2 edition of **high-order direct solver for Helmholtz equations with Neumann boundary conditions** found in the catalog.

high-order direct solver for Helmholtz equations with Neumann boundary conditions

Xian-He Sun

- 330 Want to read
- 20 Currently reading

Published
**1997**
by Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, National Technical Information Service, distributor in Hampton, VA, [Springfield, Va
.

Written in English

- Finite differences -- Data processing.,
- Fourier transformations.,
- Helmholtz equation -- Numerical solutions.,
- Neumann problem.

**Edition Notes**

Other titles | High order direct solver for Helmholtz equations with Neumann boundary conditions, ICASE 25th anniversary |

Statement | Xian-He Sun, Yu Zhuang. |

Series | ICASE report -- no. 97-11, NASA contractor report -- 201658, NASA contractor report -- NASA CR-201658. |

Contributions | Zhuang, Yu., Institute for Computer Applications in Science and Engineering., Langley Research Center. |

The Physical Object | |
---|---|

Pagination | i, 25 p. |

Number of Pages | 25 |

ID Numbers | |

Open Library | OL20920182M |

A High-Order Fast Direct Solver for Singular Poisson Equations Yu Zhuang and Xian-He Sun Department of Computer Science, Illinois Institute of Technology, Chicago, Illinois Received October 7, ; revised Aug We present a fourth order numerical solution method for the singular Neumann boundary problem of Poisson equations. The solution of elliptic partial differential equations on regions with corners is a famously refractory problem. The solutions are known to be singular at corners, and one of the major difficulties has been finding a precise description of their behavior. In this paper, we observe that when the Helmholtz equation is solved using integral equations, the solutions are .

The Dirichlet Problem for the Helmholtz Equation Since the integrand in (4.t7) is infinitely differentiable for P0, pCB and B is. not infinite, it follows that Ur and in fact is infinitely differentiable. as long as p and Po are not on the boundary. deﬁnes the boundary condition on /. When we use a PML, the positive parameter 7 gives the thickness of the layer and @ gives the trace of on the boundary /. Thus, the problem is a variable-coefﬁcient Helmholtz equation with Dirichlet boundary conditions on all the boundaries. In the case 7, we use a second-order absorbing boundary condition File Size: KB.

This paper deals with the solution of the Helmholtz equation on polygonal domains with either Dirichlet or Neumann boundary conditions. There are two additional boundary conditions that have not yet been analyzed in detail: the Robin condition, which specifies a linear combination of the values of the solution and the values of its derivative. Solving the Helmholtz equation on a square with Neumann boundary conditions. Thanks for contributing an answer to Mathematics Stack Exchange! Please be sure to answer the question. Provide details and share your research! Poisson partial differential equation under Neumann boundary conditions. 1.

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A High-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions Xian-He Sun* Yu Zhuang Department of Computer Science Louisiana State University Baton Rouge, LA Abstract In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular Size: 1MB.

In this study, a compact nite-di erence discretization is rst developed for Helmholtz equations on rectangular domains. Special treatments, then, are introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and separability.

Finally, a Fast Fourier Transform (FFT) based technique is used to yield a fast direct solver. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains.

Special treatments, then, are introduced for Neumann and Neumann-Dirichlet boundary conditions to achieve accuracy and sep-arability. A high-order direct solver for Helmholtz equations with Neumann boundary conditions. By Xian-he Sun and Yu ZhuangXian-he Sun and Yu Zhuang. Abstract.

In this study, a compact finite-difference discretization is first developed for Helmholtz equations on rectangular domains. Special treatments, then, are introduced for Neumann and Neumann.

We demonstrate the resulting numerical capabilities by solving a range of nonstandard boundary value problems for the Helmholtz equation. These include problems with variable coefficient Robin boundary conditions (including discontinuous coefficients) and problems with mixed (Dirichlet/Neumann) boundary by: A high-order direct solver for Helmholtz equations with Neumann boundary conditions.

By Xian-he Sun and Yu Zhuang. Abstract. In this study, a compact nite-di erence discretization is rst developed for Helmholtz equations on rectangular domains. Special treatments, then, are introduced for Neumann and Neumann-Dirichlet boundary conditions to Author: Xian-he Sun and Yu Zhuang.

We present a fourth order numerical solution method for the singular Neumann boundary problem of Poisson equations.

Such problems arise in the solution process of incompressible Navier–Stokes equations and in the time-harmonic wave propagation in the frequence space with the zero by: Using certain boundary conditions, in our case the Neumann condition for this integral equation, we hope.

to –nd an approximate solution to exterior boundary value problem. As we will use Green™s Theorem, we. solve the Helmholtz equation only on the boundary Author: Jane Pleskunas.

Helmholtz Equation and High Frequency Approximations. 1 The Helmholtz equation. TheHelmholtzequation, u(x) + n(x)2!2u(x) = f(x); x2Rd; (1) is a time-independent linear partial diﬀerential equation. The interpretation of the unknown u(x) and the parameters n(x),!and f(x) depends on what the equation Size: KB.

partial diﬀerential equation (the Helmholtz equation) which is to be solved subject to the requirement that certain boundary conditions hold (e.g. the impedance boundary condition and, when the domain is unbounded, also the Sommerfeld radiation condition, which can be viewed as a boundary condition at inﬁnity).

A high-order direct solver for helmholtz equations with neumann boundary conditions Author: Xian-He Sun ; Yu Zhuang ; Institute for Computer Applications in Science and Engineering. HELMHOLTZ EQUATION WITH ARTIFICIAL BOUNDARY CONDITIONS IN A TWO-DIMENSIONAL WAVEQUIDE D.A.

MITSOUDIS yx, CH. MAKRIDAKIS zx, AND M. PLEXOUSAKIS Abstract. We consider a time-harmonic acoustic wave propagation problem in a two dimensional water waveguide con ned between a horizontal surface and a locally varying File Size: KB.

One of the high-order schemes is based on generalizations of the Padé approximation. The second scheme is based on high-order approximation to the derivative calculated from the Helmholtz equation itself. A symmetric high-order representation is developed for a Neumann boundary by: We solve a Dirichlet boundary problem for the Helmholtz equation.

We also extend the method to the solution of mixed problems, where Dirichlet boundary conditions are specified on some faces and Neumann boundary conditions are specified on other faces.

High-order accuracy is achieved by a comparatively small number of by: A High-Order Fast Direct Solver for Singular Poisson Equations. of the eigenvalues analysis to Neumann boundary conditions and non-uniform meshes. A High-Order Direct Solver for Helmholtz.

or the Helmholtz equation () Δu+k2u = u xx +u yy +u zz +k2u = f(x,y,z) in a 3-D domain Ω with Dirichlet () u =Φ(x,y)on∂Ω boundary conditions by domain decomposition (DD) methods. The present 3-D algorithm is based on the fast spectral Helmholtz solver which was developed in [6].

It incorporates the application of the FFT with a prelimi. 2 = 2, the \homogenizing" function is u. 1(x;t) = 3 2 x2 5x + 3 4 t: Subtracting this from u yields a problem with homogeneous boundary conditions and initial condition u(x;0) = 0 u.

1(x;0) = 3 2 x2 + 5x: Daileda Neumann and Robin conditions. • Helmholtz’ equation • Classiﬁcation of second order, linear PDEs • Hyperbolic equations and the wave equation 2.

Lecture Two: Solutions to PDEs with boundary conditions and initial conditions • Boundary and initial conditions • Cauchy, Dirichlet, and Neumann conditions • Well-posed problems • Existence and uniqueness theoremsCited by: 2.

Key words. Half–plane, Boundary integral equations, Helmholtz equation, uniqueness. Introduction. In this paper a boundary integral equation formulation for the two–dimensional Helmholtz equation in a locally perturbed half–plane is developed to calculate sound propagation out of a cutting of arbitrary cross–section and surface.

Heat equation Our goal is to solve the following problem ut = Duxx + f(x,t), x 2(0, a), (1) u(x,0) = f(x), (2) and u satisﬁes one of the above boundary conditions. In order to achieve this goal we ﬁrst consider a problem when f(x,t) = 0, h(t) = 0, g(t) = 0 and use the method of separation of variables to obtain solution.

To illustrate File Size: KB. Pressure poisson equation. Abstract. Studying an inverse problem always requires a solid knowledge of the theory for the corresponding direct problem. Therefore, the following two chapters of our book are devoted to presenting the foundations of obstacle scattering problems for time-harmonic acoustic waves, i.e., to exterior boundary value problems for the scalar Helmholtz : David Colton, Rainer Kress.A High-Order Accurate Compact Finite Difference Algorithm for the Incompressible Navier-Stokes Equations.

() A high-Order Direct Solver for Helmholtz Equations with Neumann Boundary Conditions, ICASE Report No. Google by: 1.