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MATHICSE Technical Report : Isogeometric analysis and proper orthogonal decomposition for the acoustic wave equation

Related publications (38)

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

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 ...

EPFL2021

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

Adaptive algorithms for two fluids flows with anisotropic finite elements and order two time discretizations

Samuel Dubuis

This thesis is devoted to the derivation of a posteriori error estimates for the numerical approximation of fluids flows separated by a free surface. Based on these estimates, error indicators are introduced and adaptive algorithms are proposed to solve th ...

EPFL2020

Novel corrector problems with exponential decay of the resonance error for numerical homogenization

Edoardo Paganoni

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 ...

EPFL2020

Topology design of general tensegrity with rigid bodies

Yafeng Wang

This study presents a general approach to the topology design of tensegrities with rigid bodies. To the best of the authors' knowledge, all existing topology design methods of tensegrities focus on tensegrities that only consist of members carrying axial f ...

PERGAMON-ELSEVIER SCIENCE LTD2020

Waves at a fluid-solid interface: Explicit versus implicit formulation of boundary conditions using a discontinuous Galerkin method

Jan Sickmann Hesthaven, Khemraj Shukla

An accurate solution of the wave equation at a fluid-solid interface requires a correct implementation of the boundary condition. Boundary conditions at acousto-elastic interface require continuity of the normal component of particle velocity and traction, ...

2019

Numerical Modelling of Two-Phase Flow with Moving Boundary Fitted Meshes

Erik Gros

In this thesis, a computational approach is used to study two-phase flow including phase change by direct numerical simulation. This approach follows the interface with an adaptive moving mesh. The incompressible Navier-Stokes equations are solved, in tw ...

EPFL2018

A monolithic algorithm for the simulation of cardiac electromechanics in the human left ventricle

Alfio Quarteroni, Antonello Gerbi

In this paper, we propose a monolithic algorithm for the numerical solution of the electromechanics model of the left ventricle in the human heart. Our coupled model integrates the monodomain equation with the Bueno-Orovio minimal model for electrophysiolo ...

AMER INST MATHEMATICAL SCIENCES-AIMS2018

Isogeometric Analysis And Proper Orthogonal Decomposition For The Acoustic Wave Equation

Alfio Quarteroni, Shengfeng Zhu

Discretization methods such as finite differences or finite elements were usually employed to provide high fidelity solution approximations for reduced order modeling of parameterized partial differential equations. In this paper, a novel discretization te ...

Edp Sciences S A2017

Verification and validation procedures with applications to plasma-edge turbulence simulations

Fabio Riva

Understanding the plasma dynamics in tokamaks is of fundamental importance to reliably predict the performances of future fusion devices. Because of the complex phenomena at play, state-of-the-art simulation codes are needed to investigate the plasma dynam ...

EPFL2017

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