Assembly of multiscale linear PDE operators

12/19/2019
by   Miroslav Kuchta, et al.
0

In numerous applications the mathematical model consists of different processes coupled across a lower dimensional manifold. Due to the multiscale coupling, finite element discretization of such models presents a challenge. Assuming that only singlescale finite element forms can be assembled we present here a simple algorithm for representing multiscale models as linear operators suitable for Krylov methods. Flexibility of the approach is demonstrated by numerical examples with coupling across dimensionality gap 1 and 2. Preconditioners for several of the problems are discussed.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

04/14/2022

Non-intrusive implementation of Multiscale Finite Element Methods: an illustrative example

Multiscale Finite Element Methods (MsFEM) are finite element type approa...
02/25/2022

Interfacing Finite Elements with Deep Neural Operators for Fast Multiscale Modeling of Mechanics Problems

Multiscale modeling is an effective approach for investigating multiphys...
07/20/2021

Fast and Multiscale Formation of Isogeometric matrices of Microstructured Geometric Models

The matrix formation associated to high-order discretizations is known t...
06/11/2021

Multiscale modeling of cancellous bone considering full coupling of mechanical, electrical and magnetic effects

Modeling of cancellous bone has important applications in the detection ...
04/28/2019

A new object-oriented framework for solving multiphysics problems via combination of different numerical methods

Many interesting phenomena are characterized by the complex interaction ...
02/22/2020

The candy wrapper problem – a temporal multiscale approach for pde/pde systems

We describe a temporal multiscale approach for the simulation of long-te...
03/01/2021

Pyramid Transform of Manifold Data via Subdivision Operators

Multiscale transform has become a key ingredient in many data processing...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.