相关论文: H-Matrix Accelerated Direct Matrix Solver for Maxw…

This paper introduces a high-order-accurate strategy for integration of singular kernels and edge-singular integral densities that appear in the context of boundary integral equation formulations of the problem of acoustic scattering. In…

We describe an efficient quantum algorithm for solving the linear matrix equation AX+XB=C, where A, B, and C are given complex matrices and X is unknown. This is known as the Sylvester equation, a fundamental equation with applications in…

Although high-order Maxwell integral equation solvers provide significant advantages in terms of speed and accuracy over corresponding low-order integral methods, their performance significantly degrades in presence of non-smooth…

Hierarchical Matrix (H-matrix) is an approximation technique which splits a target dense matrix into multiple submatrices, and where a selected portion of submatrices are low-rank approximated. The technique substantially reduces both time…

Matrix diagonalization is almost always involved in computing the density matrix needed in quantum chemistry calculations. In the case of modest matrix sizes ($\lesssim$ 5000), performance of traditional dense diagonalization algorithms on…

Maxwell interface problems are of great importance in many electromagnetic applications. Unfitted mesh methods are especially attractive in 3D computation as they can circumvent generating complex 3D interface-fitted meshes. However, many…

A coupled hybridizable discontinuous Galerkin (HDG) and boundary integral (BI) method is proposed to efficiently analyze electromagnetic scattering from inhomogeneous/composite objects. The coupling between the HDG and the BI equations is…

Boundary integral methods for the solution of boundary value PDEs are an alternative to `interior' methods, such as finite difference and finite element methods. They are attractive on domains with corners, particularly when the solution…

Helmholtz decompositions of the elastic fields open up new avenues for the solution of linear elastic scattering problems via boundary integral equations (BIE) [Dong, Lai, Li, Mathematics of Computation,2021]. The main appeal of this…

Developing efficient solvers for large-scale multi-term linear matrix equations remains a central challenge in numerical linear algebra and is still largely unresolved. This paper introduces a methodology leveraging CUR decomposition for…

We present a novel technique by which highly-segmented electrostatic configurations can be solved. The Robin Hood method is a matrix-inversion algorithm optimized for solving high density boundary element method (BEM) problems. We…

Complex valued systems with an indefinite matrix term arise in important applications such as for certain time-harmonic partial differential equations such as the Maxwell's equation and for the Helmholtz equation. Complex systems with…

We developed a fast numerical algorithm for solving the three dimensional vectorial Helmholtz equation that arises in electromagnetic scattering problems. The algorithm is based on electric field integral equations and is essentially a…

In this paper, several row and column orthogonal projection methods are proposed for solving matrix equation $AXB=C$, where the matrix $A$ and $B$ are full rank or rank deficient and equation is consistent or not. These methods are…

We present and analyze fully discrete Nystr\"om methods for the solution of three classes of well conditioned boundary integral equations for the solution of two dimensional scattering problems by homogeneous dielectric scatterers.…

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…

An efficient direct solver for volume integral equations with O(N) complexity for a broad range of problems is presented. The solver relies on hierarchical compression of the discretized integral operator, and exploits that off-diagonal…

This paper presents a computationally efficient model predictive control formulation that uses an integral Chebyshev collocation method to enable rapid operations of autonomous agents. By posing the finite-horizon optimal control problem…

We introduce a fast direct solver for variable-coefficient elliptic partial differential equations on surfaces based on the hierarchical Poincar\'e-Steklov method. The method takes as input an unstructured, high-order quadrilateral mesh of…

Recently, the efficient numerical solution of Hamiltonian problems has been tackled by defining the class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). Their derivation relies on the expansion of…