Publications related to BECOOL: Ballooning eigensolver with COOL finite elements

Singular quadratic eigenvalue problems: linearization and weak condition numbers

The numerical solution of singular eigenvalue problems is complicated by the fact that small perturbations of the coefficients may have an arbitrarily bad effect on eigenvalue accuracy. However, it has been known for a long time that such perturbations are ...

SPRINGER2023

THE WEYL LAW OF TRANSMISSION EIGENVALUES AND THE COMPLETENESS OF GENERALIZED TRANSMISSION EIGENFUNCTIONS WITHOUT COMPLEMENTING CONDITIONS

Hoài-Minh Nguyên, Jean Louis-Alexandre Fornerod

The transmission eigenvalue problem is a system of two second-order elliptic equations of two unknowns equipped with the Cauchy data on the boundary. In this work, we establish the Weyl law for the eigenvalues and the completeness of the generalized eigenf ...

Philadelphia2023

Robust Differentiable SVD

Pascal Fua, Mathieu Salzmann, Zheng Dang, Wei Wang, Yinlin Hu

Eigendecomposition of symmetric matrices is at the heart of many computer vision algorithms. However, the derivatives of the eigenvectors tend to be numerically unstable, whether using the SVD to compute them analytically or using the Power Iteration (PI) ...

2021

Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations

Giacomo Garegnani

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 ...

EPFL2021

Complementary Asymptotically Sharp Estimates for Eigenvalue Means of Laplacians

Joachim Stubbe, Luigi Provenzano

We present asymptotically sharp inequalities, containing a 2nd term, for the Dirichlet and Neumann eigenvalues of the Laplacian on a domain, which are complementary to the familiar Berezin-Li-Yau and Kroger inequalities in the limit as the eigenvalues tend ...

OXFORD UNIV PRESS2021

Compress-and-restart block Krylov subspace methods for Sylvester matrix equations

Daniel Kressner, Stefano Massei, Kathryn Dianne Lund

Block Krylov subspace methods (KSMs) comprise building blocks in many state-of-the-art solvers for large-scale matrix equations as they arise, for example, from the discretization of partial differential equations. While extended and rational block Krylov ...

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

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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 ...

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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

A high-order discontinuous Galerkin approximation to ordinary differential equations with applications to elastodynamics

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The aim of this work is to propose and analyse a new high-order discontinuous Galerkin finite element method for the time integration of a Cauchy problem for second-order ordinary differential equations. These equations typically arise after space semidisc ...

OXFORD UNIV PRESS2018

BECOOL: Ballooning eigensolver with COOL finite elements

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Singular quadratic eigenvalue problems: linearization and weak condition numbers

THE WEYL LAW OF TRANSMISSION EIGENVALUES AND THE COMPLETENESS OF GENERALIZED TRANSMISSION EIGENFUNCTIONS WITHOUT COMPLEMENTING CONDITIONS

Robust Differentiable SVD

Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations

Complementary Asymptotically Sharp Estimates for Eigenvalue Means of Laplacians

Compress-and-restart block Krylov subspace methods for Sylvester matrix 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

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

A high-order discontinuous Galerkin approximation to ordinary differential equations with applications to elastodynamics

THE WEYL LAW OF TRANSMISSION EIGENVALUES AND THE COMPLETENESS OF GENERALIZED TRANSMISSION EIGENFUNCTIONS WITHOUT COMPLEMENTING CONDITIONS

Probabilistic and Bayesian methods for uncertainty quantification of deterministic and stochastic differential equations

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

Singular quadratic eigenvalue problems: linearization and weak condition numbers

Complementary Asymptotically Sharp Estimates for Eigenvalue Means of Laplacians

Robust Differentiable SVD

Compress-and-restart block Krylov subspace methods for Sylvester matrix equations

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

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

A high-order discontinuous Galerkin approximation to ordinary differential equations with applications to elastodynamics