##### Department of Mathematics,

University of California San Diego

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### Math 278A - Center for Computational Mathematics Seminar

## Andre Jurgen Massing

#### Norwegian University of Science and Technology

## Cut finite element methods for complex multi-physics problems

##### Abstract:

Many advanced computational problems in engineering and biologyrequire the numerical solution of multidomain, multidimension, multiphysics and multimaterial problems with interfaces. When the interface geometry is highly complex or evolving in time, the generation of conforming meshes may become prohibitively expensive, thereby severely limiting the scope of conventional discretization methods.

In this talk we focus on recent, so-called cut finite element methods (CutFEM) as one possible remedy. The main idea is to design a discretization method which allows for the embedding of purely surface-based geometry representations into structured and easy-to-generate background meshes.

In the first part of the talk, we explain how the CutFEM framework leads to accurate and optimal convergent discretization schemes for a variety of PDEs posed on complex geometries. Furthermore, we demonstrate their effectiveness when discretizing PDEs on evolving domains, including Navier-Stokes equations and fluid-structure interaction problems with large deformations. In the second part of the talk, we show that the CutFEM framework can also be used to discretize surface-bound PDEs as well as mixed-dimensional problems where PDEs are posed on domains of different topological dimensionality.

As a particular example, we consider the so-called Extracellular-Membran-Intracel

### April 2, 2024

### 11:00 AM

AP&M 2402 and Zoom ID 982 8500 1195

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