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Optimal design of cylindrical shells

Peter Nestler, Werner H. Schmidt (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

The present paper studies an optimization problem of dynamically loaded cylindrical tubes. This is a problem of linear elasticity theory. As we search for the optimal thickness of the tube which minimizes the displacement under forces, this is a problem of shape optimization. The mathematical model is given by a differential equation (ODE and PDE, respectively); the mechanical problem is described as an optimal control problem. We consider both the stationary (time independent) and the transient...

Optimized Schwarz coupling of Bidomain and Monodomain models in electrocardiology

Luca Gerardo-Giorda, Mauro Perego, Alessandro Veneziani (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The Bidomain model is nowadays one of the most accurate mathematical descriptions of the action potential propagation in the heart. However, its numerical approximation is in general fairly expensive as a consequence of the mathematical features of this system. For this reason, a simplification of this model, called Monodomain problem is quite often adopted in order to reduce computational costs. Reliability of this model is however questionable, in particular in the presence of applied currents...

Optimized Schwarz coupling of Bidomain and Monodomain models in electrocardiology

Luca Gerardo-Giorda, Mauro Perego, Alessandro Veneziani (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

The Bidomain model is nowadays one of the most accurate mathematical descriptions of the action potential propagation in the heart. However, its numerical approximation is in general fairly expensive as a consequence of the mathematical features of this system. For this reason, a simplification of this model, called Monodomain problem is quite often adopted in order to reduce computational costs. Reliability of this model is however questionable, in particular in the presence of applied currents...

Optimized Schwarz Methods for the Bidomain system in electrocardiology

Luca Gerardo-Giorda, Mauro Perego (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

The propagation of the action potential in the heart chambers is accurately described by the Bidomain model, which is commonly accepted and used in the specialistic literature. However, its mathematical structure of a degenerate parabolic system entails high computational costs in the numerical solution of the associated linear system. Domain decomposition methods are a natural way to reduce computational costs, and Optimized Schwarz Methods have proven in the recent years their effectiveness in...

Option valuation under the VG process by a DG method

Jiří Hozman, Tomáš Tichý (2021)

Applications of Mathematics

The paper presents a discontinuous Galerkin method for solving partial integro-differential equations arising from the European as well as American option pricing when the underlying asset follows an exponential variance gamma process. For practical purposes of numerical solving we introduce the modified option pricing problem resulting from a localization to a bounded domain and an approximation of small jumps, and we discuss the related error estimates. Then we employ a robust numerical procedure...

Origins, analysis, numerical analysis, and numerical approximation of a forward-backward parabolic problem

A. Kadir Aziz, Donald A. French, Soren Jensen, R. Bruce Kellogg (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider the analysis and numerical solution of a forward-backward boundary value problem. We provide some motivation, prove existence and uniqueness in a function class especially geared to the problem at hand, provide various energy estimates, prove a priori error estimates for the Galerkin method, and show the results of some numerical computations.

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