newton is applied to obtain a differential equation. From this equation and boundary condition ...

2019

Electrical conductivity of hot Abelian plasma with scalar charge carriers

Oleksandr Sobol

We study the electrical conductivity of hot Abelian plasma containing scalar charge carriers in the leading logarithmic order in coupling constant alpha using the Boltzmann kinetic equation. The leading contribution to the collision integral is due to the ...

2019

Machine learning for fast and reliable solution of time-dependent differential equations

Alfio Quarteroni, Francesco Regazzoni

We propose a data-driven Model Order Reduction (MOR) technique, based on Artificial Neural Networks (ANNs), applicable to dynamical systems arising from Ordinary Differential Equations (ODEs) or time-dependent Partial Differential Equations (PDEs). Unlike ...

2019

Solving differential equations with topological acoustic metamaterials

Romain Christophe Rémy Fleury, Farzad Zangeneh Nejad

The conventional idea of analog computing has recently been revived by recent developments of the fields of metamaterials and ultrafast optics, allowing one to perform signal-processing tasks at the speed of wave propagation with high efficiency. Despite t ...

2019

Low-Rank Updates And A Divide-And-Conquer Method For Linear Matrix Equations

Daniel Kressner, Stefano Massei

Linear matrix equations, such as the Sylvester and Lyapunov equations, play an important role in various applications, including the stability analysis and dimensionality reduction of linear dynamical control systems and the solution of partial differentia ...

SIAM PUBLICATIONS2019

Simulation and Optimization of Partial Differential-Algebraic Equations with a Separation of Time Scales

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MATHICSE technical Report : Stabilized explicit multirate methods for stiff differential equations

Dynamical System Modeling of Self-Regulated Systems Undergoing Multiple Excitations: First Order Differential Equation Approach

On the stability of blowup solutions for the critical corotational wave-map problem

Hybrid high-resolution RBF-ENO method

Optimal lower bounds on hitting probabilities for stochastic heat equations in spatial dimension k >= 1

Meta-concrete by means of discrete element method

Electrical conductivity of hot Abelian plasma with scalar charge carriers

Machine learning for fast and reliable solution of time-dependent differential equations

Solving differential equations with topological acoustic metamaterials

Low-Rank Updates And A Divide-And-Conquer Method For Linear Matrix Equations

Dynamical System Modeling of Self-Regulated Systems Undergoing Multiple Excitations: First Order Differential Equation Approach

Meta-concrete by means of discrete element method

Optimal lower bounds on hitting probabilities for stochastic heat equations in spatial dimension k >= 1

Machine learning for fast and reliable solution of time-dependent differential equations

Hybrid high-resolution RBF-ENO method

Solving differential equations with topological acoustic metamaterials

On the stability of blowup solutions for the critical corotational wave-map problem

MATHICSE technical Report : Stabilized explicit multirate methods for stiff differential equations

Electrical conductivity of hot Abelian plasma with scalar charge carriers

Low-Rank Updates And A Divide-And-Conquer Method For Linear Matrix Equations