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Chapter and Conference Paper
Domain Decomposition Solvers for Operators with Fractional Interface Perturbations
Mathematical models featuring interaction of physical systems across a common interface describe numerous phenomena in engineering, environmental sciences and medicine.
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Chapter
Robust Preconditioning of Mixed-Dimensional PDEs on 3d-1d Domains Coupled with Lagrange Multipliers
In the context of micro-circulation, the coexistence of two distinct length scales—the vascular radius and the tissue/organ scale—with a substantial difference in magnitude, poses significant challenges. To ha...
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Article
Open AccessA cell-based framework for modeling cardiac mechanics
Cardiomyocytes are the functional building blocks of the heart—yet most models developed to simulate cardiac mechanics do not represent the individual cells and their surrounding matrix. Instead, they work on ...
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Article
Open AccessSleep cycle-dependent vascular dynamics in male mice and the predicted effects on perivascular cerebrospinal fluid flow and solute transport
Perivascular spaces are important highways for fluid and solute transport in the brain enabling efficient waste clearance during sleep. However, the underlying mechanisms augmenting perivascular flow in sleep ...
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Chapter and Conference Paper
Rational Approximation Preconditioners for Multiphysics Problems
We consider a class of mathematical models describing multiphysics phenomena interacting through interfaces. On such interfaces, the traces of the fields lie (approximately) in the range of a weighted sum of t...
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Article
Robust Approximation of Generalized Biot-Brinkman Problems
The generalized Biot-Brinkman equations describe the displacement, pressures and fluxes in an elastic medium permeated by multiple viscous fluid networks and can be used to study complex poromechanical interac...
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Article
Open AccessInvestigating molecular transport in the human brain from MRI with physics-informed neural networks
In recent years, a plethora of methods combining neural networks and partial differential equations have been developed. A widely known example are physics-informed neural networks, which solve problems involv...
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Chapter
Chapter 6 Digital tracing, validation, and reporting
Manual contact tracing has been a key component in controlling the outbreak of the COVID-19 pandemic. The identification and isolation of close contacts of confirmed cases have successfully interrupted transmi...
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Chapter
Solving the EMI Equations using Finite Element Methods
This chapter discusses 2 X 2 symmetric variational formulations and associated finite element methods for the EMI equations. We demonstrate that the presented methods converge at expected rates, and compare th...
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Chapter
Improving Neural Simulations with the EMI Model
Mathematical modeling of neurons is an essential tool to investigate neuronal activity alongside with experimental approaches. However, the conventional modeling framework to simulate neuronal dynamics and ext...
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Chapter and Conference Paper
Assembly of Multiscale Linear PDE Operators
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 present...
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Chapter
Iterative Solvers for EMI Models
This chapter deals with iterative solution algorithms for the four EMI formulations derived in (17, Chapter 5). Order optimal monolithic solvers robust with respect to material parameters, the number of degree...
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Chapter and Conference Paper
Sub-voxel Perfusion Modeling in Terms of Coupled 3d-1d Problem
We study perfusion by a multiscale model coupling diffusion in the tissue and diffusion along the one-dimensional segments representing the vasculature. We propose a block-diagonal preconditioner for the model...
