相关论文: Preconditioning the bidomain model with almost lin…
We consider the primal and dual forms of the optimality conditions for PDE-contrained optimization problems arising in Data-Driven Computational Mechanics when specialized to the reaction-diffusion context. Starting with the continuous…
Spatially distributed problems are often approximately modelled in terms of partial differential equations (PDEs) for appropriate coarse-grained quantities (e.g. concentrations). The derivation of accurate such PDEs starting from finer…
A balancing domain decomposition by constraints (BDDC) algorithm with adaptive primal constraints in variational form is introduced and analyzed for high-order mortar discretization of two-dimensional elliptic problems with high varying and…
The joint prediction of continuous fields and statistical estimation of the underlying discrete parameters is a common problem for many physical systems, governed by PDEs. Hitherto, it has been separately addressed by employing operator…
The penetrations of lithium-ion batteries in transport, energy and communication systems are increasing rapidly. A meticulous model applicable for precise in-situ monitoring and convenient online controlling is in sought to bridge the gap…
CoronaryHemodynamics is a comprehensive simulation package developed on the OpenFOAM platform, designed specifically for coronary artery hemodynamics analysis. The package integrates a complete suite of tools for simulation preparation,…
The $p$-step backwards difference formula (BDF) for solving the system of ODEs can result in a kind of all-at-once linear systems, which are solved via the parallel-in-time preconditioned Krylov subspace solvers (see McDonald, Pestana, and…
The structure and function of biological molecules are strongly influenced by the water and dissolved ions that surround them. This aqueous solution (solvent) exerts significant electrostatic forces in response to the biomolecule's…
Cardiac digital twins provide a physics and physiology informed framework to deliver predictive and personalized medicine. However, high-fidelity multi-scale cardiac models remain a barrier to adoption due to their extensive computational…
The presented multi-scale, closed-loop blood circulation model includes arterial, venous, and portal venous systems, heart-pulmonary circulation, and micro-circulation in capillaries. One-dimensional models simulate large blood vessel flow,…
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 problem of a 3d-1d coupling and the main objective is to…
This article proposes a dynamical system modeling approach for the analysis of longitudinal data of self-regulated systems experiencing multiple excitations. The aim of such an approach is to focus on the evolution of a signal (e.g., heart…
We introduce a multiphysics and geometric multiscale computational model, suitable to describe the hemodynamics of the whole human heart, driven by a four-chamber electromechanical model. We first present a study on the calibration of the…
Optimization problems with constraints in the form of a partial differential equation arise frequently in the process of engineering design. The discretization of PDE-constrained optimization problems results in large-scale linear systems…
The Neumann problem of linear elasticity is singular with a kernel formed by the rigid motions of the body. There are several tricks that are commonly used to obtain a non-singular linear system. However, they often cause reduced accuracy…
This paper presents a new method for conditional probability density simulation. The method is design to work with unstructured data set when data are not characterized by the same covariates yet share common information. Specific examples…
Solving the linear elasticity and Stokes equations by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions. The one-level domain decomposition preconditioners are based on the…
In this paper, we consider the numerical approximation of the quasi-static, linear Biot model in a 3D domain $\Omega$ when the right-hand side of the mass balance equation is concentrated on a 1D line source $\delta_{\Lambda}$. This model…
In this paper, we study a class of inexact block triangular preconditioners for double saddle-point symmetric linear systems arising from the mixed finite element and mixed hybrid finite element discretization of Biot's poroelasticity…
This work introduces nodal auxiliary space preconditioners for discretizations of mixed-dimensional partial differential equations. We first consider the continuous setting and generalize the regular decomposition to this setting. With the…