Publications related to Numerical Methods for First and Second Order Fully Nonlinear Partial Differential Equations

Numerical Approximation Of Orthogonal Maps

Marco Picasso, Alexandre Caboussat, Dimitrios Gourzoulidis

Orthogonal maps are the solutions of the mathematical model of paper-folding, also called the origami problem. They consist of a system of first-order fully nonlinear equations involving the gradient of the solution. The Dirichlet problem for orthogonal ma ...

2019

Performance Assessment of Kron Reduction in the Numerical Analysis of Polyphase Power Systems

Mario Paolone, Andreas Martin Kettner

This paper investigates the impact of Kron reduction on the performance of numerical methods applied to the analysis of unbalanced polyphase power systems. Specifically, this paper focuses on power-flow study, state estimation, and voltage stability assess ...

IEEE2019

An algebraic least squares reduced basis method for the solution of nonaffinely parametrized Stokes equations

Alfio Quarteroni, Simone Deparis, Andrea Manzoni, Niccolò Dal Santo

In this paper we propose a new, purely algebraic, Petrov-Galerkin reduced basis (RB) method to solve the parametrized Stokes equations, where parameters serve to identify the (variable) domain geometry. Our method is obtained as an algebraic least squares ...

ELSEVIER SCIENCE SA2019

MATHICSE Technical Report: Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial\ viscosity tuned by neural networks

Jan Sickmann Hesthaven, Niccolo' Discacciati, Deep Ray

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

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

Stefano Massei

Evaluating the action of a matrix function on a vector, that is

x=f(\mathcal M)v

, is an ubiquitous task in applications. When

\mathcal M

is large, one usually relies on Krylov projection methods. In this paper, we provide effective choices for the pole ...

2019

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

A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations

Assyr Abdulle, Giacomo Rosilho De Souza

A local weighted discontinuous Galerkin gradient discretization method for solving elliptic equations is introduced. The local scheme is based on a coarse grid and successively improves the solution solving a sequence of local elliptic problems in high gra ...

EDP SCIENCES S A2019

Adaptive Isogeometric Methods With Hierarchical Splines: An Overview

Annalisa Buffa, Rafael Vazquez Hernandez

We consider an adaptive isogeometric method (AIGM) based on (truncated) hierarchical B-splines and present the study of its numerical properties. By following [10, 12, 11], optimal convergence rates of the AIGM can be proved when suitable approximation cla ...

2019

A Least-Squares/Relaxation Method for the Numerical Solution of the Three-Dimensional Elliptic Monge-Ampere Equation

Alexandre Caboussat, Dimitrios Gourzoulidis

In this article, we address the numerical solution of the Dirichlet problem for the three-dimensional elliptic Monge-Ampere equation using a least-squares/relaxation approach. The relaxation algorithm allows the decoupling of the differential operators fro ...

SPRINGER/PLENUM PUBLISHERS2018

MATHICSE Technical Report : Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration

Assyr Abdulle, Giacomo Garegnani

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, ...

MATHICSE2018

Numerical Methods for First and Second Order Fully Nonlinear Partial Differential Equations

Graph Chatbot

Chat with Graph Search

Numerical Approximation Of Orthogonal Maps

Performance Assessment of Kron Reduction in the Numerical Analysis of Polyphase Power Systems

An algebraic least squares reduced basis method for the solution of nonaffinely parametrized Stokes equations

MATHICSE Technical Report: Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial\ viscosity tuned by neural networks

Rational Krylov for Stieltjes matrix functions: convergence and pole selection

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

A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations

Adaptive Isogeometric Methods With Hierarchical Splines: An Overview

A Least-Squares/Relaxation Method for the Numerical Solution of the Three-Dimensional Elliptic Monge-Ampere Equation

MATHICSE Technical Report : Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration

An algebraic least squares reduced basis method for the solution of nonaffinely parametrized Stokes equations

A Least-Squares/Relaxation Method for the Numerical Solution of the Three-Dimensional Elliptic Monge-Ampere Equation

Numerical Approximation Of Orthogonal Maps

MATHICSE Technical Report: Controlling oscillations in high-order Discontinuous Galerkin schemes using artificial\ viscosity tuned by neural networks

Performance Assessment of Kron Reduction in the Numerical Analysis of Polyphase Power Systems

A local discontinuous Galerkin gradient discretization method for linear and quasilinear elliptic equations

MATHICSE Technical Report : Random time step probabilistic methods for uncertainty quantification in chaotic and geometric numerical integration

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

Adaptive Isogeometric Methods With Hierarchical Splines: An Overview

Rational Krylov for Stieltjes matrix functions: convergence and pole selection