A finite volume scheme for cardiac propagation in media with isotropic conductivities
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Wave phenomena manifest in nature as electromagnetic waves, acoustic waves, and gravitational waves among others.Their descriptions as partial differential equations in electromagnetics, acoustics, and fluid dynamics are ubiquitous in science and engineeri ...
Removing geometrical details from a complex domain is a classical operation in computer aided design for simulation and manufacturing. This procedure simplifies the meshing process, and it enables faster simulations with less memory requirements. But depen ...
This thesis focuses on the numerical analysis of partial differential equations (PDEs) with an emphasis on first and second-order fully nonlinear PDEs. The main goal is the design of numerical methods to solve a variety of equations such as orthogonal maps ...
Multiscale problems, such as modelling flows through porous media or predicting the mechanical properties of composite materials, are of great interest in many scientific areas. Analytical models describing these phenomena are rarely available, and one mus ...
In the present paper, a multi-step reconstruction procedure is proposed for high order finite volume schemes on unstructured grids using compact stencil. The procedure is a recursive algorithm that can eventually provide sufficient relations for high order ...
Modeling wave propagation in highly heterogeneous media is of prime importance in engineering applications of diverse nature such as seismic inversion, medical imaging or the design of composite materials. The numerical approximation of such multiscale phy ...
In this paper we consider, from the numerical point of view, a thermoelastic diffusion porous problem. This is written as a coupled system of two hyperbolic equations, for the displacement and porosity fields, and two parabolic equations, for the temperatu ...
In this work, we present a PDE-aware deep learning model for the numerical solution to the inverse problem of electrocardiography. The model both leverages data availability and exploits the knowledge of a physically based mathematical model, expressed by ...
We present a novel high-order discontinuous Galerkin discretization for the spherical shallow water equations, able to handle wetting/drying and non-conforming, curved meshes in a well-balanced manner. This requires a well-balanced discretization, that can ...
In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the electric potential ...