3 edition of **Effect of triangular element orientation on finite element solutions of the Helmholtz equation** found in the catalog.

Effect of triangular element orientation on finite element solutions of the Helmholtz equation

Kenneth J. Baumeister

- 125 Want to read
- 36 Currently reading

Published
**1986**
by NASA, For sale by the National Technical Information Service in [Washington, D.C.], [Springfield, Va
.

Written in English

- Helmholtz equation.,
- Finite element method.,
- Triangle.

**Edition Notes**

Statement | Kenneth J. Baumeister. |

Series | NASA technical memorandum -- 87351. |

Contributions | United States. National Aeronautics and Space Administration. |

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

Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL17835344M |

Preface This is a set of lecture notes on ﬁnite elements for the solution of partial differential equations. The approach taken is mathematical in nature with a strong focus on the. objects. The mathematical formulationconsists ofthe Helmholtz equation inthe exterior domain accompanied by the Sommerfeld radiation condition and Neumann boundary condition on the boundary of the scatterer (rigid scattering). Problems ofthe described type areusually solved using various versions of the Bound-ary Element Method (BEM) [9].

Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.. Visit Stack Exchange. Combining comparison functions and finite element approximations in CFD [microform] / Kenneth J. Baumeister and Joseph F. Baumeister National Aeronautics and Space Administration ; National Technical Information Service, distributor [Washington, DC]: [Springfield, Va Australian/Harvard Citation.

Elements of function spaces As will become apparent in subsequent chapters, the accuracy of ﬁnite element ap-proximations to partial diﬀerential equations very much depends on the smoothness of the analytical solution to the equation under consideration, and this in turn hinges on the smoothness of the data. The simplest type of two-dimensional finite element assumes a linear, or firs-order, variation of the unknown potential T over the element. y x Fig.3 Triangular finite element in the xy plane. Within this first-order element T is related to the three unknown T values at the three triangular grid points according to TTkkabkxck kmn =++ = ∑ (y l.

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In this paper we address the generalized finite element method for the Helmholtz equation. We obtain our method by employing the finite element method on Cartesian meshes, which may overlap the boundaries of the problem domain, and by enriching the approximation by plane waves pasted into the finite element basis at each mesh vertex by the partition of unity Cited by: Get this from a library.

Effect of triangular element orientation on finite element solutions of the Helmholtz equation. [Kenneth J Baumeister. The Galerkin finite element solutions for the scalar homogeneous Helmholtz equation are presented for no reflection, hard wall, and potential relief exit terminations with a variety of triangular element orientations.

For this group of problems, the correlation between the accuracy of the solution and the orientation of the linear triangle is : Kenneth J. Baumeister. Effect of triangular element orientation on finite element solutions of the Helmholtz equation.

By K. Baumeister. Abstract. The Galerkin finite element solutions for the scalar homogeneous Helmholtz equation are presented for no reflection, hard wall, and potential relief exit terminations with a variety of triangular element orientations. Author: K. Baumeister.

EFFECT OF TRIANGULAR ELEMENT ORIENTATION ON FINITE ELEMENT SOLUTIONS OF THE HELMHOLTZ EQUATION Kenneth J. Baumeister National Aeronautics and Space Administration Lewis Research Center Cleveland, Ohio ABSTRACT The Galerkin finite element solutions for the scalar homogeneous Helmholtz equation are presented for.

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The theory for integrating the element matrices for rectangular, triangular and quadrilateral finite elements for the solution of the Helmholtz equation for very short waves is presented.

A numerical integration scheme is developed. Samples of Maple and Fortran code for the evaluation of integration abscissæ and weights are made available.

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Table can be used for GQ integration of triangular elements. Solve equation by using decomposition complex "wave number" on real and imaginary parts. We concentrate on the use of numerical method based on finite elements. The problem of solving Helmholtz equation becomes one of sparse matrix which solve by using the biconjugate gradient method.

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