相关论文: Preconditioning the bidomain model with almost lin…
We investigate the modeling and simulation of ionic transport and charge conservation in lithium-ion batteries (LIBs) at the microscale. It is a multiphysics problem that involves a wide range of time scales. The associated computational…
The simulation of three dimensional magnetostatic problems plays an important role, for example when simulating synchronous electric machines. Building on prior work that developed a domain decomposition algorithm using isogeometric…
Next-generation lithium-ion batteries with silicon anodes have positive characteristics due to higher energy densities compared to state-of-the-art graphite anodes. However, the large volume expansion of silicon anodes can cause high…
The 1+1D O(3) non-linear {\sigma}-model is a model system for future quantum lattice simulations of other asymptotically-free theories, such as non-Abelian gauge theories. We find that utilizing dimensional reduction can make efficient use…
In this paper we present a unified framework for constructing spectrally equivalent low-order-refined discretizations for the high-order finite element de Rham complex. This theory covers diffusion problems in $H^1$, $H({\rm curl})$, and…
A finite-element discretization of such an equation yields a linear system whose conditioning worsens as the variations in the values of PDE coefficients becomes large. This paper introduces a procedure by which the discrete system obtained…
An important paradigm in smart health is developing diagnosis tools and monitoring a patient's heart activity through processing Electrocardiogram (ECG) signals is a key example, sue to high mortality rate of heart-related disease. However,…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
The mathematical P2D model is a system of strongly coupled nonlinear parabolic-elliptic equations that describes the electrodynamics of lithium-ion batteries. In this paper, we present the numerical analysis of a finite element-implicit…
We present a preconditioning method for the linear systems arising from the boundary element discretization of the Laplace hypersingular equation on a $2$-dimensional triangulated surface $\Gamma$ in $\mathbb{R}^3$. We allow $\Gamma$ to…
We consider a Preconditioned Overdamped Langevin algorithm that does not alter the invariant distribution (up to controllable discretisation errors) and ask whether preconditioning improves the standard model in terms of reducing the…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
We study preconditioners for a model problem describing the coupling of two elliptic subproblems posed over domains with different topological dimension by a parameter dependent constraint. A pair of parameter robust and efficient…
Arrhythmias are potentially fatal disruptions to the normal heart rhythm, but their underlying dynamics is still poorly understood. Theoretical modeling is an important tool to fill this gap. Typical studies often employ detailed…
In this article we propose and numerically implement a mathematical model for the simulation of three-dimensional semiconductor devices characterized by an heterogeneous material structure. The model consists of a system of nonlinearly…
We present a combined numerical and data-driven workflow for efficient prediction of nonlinear, instationary convection-diffusion-reaction dynamics on a two-dimensional phenotypic domain, motivated by macroscopic modeling of cancer cell…
We describe a parallel solver for the discretized weakly singular space-time boundary integral equation of the spatially two-dimensional heat equation. The global space-time nature of the system matrices leads to improved parallel…
A surrogate-based topology optimisation algorithm for linear elastic structures under parametric loads and boundary conditions is proposed. Instead of learning the parametric solution of the state (and adjoint) problems or the optimisation…
The iterative diagonalization of a sequence of large ill-conditioned generalized eigenvalue problems is a computational bottleneck in quantum mechanical methods employing a nonorthogonal basis for {\em ab initio} electronic structure…
The simulation of large ensembles of particles is usually parallelized by partitioning the domain spatially and using message passing to communicate between the processes handling neighboring subdomains. The particles are represented as…