Derivation and analysis of coupled PDEs on manifolds with high dimensionality gap arising from topological model reduction
Multiscale methods based on coupled partial differential equations defined on bulk and
embedded manifolds are still poorly explored from the theoretical standpoint, although they …
embedded manifolds are still poorly explored from the theoretical standpoint, although they …
Mathematical modeling, analysis and numerical approximation of second-order elliptic problems with inclusions
T Köppl, E Vidotto, B Wohlmuth… - Mathematical Models and …, 2018 - World Scientific
Many biological and geological systems can be modeled as porous media with small
inclusions. Vascularized tissue, roots embedded in soil or fractured rocks are examples of …
inclusions. Vascularized tissue, roots embedded in soil or fractured rocks are examples of …
Analysis and approximation of mixed-dimensional PDEs on 3D-1D domains coupled with Lagrange multipliers
Coupled partial differential equations (PDEs) defined on domains with different
dimensionality are usually called mixed-dimensional PDEs. We address mixed-dimensional …
dimensionality are usually called mixed-dimensional PDEs. We address mixed-dimensional …
Hybrid models for simulating blood flow in microvascular networks
In this paper, we are concerned with the simulation of blood flow in microvascular networks
and the surrounding tissue. To reduce the computational complexity of this issue, the …
and the surrounding tissue. To reduce the computational complexity of this issue, the …
A singularity removal method for coupled 1D–3D flow models
In reservoir simulations, the radius of a well is inevitably going to be small compared to the
horizontal length scale of the reservoir. For this reason, wells are typically modelled as lower …
horizontal length scale of the reservoir. For this reason, wells are typically modelled as lower …
Modeling tissue perfusion in terms of 1d-3d embedded mixed-dimension coupled problems with distributed sources
We present a new method for modeling tissue perfusion on the capillary scale. The
microvasculature is represented by a network of one-dimensional vessel segments …
microvasculature is represented by a network of one-dimensional vessel segments …
Mathematical analysis, finite element approximation and numerical solvers for the interaction of 3d reservoirs with 1d wells
We develop a mathematical model for the interaction of a three-dimensional reservoir with
the flow through wells, namely narrow cylindrical channels cutting across the reservoir. Leak …
the flow through wells, namely narrow cylindrical channels cutting across the reservoir. Leak …
Splitting method for elliptic equations with line sources
In this paper, we study the mathematical structure and numerical approximation of elliptic
problems posed in a (3D) domain Ω when the right-hand side is a (1D) line source Λ. The …
problems posed in a (3D) domain Ω when the right-hand side is a (1D) line source Λ. The …
[图书][B] Mixed-dimension models for flow and transport processes in porous media with embedded tubular network systems
T Koch - 2020 - elib.uni-stuttgart.de
Flow in vascularized biological tissue, root water uptake, or flow around injection or
extraction wells can be modeled by coupled mixed-dimensional PDE systems …
extraction wells can be modeled by coupled mixed-dimensional PDE systems …
Preconditioning trace coupled 3d‐1d systems using fractional Laplacian
Multiscale or multiphysics problems often involve coupling of partial differential equations
posed on domains of different dimensionality. In this work, we consider a simplified model …
posed on domains of different dimensionality. In this work, we consider a simplified model …