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We propose a fast collocation method based on Krylov subspace iterative solver on general nonuniform grids for the fractional Laplacian problem, in which the fractional operator is presented in a singular integral formulation. The method is…
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…
We present an indirect higher order boundary element method utilising NURBS mappings for exact geometry representation and an interpolation-based fast multipole method for compression and reduction of computational complexity, to counteract…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
The paper explores the numerical stability and the computational efficiency of a direct method for unfolding the resolution function from the measurements of the neutron induced reactions. A detailed resolution function formalism is laid…
A linearly implicit conservative difference scheme is applied to discretize the attractive coupled nonlinear Schr\"odinger equations with fractional Laplacian. Complex symmetric linear systems can be obtained, and the system matrices are…
We present novel model reduction methods for rapid solution of parametrized nonlinear partial differential equations (PDEs) in real-time or many-query contexts. Our approach combines reduced basis (RB) space for rapidly convergent…
This paper presents an efficient numerical method for solving fractional optimal control problems using an operational matrix for a fractional wavelet. Using well-known formulae such as Caputo and Riemann-Liouville operators to determine…
We prove existence and uniqueness of strong (pointwise) solutions to a linear nonlocal strongly coupled hyperbolic system of equations posed on all of Euclidean space. The system of equations comes from a linearization of a nonlocal model…
Fast and accurate solutions of time-dependent partial differential equations (PDEs) are of pivotal interest to many research fields, including physics, engineering, and biology. Generally, implicit/semi-implicit schemes are preferred over…
In this paper, we investigate the existence of weak solution for a fractional type problems driven by a nonlocal operator of elliptic type in a fractional Orlicz-Sobolev space, with homogeneous Dirichlet boundary conditions. We first extend…
In this paper, an efficient solver for the Helmholtz equation using a noval approximation space is developed. The ingradients of the method include the approximation space recently proposed, a discontinuous Galerkin scheme extensively used,…
Unoriented surface reconstruction is an important task in computer graphics and has extensive applications. Based on the compact support of wavelet and orthogonality properties, classic wavelet surface reconstruction achieves good and fast…
In this paper, we investigate the use of compactly supported divergence-free wavelets for the representation of the Navier-Stokes solution. After reminding the theoretical construction of divergence-free wavelet vectors, we present in…
We consider a space-time variational formulation of parabolic initial-boundary value problems in anisotropic Sobolev spaces in combination with a Hilbert-type transformation. This variational setting is the starting point for the space-time…
A high precision, and space time fully decoupled, wavelet formulation numerical method is developed for a class of nonlinear initial boundary value problems. This method is established based on a proposed Coiflet based approximation scheme…
A domain decomposition method for the solution of general variable-coefficient elliptic partial differential equations on regular domains is introduced. The method is based on tessellating the domain into overlapping thin slabs or shells,…
We study the problem of decomposition (non-commutative factorization) of linear ordinary differential operators near an irregular singular point. The solution (given in terms of the Newton diagram and the respective characteristic numbers)…
We introduce a new general purpose multiresolution preconditioner for symmetric linear systems. Most existing multiresolution preconditioners use some standard wavelet basis that relies on knowledge of the geometry of the underlying domain.…
We show how to perform sparse approximate Gaussian elimination for Laplacian matrices. We present a simple, nearly linear time algorithm that approximates a Laplacian by a matrix with a sparse Cholesky factorization, the version of Gaussian…