Polynomial basis functions for curved elements using hyperbolas
نویسندگان
چکیده
منابع مشابه
Effective computation of matrix elements between polynomial basis functions
Two methods of evaluating matrix elements of a function in a polynomial basis are considered: the expansion method, where the function is expanded in the basis and the integrals are evaluated analytically, and the numerical method, where the integration is performed directly using numerical quadrature. A reduced grid is proposed for the latter which makes use of the symmetry of the basis. Compa...
متن کاملOn the Calculation of Matrix Elements between Polynomial Basis Functions
A method of evaluating matrix elements between polynomial basis functions is proposed involving the explicit expansion of the operator in terms of the polynomial. The method is shown to have several advantages over the direct evaluation of these matrix elements by Gaussian quadrature, including savings of up to a factor of 6N for an N-dimensional integral. Application to the calculation of poly...
متن کاملPolyhedral Finite Elements Using Harmonic Basis Functions
Finite element simulations in computer graphics are typically based on tetrahedral or hexahedral elements, which enables simple and efficient implementations, but in turn requires complicated remeshing in case of topological changes or adaptive refinement. We propose a flexible finite element method for arbitrary polyhedral elements, thereby effectively avoiding the need for remeshing. Our poly...
متن کاملA New Collocation Scheme Using Non-polynomial Basis Functions
In this paper, we construct a set of non-polynomial basis functions from a generalised Birkhoff interpolation problem involving the operator: Lλ = d2/dx2 − λ2 with constant λ. With a direct inverting the operator, the basis can be pre-computed in a fast and stable manner. This leads to new collocation schemes for general second-order boundary value problems with (i) the matrix corresponding to ...
متن کاملContouring Curved Quadratic Elements
We show how to extract a contour line (or isosurface) from quadratic elements—specifically from quadratic triangles and tetrahedra. We also devise how to transform the resulting contour line (or surface) into a quartic curve (or surface) based on a curved-triangle (curved-tetrahedron) mapping. A contour in a bivariate quadratic function defined over a triangle in parameter space is a conic sect...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1990
ISSN: 0898-1221
DOI: 10.1016/0898-1221(90)90006-6