相关论文: Singular Value Decompositions for Single-Curl Oper…

A new approach is presented to compute the seismic normal modes of a fully heterogeneous, rotating planet. Special care is taken to separate out the essential spectrum in the presence of a fluid outer core. The relevant…

We present a new formulation of the hyperbolic singular value decomposition (HSVD) for an arbitrary complex (or real) matrix without hyperexchange matrices and redundant invariant parameters. In our formulation, we use only the concept of…

We solve Maxwell's eigenvalue problem via isogeometric boundary elements and a contour integral method. We discuss the analytic properties of the discretisation, outline the implementation, and showcase numerical examples.

We introduce a new system of surface integral equations for Maxwell's transmission problem in three dimensions. This system has two remarkable features, both of which we prove. First, it is well-posed at all frequencies. Second, the…

Convolutional neural networks (CNNs) have long been the paradigm of choice for robust medical image processing (MIP). Therefore, it is crucial to effectively and efficiently deploy CNNs on devices with different computing capabilities to…

Solving large-scale Generalized Eigenvalue Problems (GEPs) is a fundamental yet computationally prohibitive task in science and engineering. As a promising direction, contour integral (CI) methods, such as the CIRR algorithm, offer an…

The quad-curl problem arises in the study of the electromagnetic interior transmission problem and magnetohydrodynamics (MHD). In this paper, we study the quad-curl eigenvalue problem and propose a mixed method using edge elements for the…

We present a method to linearize, without approximation, a specific class of eigenvalue problems with eigenvector nonlinearities (NEPv), where the nonlinearities are expressed by scalar functions that are defined by a quotient of linear…

Over the past decades, transformations between different classes of eigenvalue problems have played a central role in the development of numerical methods for eigenvalue computations. One of the most well-known and successful examples of…

Neural operators (NOs) struggle with high-contrast multiscale partial differential equations (PDEs), where fine-scale heterogeneities cause large errors. To address this, we use the Generalized Multiscale Finite Element Method (GMsFEM) that…

This article presents the numerical eigensolver to find the resonant frequencies of 3-D closed cavity resonators filled with both electric and magnetic lossy, anisotropic media. By introducing a dummy variable with zero value in the 3-D…

We construct an extended Lagrange FE space to solve the Maxwell equation and its eigenvalue problem in $\mathbb R^d$ $(d=2,3)$, which is the sum of the vectorial $p-$order Lagrange FE space ($p\ge1$) and the gradient of the $p+1-$order…

This paper investigates the eigenvalue problem of integral operators whose kernels can be expressed as a finite sum of pairwise products of single-variable functions, making them separable. By consdiering the matrix form of the separable…

We consider an $\ell_1$-regularized inverse problem where both the forward and regularization operators have a Kronecker product structure. By leveraging this structure, a joint decomposition can be obtained using generalized singular value…

The sparse generalized eigenvalue problem arises in a number of standard and modern statistical learning models, including sparse principal component analysis, sparse Fisher discriminant analysis, and sparse canonical correlation analysis.…

For any fixed positive integer $r$ and a given budget $k$, the $r$-\textsc{Eigenvalue Vertex Deletion} ($r$-EVD) problem asks if a graph $G$ admits a subset $S$ of at most $k$ vertices such that the adjacency matrix of $G\setminus S$ has at…

We develop a new homotopy method for solving multiparameter eigenvalue problems (MEPs) called the fiber product homotopy method. For a $k$-parameter eigenvalue problem with matrices of sizes $n_1,\dots ,n_k = O(n)$, fiber product homotopy…

A multigrid method is proposed in this paper to solve eigenvalue problems by the finite element method based on the shifted-inverse power iteration technique. With this scheme, solving eigenvalue problem is transformed to a series of…

Objective: Global Maxwell Tomography (GMT) is a recently introduced volumetric technique for noninvasive estimation of electrical properties (EP) from magnetic resonance measurements. Previous work evaluated GMT using ideal radiofrequency…

In this paper, we introduce a finite element method employing the Ned\'el\'ec element space for solving the Maxwell's transmission eigenvalue problem in anisotropic media. The well-posedness of the source problems are derived using $\mathbb…