Related papers: A Functionally Connected Element Method for Solvin…
In this paper we present a Fourier feature based deep domain decomposition method (F-D3M) for partial differential equations (PDEs). Currently, deep neural network based methods are actively developed for solving PDEs, but their efficiency…
We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of…
We introduce a framework for generating, organizing, and reasoning with computational knowledge. It is motivated by the observation that most problems in Computational Sciences and Engineering (CSE) can be formulated as that of completing…
The method of fundamental solutions (MFS) is a numerical method for solving boundary value problems involving linear partial differential equations. It is well known that it can be very effective assuming regularity of the domain and…
This paper presents a high-order method for solving an interface problem for the Poisson equation on embedded meshes through a coupled finite element and integral equation approach. The method is capable of handling homogeneous or…
In this paper we present a new framework for the solution of active contour models on graphs. With the use of the Finite Element Method we generalize active contour models on graphs and reduce the problem from a partial differential…
Functional data analysis involves data described by regular functions rather than by a finite number of real valued variables. While some robust data analysis methods can be applied directly to the very high dimensional vectors obtained…
This paper investigates an efficient exponential integrator generalized multiscale finite element method for solving a class of time-evolving partial differential equations in bounded domains. The proposed method first performs the spatial…
Mixed dimensional partial differential equations (PDEs) are equations coupling unknown fields defined over domains of differing topological dimension. Such equations naturally arise in a wide range of scientific fields including geology,…
The implementation of discontinuous functions occurs in many of today's state-of-the-art partial differential equation solvers. However, in finite element methods, this poses an inherent difficulty: efficient quadrature rules available when…
We present a new finite element method, called $\phi$-FEM, to solve numerically elliptic partial differential equations with natural (Neumann or Robin) boundary conditions using simple computational grids, not fitted to the boundary of the…
This paper proposes a finite element method for solving the periodic steady-state problem for the scalar-valued and vector-valued Poisson equations, a simple reduction model of the Maxwell equations under the Coulomb gauge. Introducing a…
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…
This paper proposes a strategy to solve the problems of the conventional s-version of finite element method (SFEM) fundamentally. Because SFEM can reasonably model an analytical domain by superimposing meshes with different spatial…
Functional connectivity (FC) is one of the most common inputs to fMRI-based predictive models, due to a combination of its simplicity and robustness. However, there may be a lack of theoretical models for the generation of FC. In this work,…
Several neural network approaches for solving differential equations employ trial solutions with a feedforward neural network. There are different means to incorporate the trial solution in the construction, for instance one may include…
This work is devoted to the development of an efficient and robust technique for accurate capturing of the electric field in multi-material problems. The formulation is based on the finite element method enriched by the introduction of…
We introduce a new class of unfitted finite element methods with high order accurate numerical integration over curved surfaces and volumes which are only implicitly defined by level set functions. An unfitted finite element method which is…
Functional graphs (FGs) model the graph structures used to analyse the behaviour of functions from a discrete set to itself. In turn, such functions are used to study real complex phenomena evolving in time. As the systems involved can be…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…