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We present a flexible discretization technique for computational models of thin tubular networks embedded in a bulk domain, for example a porous medium. These systems occur in the simulation of fluid flow in vascularized biological tissue,…
An optimization-based strategy is proposed for coupling three-dimensional and one-dimensional problems (3D-1D coupling) in the context of soil-root interaction simulations. This strategy, originally designed to tackle generic 3D-1D coupled…
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 embedded in the extra-vascular space. Vascular and extra-vascular space…
This paper presents a distributed nonlinear model predictive control that uses alternating direction method of mul tipliers for district heating networks. Exploiting a graph-based modeling of the thermal dynamics, our controller optimizes…
We develop a complementarity-constrained nonlinear optimization model for the time-dependent control of district heating networks. The main physical aspects of water and heat flow in these networks are governed by nonlinear and hyperbolic…
Modeling unsaturated flow through soils with water uptake by plan root has many applications in agriculture and water resources management. In this study, our aim is to develop efficient numerical techniques for solving the Richards…
A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…
In this work, we consider compressible single-phase flow problems in a porous media containing a fracture. In the latter, a non-linear pressure-velocity relation is prescribed. Using a non-overlapping domain decomposition procedure, we…
Control of water distribution networks (WDNs) can be represented by an optimization problem with hydraulic models describing the nonlinear relationship between head loss, water flow, and demand. The problem is difficult to solve due to the…
In this paper we study a system of advection-diffusion equations in a bulk domain coupled to an advection-diffusion equation on an embedded surface. Such systems of coupled partial differential equations arise in, for example, the modeling…
In order to identify a system (module) embedded in a dynamic network, one has to formulate a multiple-input estimation problem that necessitates certain nodes to be measured and included as predictor inputs. However, some of these nodes may…
We propose a novel numerical approach for nonlocal diffusion equations [8] with integrable kernels, based on the relationship between the backward Kolmogorov equation and backward stochastic differential equations (BSDEs) driven by L\`{e}vy…
This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. The idea comes from the observation that convolutional layers can be used to express a discretisation as a neural network…
The paper develops a hybrid method for solving a system of advection--diffusion equations in a bulk domain coupled to advection--diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in…
A mechanical model and numerical method for the simultaneous analysis of Reissner-Mindlin shells with geometries implied by a continuous set of level sets (isosurfaces) over some three-dimensional bulk domain is presented. A…
The numerical simulation of large-scale multiphase flow in porous media is of considerable importance across various application fields, particularly in the petroleum industry. The fully implicit method is preferred in reservoir simulations…
A mechanical model and numerical method for structural membranes implied by all isosurfaces of a level-set function in a three-dimensional bulk domain are proposed. The mechanical model covers large displacements in the context of the…
This paper presents a novel online identification algorithm for nonlinear regression models. The online identification problem is challenging due to the presence of nonlinear structure in the models. Previous works usually ignore the…
In the present paper a detailed mathematical model is derived for district heating networks. After semidiscretization of the convective heat equation and introducing coupling conditions at the nodes of the network one gets a…
Nonlinear partial differential equations (PDEs) are used to model dynamical processes in a large number of scientific fields, ranging from finance to biology. In many applications standard local models are not sufficient to accurately…