Results 1  10
of
22
A New Discrete Transparent Boundary Condition for Standard and Wide Angle "Parabolic" Equations in Underwater Acoustics
"... This paper is concerned with transparent boundary conditions (TBCs) for standard and wide angle “parabolic” equations (SPE, WAPE) in the application to underwater acoustics (assuming cylindrical symmetry). Existing discretizations of these TBCs have accuracy problems and render the overall Crank–Nic ..."
Abstract

Cited by 48 (16 self)
 Add to MetaCart
(Show Context)
This paper is concerned with transparent boundary conditions (TBCs) for standard and wide angle “parabolic” equations (SPE, WAPE) in the application to underwater acoustics (assuming cylindrical symmetry). Existing discretizations of these TBCs have accuracy problems and render the overall Crank–Nicolson finite difference method only conditionally stable. Here, a novel discrete TBC is derived from the discrete whole–space problem that yields an unconditionally stable scheme. The superiority of the new discrete TBC over existing discretizations is illustrated on several benchmark problems.
Solving timeharmonic scattering problems based on the pole condition: Convergence of the PML method
, 2001
"... In this paper we study the PML method for Helmholtztype scattering problems with radially symmetric potential. The PML method consists in surrounding the computational domain by a Perfectly Matched sponge Layer. We prove that the approximate solution obtained by the PML method converges exponential ..."
Abstract

Cited by 46 (9 self)
 Add to MetaCart
In this paper we study the PML method for Helmholtztype scattering problems with radially symmetric potential. The PML method consists in surrounding the computational domain by a Perfectly Matched sponge Layer. We prove that the approximate solution obtained by the PML method converges exponentially fast to the true solution in the computational domain as the thickness of the sponge layer tends to infinity. This is a generalization of results by Lassas and Somersalo based on boundary integral equation techniques. Here we use techniques based on the pole condition instead. This makes it possible to treat problems without an explicitly known fundamental solution
A review of transparent and artificial boundary conditions techniques for linear and nonlinear Schrödinger equations
, 2008
"... ..."
Mathematical Concepts of Open Quantum Boundary Conditions
, 2000
"... This paper is concerned with the derivation and the numerical discretization of open boundary conditions for the 1D Schrödinger equation in order to simulate quantum devices. New discrete transparent boundary conditions are presented that are able to handle the situation of a continuous plane wave i ..."
Abstract

Cited by 30 (6 self)
 Add to MetaCart
This paper is concerned with the derivation and the numerical discretization of open boundary conditions for the 1D Schrödinger equation in order to simulate quantum devices. New discrete transparent boundary conditions are presented that are able to handle the situation of a continuous plane wave inux into a device. Also, we give a review of various formulations of boundary conditions that are used within the Schrödinger and the Wigner formalism of quantum mechanics, and we discuss their mathematical properties.
Discrete Transparent Boundary Conditions for SchrödingerType Equations
 J. COMP. PHYS
, 1996
"... We present a general technique for constructing nonlocal transparent boundary ..."
Abstract

Cited by 18 (4 self)
 Add to MetaCart
We present a general technique for constructing nonlocal transparent boundary
Numerical schemes for the simulation of the twodimensional Schrödinger equation using nonreflecting boundary conditions
, 2004
"... Abstract. This paper adresses the construction and study of a CrankNicolsontype discretization of the twodimensional linear Schrödinger equation in a bounded domain Ω with artificial boundary conditions set on the arbitrarily shaped boundary of Ω. These conditions present the features of being di ..."
Abstract

Cited by 18 (6 self)
 Add to MetaCart
(Show Context)
Abstract. This paper adresses the construction and study of a CrankNicolsontype discretization of the twodimensional linear Schrödinger equation in a bounded domain Ω with artificial boundary conditions set on the arbitrarily shaped boundary of Ω. These conditions present the features of being differential in space and nonlocal in time since their definition involves some time fractional operators. After having proved the wellposedness of the continuous truncated initial boundary value problem, a semidiscrete CrankNicolsontype scheme for the bounded problem is introduced and its stability is provided. Next, the full discretization is realized by way of a standard finiteelement method to preserve the stability of the scheme. Some numerical simulations are given to illustrate the effectiveness and flexibility of the method. 1.
Fast Evaluation of Nonreflecting Boundary Conditions for the Schrödinger Equation in One Dimension
, 2004
"... ..."
Discrete non–local boundary conditions for Split–Step Padé Approximations of the One–Way Helmholtz Equation
"... This paper deals with the efficient numerical solution of the two–dimensional one– way Helmholtz equation posed on an unbounded domain. In this case one has to introduce artificial boundary conditions to confine the computational domain. The main topic of this work is the construction of so–called d ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
(Show Context)
This paper deals with the efficient numerical solution of the two–dimensional one– way Helmholtz equation posed on an unbounded domain. In this case one has to introduce artificial boundary conditions to confine the computational domain. The main topic of this work is the construction of so–called discrete transparent boundary conditions for stateoftheart parabolic equations methods, namely a split–step discretization of the high–order parabolic approximation and the split–step Padé algorithm of Collins. Finally, several numerical examples arising in optics and underwater acoustics illustrate the efficiency and accuracy of our approach.
Krylov Subspace Spectral Methods for the TimeDependent Schrödinger Equation with NonSmooth Potentials
, 2010
"... This paper presents modifications of ..."
An Alternative Derivation of the Exact DtNMap on a Circle
, 1998
"... The paper supplies an alternative derivation of the exact boundary conditions needed for the solution of timeharmonic acoustic scattering problems modeled by the Helmholtz equation. The main idea is to consider the exterior domain problem as an initial value problem with initial data given on the b ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
The paper supplies an alternative derivation of the exact boundary conditions needed for the solution of timeharmonic acoustic scattering problems modeled by the Helmholtz equation. The main idea is to consider the exterior domain problem as an initial value problem with initial data given on the boundary of a disc or sphere. The solution of the exterior domain problem is obtained via Laplace transformation techniques, where the asymptotic Sommerfeld radiation condition is reformulated accordingly.