Publications related to Explicit and implicit methods

Upper bounds for the reach-avoid probability via robust optimization

Maryam Kamgarpour, John Lygeros, Tyler Summers

We consider finite horizon reach-avoid problems for discrete time stochastic systems. Our goal is to construct upper bound functions for the reach-avoid probability by means of tractable convex optimization problems. We achieve this by restricting attentio ...

2015

MATHICSE Technical Report : Finite element heterogeneous multiscale method for nonlinear monotone parabolic homogenization problems

Assyr Abdulle, Martin Ernst Huber

We propose a multiscale method based on a finite element heterogeneous multiscale method (in space) and the implicit Euler integrator (in time) to solve nonlinear monotone parabolic problems with multiple scales due to spatial heterogeneities varying rapid ...

MATHICSE2014

A decoupled and unconditionally convergent linear FEM integrator for the Landau-Lifshitz-Gilbert equation with magnetostriction

Jonathan Rochat

To describe and simulate dynamic micromagnetic phenomena, we consider a coupled system of the non-linear Landau-Lifshitz-Gilbert equation and the conservation of momentum equation. This coupling allows one to include magnetostrictive effects into the simul ...

Oxford University Press2014

Inexact accurate partitioned algorithms for fluid-structure interaction problems with finite elasticity in haemodynamics

Fabio Nobile, Christian Vergara

In this paper we consider the numerical solution of the three-dimensional fluid–structure interaction problem in haemodynamics, in the case of real geometries, physiological data and finite elasticity vessel deformations. We study some new inexact schemes, ...

Elsevier2014

A two-period model with portfolio choice: Understanding results from different solution methods

Serhiy Stepanchuk

Using a stylized two-period model we compare portfolio solutions from two local solution approaches - the approach of Judd and Guu (2001) and the approach of Devereux and Sutherland (2010, 2011) - with the true nonlinear portfolio solution. (C) 2014 The Au ...

Elsevier2014

Projective Dynamics: Fusing Constraint Projections for Fast Simulation

Mark Pauly, Ladislav Kavan, Sofien Bouaziz

We present a new method for implicit time integration of physical systems. Our approach builds a bridge between nodal Finite Element methods and Position Based Dynamics, leading to a simple, efficient, robust, yet accurate solver that supports many differe ...

Assoc Computing Machinery2014

Splitting methods in control

Colin Neil Jones, Ye Pu, Georgios Stathopoulos, Alexander Szücs

The need for optimal control of processes under a restricted amount of resources renders first order optimization methods a viable option. Although computationally cheap, these methods typically suffer from slow convergence rates. In this work we discuss t ...

IEEE2014

Determination of Inner and Outer Bounds of Reachable Sets Through Subpavings

Francisco Fernandes Castro Rego

The computation of the reachable set of states of a given dynamic system is an important step to verify its safety during operation. There are different methods of computing reachable sets, namely interval integration, capture basin, methods involving the ...

2014

Stable blow up dynamics for energy supercritical wave equations

Roland Donninger

We study the semilinear wave equation

\displaystyle \partial _t^2 \psi -\Delta \psi =\vert\psi \vert^{p-1}\psi

for

p > 3

with radial data in three spatial dimensions. There exists an explicit solution which blows up at

t=T>0

given by $\displaystyl ...

American Mathematical Society2014

Coupled Mathematical Models for Heart Integration: A Stability Study

Andrea Di Blasio

In this thesis we consider a fully coupled model which aims at reproducing some qualitative features of the electro-mechanical activity of the heart. The models used to describe both the electrical and mechanical activities are relatively simple. However, ...

2014

Explicit and implicit methods

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Upper bounds for the reach-avoid probability via robust optimization

MATHICSE Technical Report : Finite element heterogeneous multiscale method for nonlinear monotone parabolic homogenization problems

A decoupled and unconditionally convergent linear FEM integrator for the Landau-Lifshitz-Gilbert equation with magnetostriction

Inexact accurate partitioned algorithms for fluid-structure interaction problems with finite elasticity in haemodynamics

A two-period model with portfolio choice: Understanding results from different solution methods

Projective Dynamics: Fusing Constraint Projections for Fast Simulation

Splitting methods in control

Determination of Inner and Outer Bounds of Reachable Sets Through Subpavings

Stable blow up dynamics for energy supercritical wave equations

Coupled Mathematical Models for Heart Integration: A Stability Study

MATHICSE Technical Report : Finite element heterogeneous multiscale method for nonlinear monotone parabolic homogenization problems

Upper bounds for the reach-avoid probability via robust optimization

A decoupled and unconditionally convergent linear FEM integrator for the Landau-Lifshitz-Gilbert equation with magnetostriction

Splitting methods in control

Determination of Inner and Outer Bounds of Reachable Sets Through Subpavings

Stable blow up dynamics for energy supercritical wave equations

Inexact accurate partitioned algorithms for fluid-structure interaction problems with finite elasticity in haemodynamics

A two-period model with portfolio choice: Understanding results from different solution methods

Projective Dynamics: Fusing Constraint Projections for Fast Simulation

Coupled Mathematical Models for Heart Integration: A Stability Study