Related papers: A Functionally Connected Element Method for Solvin…
In this paper, we propose an efficient parallelization strategy for boundary element method (BEM) solvers that perform the electromagnetic analysis of structures with lossy conductors. The proposed solver is accelerated with the adaptive…
In most of standard Finite Element (FE) codes it is not easy to calculate dispersion relations from periodic materials. Here we propose a new strategy to calculate such dispersion relations with available FE codes using user element…
In this paper, based on the combination of finite element mesh and neural network, a novel type of neural network element space and corresponding machine learning method are designed for solving partial differential equations. The…
In this paper, we present a robust and efficient unfitted concurrent multiscale method for continuum-continuum coupling, based on the Cut Finite Element Method (CutFEM). The computational domain is defined using approximate signed distance…
A highly efficient fast boundary element method (BEM) for solving large-scale engineering acoustic problems in a broad frequency range is developed and implemented. The acoustic problems are modeled by the Burton-Miller boundary integral…
The finite cell method (FCM) belongs to the class of immersed boundary methods, and combines the fictitious domain approach with high-order approximation, adaptive integration and weak imposition of unfitted Dirichlet boundary conditions.…
Incorporating covariates into functional principal component analysis (PCA) can substantially improve the representation efficiency of the principal components and predictive performance. However, many existing functional PCA methods do not…
Modeling the behavior of coupled networks is challenging due to their intricate dynamics. For example in neuroscience, it is of critical importance to understand the relationship between the functional neural processes and anatomical…
A moving mesh finite element method is studied for the numerical solution of Bernoulli free boundary problems. The method is based on the pseudo-transient continuation with which a moving boundary problem is constructed and its steady-state…
The paper is concerned with the development of efficient and accurate solution procedures for the isogeometric boundary element method (BEM) when applied to problems that contain inclusions that have elastic properties different to the…
In functional MRI (fMRI), effective connectivity analysis aims at inferring the causal influences that brain regions exert on one another. A common method for this type of analysis is structural equation modeling (SEM). We here propose a…
Based upon two overlapped, body-unfitted meshes, a type of unified-field monolithic fictitious domain-finite element method (UFMFD-FEM) is developed in this paper for moving interface problems of dynamic fluid-structure interactions (FSI)…
This paper presents a new stochastic finite element method for computing structural stochastic responses. The method provides a new expansion of stochastic response and decouples the stochastic response into a combination of a series of…
We develop an essentially optimal numerical method for solving multiscale Maxwell wave equations in a domain $D\subset{\mathbb R}^d$. The problems depend on $n+1$ scales: one macroscopic scale and $n$ microscopic scales. Solving the…
The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…
We survey some of our recent results on existence, uniqueness and regularity of function solutions to parabolic and transport type partial differential equations driven by non-differentiable noises. When applied pathwise to random…
We present a framework for solving time-dependent partial differential equations (PDEs) in the spirit of the random feature method. The numerical solution is constructed using a space-time partition of unity and random feature functions.…
Many combinatorial optimisation problems can be modelled as valued constraint satisfaction problems. In this paper, we present a polynomial-time algorithm solving the valued constraint satisfaction problem for a fixed number of variables…
We propose a Pretrained Finite Element Method (PFEM),a physics driven framework that bridges the efficiency of neural operator learning with the accuracy and robustness of classical finite element methods (FEM). PFEM consists of a physics…
Many analyses of functional magnetic resonance imaging (fMRI) examine functional connectivity (FC), or the statistical dependencies among distant brain regions. These analyses are typically exploratory, guiding future confirmatory research.…