相关论文: Two-level preconditioners for the Helmholtz equati…
The double-layer potential plays an important role in solving boundary value problems for elliptic equations, and in the study of which for a certain equation, the properties of the fundamental solutions of the given equation are used. All…
This paper addresses the construction and analysis of a class of domain decomposition methods for the iterative solution of the quasi-static Biot problem in three-field formulation. The considered discrete model arises from time…
In this paper, we present a multiscale framework for solving the Helmholtz equation in heterogeneous media without scale separation and in the high frequency regime where the wavenumber $k$ can be large. The main innovation is that our…
This paper deals with two domain decomposition methods for two dimensional linear Schr{\"o}dinger equation, the Schwarz waveform relaxation method and the domain decomposition in space method. After presenting the classical algorithms, we…
This article simply presents several coordinate systems for 2 and 3-dimensional hyperbolic spaces, describing the general solutions of Helmholtz equation in each one of these systems.
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 define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the…
The preferred basis problem is mentioned in the literature in connection with the measurement problem and with the Many World Interpretation. It is argued that this problem actually corresponds to two inequivalent problems: (i) the…
In this work the detailed geometrical description of all possible orthogonal and nonorthogonal systems of coordinates, which allow separation of variables of two-dimensional Helmholtz equation is given as for two-sheeted (upper sheet)…
This paper is concerned with solving the Helmholtz exterior Dirichlet and Neumann problems with large wavenumber $k$ and smooth obstacles using the standard second-kind boundary integral equations. We consider Galerkin and collocation…
In this paper, we consider flow simulation in highly heterogeneous media that has many practical applications in industry. To enhance mass conservation, we write the elliptic problem in a mixed formulation and introduce a robust two-grid…
Using the bicomplex numbers $\mathbb{T}$ which is a commutative ring with zero divisors defined by $\mathbb{T}=\{w_0 + w_1 i_1 + w_2 i_2 + w_3 j | w_0, w_1, w_2, w_3 \in \mathbb{R}\}$ where $i_{1}^{2} = -1, i_{2}^{2} = -1, j^2 = 1, i_1 i_2…
In this paper we consider a class of robust multilevel precontioners for the Helmholtz equation with high wave number. The key idea in this work is to use the continuous interior penalty finite element methods (CIP-FEM) studied in…
We consider a class of doubly nonlinear degenerate hyperbolic-parabolic equations with homogeneous Dirichlet boundary conditions, for which we first establish the existence and uniqueness of entropy solutions. We then turn to the…
Mortar methods are widely used techniques for discretizations of partial differential equations and preconditioners for the algebraic systems resulting from the discretizations. For problems with high contrast and multiple scales, the…
Solving the normal equations corresponding to large sparse linear least-squares problems is an important and challenging problem. For very large problems, an iterative solver is needed and, in general, a preconditioner is required to…
We construct finite-dimensional approximations of solution spaces of divergence form operators with $L^\infty$-coefficients. Our method does not rely on concepts of ergodicity or scale-separation, but on the property that the solution space…
In this short note we consider several widely used L^2-orthogonal Helmholtz decompositions for bounded domains in R^3. It is well known that one part of the decompositions is a subspace of the space of functions with zero mean. We refine…
We describe the space of (all) invariant deformation quantizations on the hyperbolic plane as solutions of the evolution of a second order hyperbolic differential operator. The construction is entirely explicit and relies on non-commutative…
We consider a finite element method for elliptic equation with heterogeneous and possibly high-contrast coefficients based on primal hybrid formulation. A space decomposition as in FETI and BDCC allows a sequential computations of the…