Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

In this work, we analyze space-time reduced basis methods for the efficient numerical simulation of haemodynamics in arteries. The classical formulation of the reduced basis (RB) method features dimensionality reduction in space, while finite difference sc ...

Chaos sets a fundamental limit to quantum-information processing schemes. We study the onset of chaos in spatially extended quantum many-body systems that are relevant to quantum optical devices. We consider an extended version of the Tavis-Cummings model ...

We establish shape holomorphy results for general weakly- and hyper-singular boundary integral operators arising from second-order partial differential equations in unbounded two-dimensional domains with multiple finite-length open arcs. After recasting th ...

We propose a local, non -intrusive model order reduction technique to accurately approximate the solution of coupled multi -component parametrized systems governed by partial differential equations. Our approach is based on the approximation of the boundar ...

Kontsevich and Soibelman reformulated and slightly generalised the topological recursion of [43], seeing it as a quantisation of certain quadratic Lagrangians in T*V for some vector space V. KS topological recursion is a procedure which takes as initial da ...

The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...

We introduce a high-order spline geometric approach for the initial boundary value problem for Maxwell's equations. The method is geometric in the sense that it discretizes in structure preserving fashion the two de Rham sequences of differential forms inv ...

This paper presents a theoretical analysis of linear interpolation as a principled method for stabilizing (large-scale) neural network training. We argue that instabilities in the optimization process are often caused by the nonmonotonicity of the loss lan ...

The accurate, robust and efficient transfer of the deformation gradient tensor between meshes of different resolution is crucial in cardiac electromechanics simulations. This paper presents a novel method that combines rescaled localized Radial Basis Funct ...

We consider the problem of nonparametric estimation of the drift and diffusion coefficients of a Stochastic Differential Equation (SDE), based on n independent replicates {Xi(t) : t is an element of [0 , 1]}13 d B(t), where alpha is an element of {0 , 1} a ...

This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...

Since the birth of Information Theory, researchers have defined and exploited various information measures, as well as endowed them with operational meanings. Some were born as a "solution to a problem", like Shannon's Entropy and Mutual Information. Other ...

Modern manufacturing engineering is based on a ``design-through-analysis'' workflow. According to this paradigm, a prototype is first designed with Computer-aided-design (CAD) software and then finalized by simulating its physical behavior, which usually i ...

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. However, ...

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 ...

This paper deals with a new analytical model for microfluidic passive mixers. Two common approaches already exist for such a purpose. On the one hand, the resolution of the advection-diffusion-reaction equation (ADRE) is the first one and the closest to ph ...

Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...

The parallel Schwarz method (PSM) is an overlapping domain decomposition (DD) method to solve partial differential equations (PDEs). Similarly to classical nonoverlapping DD methods, the PSM admits a substructured formulation, that is, it can be formulated ...

The Internodes method is a general purpose method to deal with non-conforming discretizations of partial differential equations on 2D and 3D regions partitioned into disjoint subdomains. In this paper we are interested in measuring how much the Internodes ...

Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis

Chat with Graph Search

SPACE-TIME REDUCED BASIS METHODS FOR PARAMETRIZED UNSTEADY STOKES EQUATIONS

Transition to chaos in extended systems and their quantum impurity models

Shape Holomorphy of Boundary Integral Operators on Multiple Open Arcs

Model reduction of coupled systems based on non-intrusive approximations of the boundary response maps

The ABCD of topological recursion

Retraction-based numerical methods for continuation, interpolation and time integration on manifolds

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

High order geometric methods with splines: fast solution with explicit time-stepping for Maxwell equations

Stable Nonconvex-Nonconcave Training via Linear Interpolation

Preserving the positivity of the deformation gradient determinant in intergrid interpolation by combining RBFs and SVD: Application to cardiac electromechanics

Nonparametric estimation for SDE with sparsely sampled paths: An FDA perspective

Positive Definite Completions and Continuous Graphical Models

A Functional Perspective on Information Measures

Stabilized isogeometric discretizations on trimmed and union geometries, and weak imposition of the boundary conditions for the Darcy flow

Adaptive analysis-aware defeaturing

PDE-Aware Deep Learning for Inverse Problems in Cardiac Electrophysiology

Analytic modelling of passive microfluidic mixers

Collapse-invariant properties of spaces equipped with signals or directions

Spectral Coarse Spaces for the Substructured Parallel Schwarz Method

Conservation of Forces and Total Work at the Interface Using the Internodes Method