相关论文: A Defect Corrected Finite Element Approach for the…
A radial basis function (RBF) method based on matrix-valued kernels is presented and analyzed for computing two types of vector decompositions on bounded domains: one where the normal component of the divergence-free part of the field is…
We present an effective field theory (EFT) for a model-independent description of deformed atomic nuclei. In leading order this approach recovers the well-known results from the collective model by Bohr and Mottelson. When higher-order…
Magnet errors in storage rings significantly degrade beam performance, impacting the brightness and stability of the light source. Therefore, beam-based correction is crucial for the safe operation of machines and the stability of radiated…
Based on the work of Xu and Zhou [Math.Comput., 69(2000), pp.881-909], we establish new three-level and multilevel finite element discretizations by local defect-correction technique. Theoretical analysis and numerical experiments show that…
We propose, analyze, and numerically validate a correction adaptive two-grid finite element method (CAT-GFEM) for nonselfadjoint or indefinite elliptic problems. In contrast to the adaptive two-grid finite element method (ATGFEM) of Li and…
A robust and fast solver for the fractional differential equation (FDEs) involving the Riesz fractional derivative is developed using an adaptive finite element method on non-uniform meshes. It is based on the utilization of hierarchical…
The density matrix renormalization group (DMRG) is a numerical method that optimizes a variational state expressed by a tensor product. We show that the ground state is not fully optimized as far as we use the standard finite system…
In this chapter, we demonstrate a general formulation of the Finite Element Method allowing to calculate the diffraction efficiencies from the electromagnetic field diffracted by arbitrarily shaped gratings embedded in a multilayered stack…
Global optimization of expensive functions has important applications in physical and computer experiments. It is a challenging problem to develop efficient optimization scheme, because each function evaluation can be costly and the…
Magnetic field errors pose a limitation in the performance of synchrotrons, as they excite non-systematic resonances, reduce dynamic aperture and may result in beam loss. Their effect can be compensated assuming knowledge of their location…
Today, interest in automotive applications notably Hybrid Electric Vehicles (HEV) has risen due to environmental concerns and the modern society's energetic dependence. Consequently, it is necessary to study and implement in these vehicle…
A technique allowing for a perturbative treatment of nonlocal corrections to the single-site dynamical mean-field theory (DMFT) in finite dimensions is developed. It is based on the observation that in the case of strong electron…
This is a study of certain finite element methods designed for convection-dominated, time-dependent partial differential equations. Specifically, we analyze high order space-time tensor product finite element discretizations, used in a…
In general, there is a mismatch between a finite element model {(FEM)} of a structure and its real behaviour. In aeronautics, this mismatch must be small because {FEM}s are a fundamental part of the development of an aircraft and of…
We present the analytical formulation and the finite element solution of a fractional-order nonlocal continuum model of a Euler-Bernoulli beam. Employing consistent definitions for the fractional-order kinematic relations, the governing…
The paper examines local approximation errors of finite difference schemes in electromagnetic analysis. Despite a long history of the subject, several accuracy-related issues have been overlooked and/or remain controversial. For example,…
The growing availability of computational resources has significantly increased the interest of the scientific community in performing complex multi-physics and multi-domain simulations. However, the generation of appropriate computational…
A finite element methodology for large classes of variational boundary value problems is defined which involves discretizing two linear operators: (1) the differential operator defining the spatial boundary value problem; and (2) a Riesz…
This paper proposes the response surface method for finite element model updating. The response surface method is implemented by approximating the finite element model surface response equation by a multi-layer perceptron. The updated…
In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…