The implementation of high-order (spectral) approximations associated with FEM is an approach to overcome the difficulties encountered in the numerical analysis of complex problems. This paper proposes the use of the spectral finite element method, originally developed for computational fluid dynamics problems, to achieve improved solutions for these types of problems. Here, the interpolation n...

Estimating the temperature field of a building envelope could be time-consuming task. The use reduced-order method is then proposed: Proper Generalized Decomposition method. solution transient heat equation re-written as function its parameters: boundary conditions, initial condition, etc. To avoid tremendous number parameters, condition parameterized. This usually done by using Orthogonal to p...

3.1.1. Existence and uniqueness. Our immediate goal is to establish the existence of a sequence of orthogonal polynomials. Although we could, in principle, determine the coefficients a j of pn in the natural basis by using the orthogonality conditions (3.1.2), it is computationally advantageous to express pn in terms of lower-order orthogonal polynomials. Let us denote Pn := span { 1, x, x, · ·...

In this work there is presented a non-traditional approach to generation of block-structured orthogonal grids on the basis of up-todate CAD systems. The features of the algorithm of constructiing orthogonal grids are explained. Examples of constructed grids are provided.

In this paper a non-traditional approach to generation of orthogonal/Cartesian grids with local refinement tetra-hedrons near STL boundary on the basis of up-to-date CAD systems is considered. The features of the algorithm of constructing orthogonal grids are explained. Examples of constructed grids are presented.

Math. Subject Classiication 62K99, 05B15 Our main result is that any three-factor Orthogonal Main EEect Plan can be uncollapsed to obtain a tight three-factor Orthogonal Main EEect Plan. We also prove a nite-basis type result for tight OMEPs.

An algorithm was developed to obtain reconstructions from truncated projections by utilizing cross-correlation of a “knowledge set” of a priori nontruncated cross-sections with a similar structure. A cross-correlation matrix was constructed for the known set of cross-sectional images. The eigenvectors of this matrix form a set of orthogonal basis vectors for the reconstructed image. The basis s...

We inductively construct an explicit (common) orthogonal eigenbasis for the elements of the Bose-Mesner algebra of the Grassmann scheme. The key step is a constructive, linear algebraic interpretation of the GoldmanRota recurrence for the number of subspaces of a finite vector space. This interpretation shows that the up operator on subspaces has an explicitly given recursive structure. Using t...

This paper presents two new sets of nonseparable discrete orthogonal Charlier and Meixner moments describing the images with noise and that are noise-free. The basis functions used by the proposed nonseparable moments are bivariate Charlier or Meixner polynomials introduced by Tratnik et al. This study discusses the computational aspects of discrete orthogonal Charlier and Meixner polynomials, ...

This paper establishes properties of discrete orthogonal projections on periodic spline spaces of order r, with knots that are equally spaced and of arbitrary multiplicity M ≤ r. The discrete orthogonal projection is expressed in terms of a quadrature rule formed by mapping a fixed J -point rule to each sub-interval. The results include stability with respect to discrete and continuous norms, c...