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Truncated Fourier Series (truncated + fourier_series)
Selected AbstractsComparative study of the least squares approximation of the modified Bessel functionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2008Jianguo XinArticle first published online: 14 DEC 200 Abstract The least squares problem of the modified Bessel function of the second kind has been considered in this study with the Fourier series, Tchebycheff and Legendre approximation. Numerical evidence shows that the Gibbs phenomenon exists in the approximation with the truncated Fourier series, thus, giving poor convergence results compared with the other polynomial bases. For the latter two cases, the Legendre series perform better than Tchebycheff series in terms of the ,2 norm of the relative errors for each order of the polynomial approximation, and the ratio of the ,2 norm of the relative errors from the corresponding approximation seems to be a constant value of 1.3. Copyright © 2006 John Wiley & Sons, Ltd. [source] On the use of Somigliana's formula and Fourier series for elasticity problems with circular boundariesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2003S. L. Crouch Abstract This paper considers the problem of an infinite, isotropic elastic plane containing an arbitrary number of non-overlapping circular holes and isotropic elastic inclusions. The holes and inclusions are of arbitrary size and the elastic properties of all of the inclusions can, if desired, be different. The analysis is based on the two-dimensional version of Somigliana's formula, which gives the displacements at a point inside a region V in terms of integrals of the tractions and displacements over the boundary S of this region. We take V to be the infinite plane, and S to be an arbitrary number of circular holes within this plane. Any (or all) of the holes can contain an elastic inclusion, and we assume for simplicity that all inclusions are perfectly bonded to the material matrix. The displacements and tractions on each circular boundary are represented as truncated Fourier series, and all of the integrals involved in Somigliana's formula are evaluated analytically. An iterative solution algorithm is used to solve the resulting system of linear algebraic equations. Several examples are given to demonstrate the accuracy and efficiency of the numerical method. Copyright © 2003 John Wiley & Sons, Ltd. [source] To compact ring branch-line coupler using nonuniform transmission lineMICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 11 2009F. Hosseini Abstract A compact ring Branch-Line Coupler (BLC) with size reduction of about 50%(in circuit area) of conventional BLCs at frequency 2 GHz is introduced. The coupler is designed by using nonuniform transmission lines (NTL) instead of Uniform Transmission Lines in each arm. The normalized width w (z)/h function of the NTLs is expanded in a truncated Fourier series. The reduced size couplers are potential building blocks for the growing wireless communication markets. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 2679,2682, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24703 [source] Null-field approach for Laplace problems with circular boundaries using degenerate kernelsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2009Jeng-Tzong Chen Abstract In this article, a semi-analytical method for solving the Laplace problems with circular boundaries using the null-field integral equation is proposed. The main gain of using the degenerate kernels is to avoid calculating the principal values. To fully utilize the geometry of circular boundary, degenerate kernels for the fundamental solution and Fourier series for boundary densities are incorporated into the null-field integral equation. An adaptive observer system is considered to fully employ the property of degenerate kernels in the polar coordinates. A linear algebraic system is obtained without boundary discretization. By matching the boundary condition, the unknown coefficients can be determined. The present method can be seen as one kind of semianalytical approaches since error only attributes to the truncated Fourier series. For the eccentric case, vector decomposition technique for the normal and tangential directions is carefully considered in implementing the hypersingular equation in mathematical essence although we transform it to summability to divergent series. The five advantages, well-posed linear algebraic system, principal value free, elimination of boundary-layer effect, exponential convergence, and mesh free, are achieved. Several examples involving infinite, half-plane, and bounded domains with circular boundaries are given to demonstrate the validity of the proposed method. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source] Fast direct solver for Poisson equation in a 2D elliptical domainNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2004Ming-Chih Lai Abstract In this article, we extend our previous work M.-C. Lai and W.-C. Wang, Numer Methods Partial Differential Eq 18:56,68, 2002 for developing some fast Poisson solvers on 2D polar and spherical geometries to an elliptical domain. Instead of solving the equation in an irregular Cartesian geometry, we formulate the equation in elliptical coordinates. The solver relies on representing the solution as a truncated Fourier series, then solving the differential equations of Fourier coefficients by finite difference discretizations. Using a grid by shifting half mesh away from the pole and incorporating the derived numerical boundary value, the difficulty of coordinate singularity can be elevated easily. Unlike the case of 2D disk domain, the present difference equation for each Fourier mode is coupled with its conjugate mode through the numerical boundary value near the pole; thus, those two modes are solved simultaneously. Both second- and fourth-order accurate schemes for Dirichlet and Neumann problems are presented. In particular, the fourth-order accuracy can be achieved by a three-point compact stencil which is in contrast to a five-point long stencil for the disk case. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 72,81, 2004 [source] | ||||||||||