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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

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

by Kenneth J. Baumeister

  • 125 Want to read
  • 36 Currently reading

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

    Subjects:
  • Helmholtz equation.,
  • Finite element method.,
  • Triangle.

  • Edition Notes

    StatementKenneth J. Baumeister.
    SeriesNASA technical memorandum -- 87351.
    ContributionsUnited States. National Aeronautics and Space Administration.
    The Physical Object
    FormatMicroform
    Pagination1 v.
    ID Numbers
    Open LibraryOL17835344M

    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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Effect of triangular element orientation on finite element solutions of the Helmholtz equation by Kenneth J. Baumeister Download PDF EPUB FB2

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.

The goal of this procedure is to formulate a boundary-value problem over a finite region such that its solution I. Harari, T.J.R. Hughes, Finite element methods for the Helmholtz equation in an exterior domain 61 is the restriction of the solution of the original problem to this finite.

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.

• Maximizing the number of quadrilateral elements in your model will provide a more reliable solution that will capture a model’s behavior more effectively.

• FEMAP has some very useful tools and functionalities to help either maximize the number of quadrilateral elements in a finite element model or eliminate triangular elements altogether.

() Iterative solution of Helmholtz problem with high-order isogeometric analysis and finite element method at mid-range frequencies. Computer Methods in Applied Mechanics and Engineering Isaac Harari's research works with 4, citations and 5, reads, including: Analytical and Numerical Shape Optimization of a Class of Structures under Mass Constraints and Self-Weight.

The finite element method (FEM), or finite element analysis (FEA), is a computational technique used to obtain approximate solutions of boundary value problems in engineering. Boundary value problems are also called field problems.

The field is the domain of interest and most often represents a physical structure. Chapter 4 – 2D Triangular Elements Page 1 of 24 2D Triangular Elements Two Dimensional FEA Frequently, engineers need to compute the stresses and deformation in relatively thin plates or sheets of material and finite element analysis is ideal for this type of computations.

We will look at the development of development of finite element. This paper presents an overview of the Trefftz finite element and its application in various engineering problems. Basic concepts of the Trefftz method are discussed, such as T-complete functions, special purpose elements, modified variational functionals, rank conditions, intraelement fields, and frame fields.

linear triangular elements. Fig.1 kV double-circuit, four-bundled power transmission line with low-reactance orientation Fig.2 Discretization of the system given in Fig. 1 Finite Element Formulation An equation governing each element is derived from the Maxwell’s equations directly by using Galerkin.

The Helmholtz Equation of secondary field, i.e. Equations (9) and (12), are the second order differential equation for the scalar field. The finite element method is used to calculate the differential Equation solution.

The finite element scheme used in this modeling is the Ritz method which completely conducted by Jin [21]. Development of an hp-Version finite element method for computational optimal control [microform]: semi- Modal element method for potential flow in nonuniform ducts [microform]: combining closed form analysis Effect of triangular element orientation on finite element solutions of the Helmholtz equation [microfor.

ME Finite Element Analysis in Thermofluids Dr. Cüneyt Sert For a triangular element, master element coordinates do not vary between -1 and 1, and we need to use a completely different GQ table, specifically designed for triangular elements.

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.

Three finite element formulations for the solution of the Helmholtz equation are considered. The performance of these methods is compared by performing a discrete dispersion analysis and by solving two canonical problems on nonuniform meshes.

2 hours ago  Abstract: An enriched finite element method is presented to numerically solve the eigenvalue problem on electromagnetic waveguides governed by the Helmholtz equation. That is, the solution of the original problem is assumed to be the limit of a family of solutions with.

* student is able intepret results of numerical simulations to reason. () Numerical solution of the acoustic wave equation using Raviart–Thomas elements. Journal of Computational and Applied Mathematics() A diagonal-mass-matrix triangular-spectral-element method based on cubature points.R. Rodriguez's 65 research works with citations and 2, reads, including: Correction to: Finite Element Approximation of the Spectrum of the Curl Operator in .2d Fem Code Matlab.