相关论文: Dense cell-by-cell systems of PDEs: approximation,…

Simulations of complex physical systems are typically realized by discretizing partial differential equations (PDEs) on unstructured meshes. While neural networks have recently been explored for surrogate and reduced order modeling of PDE…

This paper is concerned with the PDE and numerical analysis of a modified one-dimensional intravascular stent model originally proposed in [4]. It is proved that the modified model has a unique weak solution using the Galerkin method…

In this paper a discretization based on discontinuous Galerkin (DG) method for an elliptic two-dimensional problem with discontinuous coefficients is considered. The problem is posed on a polygonal region $\Omega$ which is a union of $N$…

Preconditioning techniques are crucial for enhancing the efficiency of solving large-scale linear equation systems that arise from partial differential equation (PDE) discretization. These techniques, such as Incomplete Cholesky…

From a mathematical perspective, the extraordinary properties of metamaterials are often reflected in the coefficients of the governing partial differential equations (PDEs). These coefficients may fall outside the assumptions of classical…

Conditional density estimation (CDE) - recovering the full conditional distribution of a response given tabular covariates - is essential in settings with heteroscedasticity, multimodality, or asymmetric uncertainty. Recent tabular…

The numerical tools to simulate the bidomain model in cardiac electrophysiology are constantly developing due to the great clinical interest and scientific advances in mathematical models and computational power. The bidomain model consists…

Mathematical models of protein-protein dynamics, such as the heterodimer model, play a crucial role in understanding many physical phenomena. This model is a system of two semilinear parabolic partial differential equations describing the…

In this article, we introduce a fast and memory efficient solver for sparse matrices arising from the finite element discretization of elliptic partial differential equations (PDEs). We use a fast direct (but approximate) multifrontal…

Discontinuous Galerkin (DG) methods offer an enormous flexibility regarding local grid refinement and variation of polynomial degrees for a variety of different problem classes. With a focus on diffusion problems, we consider DG…

A system of partial differential equations (PDEs) is derived to compute the full-field stress from an observed kinematic field when the flow rule governing the plastic deformation is unknown. These equations generalize previously proposed…

In this paper, we propose a novel multiscale model reduction strategy tailored to address the Poisson equation within heterogeneous perforated domains. The numerical simulation of this intricate problem is impeded by its multiscale…

We deal with the Finite Element Tearing and Interconnecting Dual Primal (FETI-DP) preconditioner for elliptic problems discretized by the virtual element method (VEM). We extend the result of [22] to the three dimensional case. We prove…

Parabolic partial differential equations (PDEs) appear in many disciplines to model the evolution of various mathematical objects, such as probability flows, value functions in control theory, and derivative prices in finance. It is often…

Fast and accurate solution of time-dependent partial differential equations (PDEs) is of key interest in many research fields including physics, engineering, and biology. Generally, implicit schemes are preferred over the explicit ones for…

The full-wave simulation of complex electromagnetic surfaces such as reflectarrays and metasurfaces is a challenging problem. In this paper, we present a macromodeling approach to efficiently simulate complex electromagnetic surfaces…

Elliptic Partial Differential Equations (PDEs) play a central role in computing the equilibrium conditions of physical problems (heat, gravitation, electrostatics, etc.). Efficient solutions to elliptic PDEs are also relevant to computer…

I provide an introduction to the application of deep learning and neural networks for solving partial differential equations (PDEs). The approach, known as physics-informed neural networks (PINNs), involves minimizing the residual of the…

Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…

Simulation of extracellular fields is one of the substantial methods used in the area of computational neuroscience. Its most common usage is validation of experimental methods as EEG and extracellular spike recordings or modeling of…