Topic
Hermite interpolation
About: Hermite interpolation is a research topic. Over the lifetime, 2090 publications have been published within this topic receiving 30351 citations.
Papers published on a yearly basis
1 / 2
Papers
1 Jan 2010
TL;DR: In this article, a cubic Hermite collocation scheme for the solution of the coupled integro-partial differential equations governing the propagation of a hydraulic fracture in a state of plane strain is described.
Abstract: article i nfo We describe a novel cubic Hermite collocation scheme for the solution of the coupled integro-partial differential equations governing the propagation of a hydraulic fracture in a state of plane strain. Special blended cubic Hermite-power-law basis functions, with arbitrary index 0b αb1, are developed to treat the singular behavior of the solution that typically occurs at the tips of a hydraulic fracture. The implementation of blended infinite elements to model semi-infinite crack problems is also described. Explicit formulae for the integrated kernels associated with the cubic Hermite and blended basis functions are provided. The cubic Hermite collocation algorithm is used to solve a number of different test problems with two distinct propagation regimes and the results are shown to converge to published similarity and asymptotic solutions. The convergence rate of the cubic Hermite scheme is determined by the order of accuracy of the tip asymptotic expansion as well as the O(h 4 ) error due to the Hermite cubic interpolation. The errors due to these two approximations need to be matched in order to achieve optimal convergence. Backward Euler time-stepping yields a robust algorithm that, along with geometric increments in the time-step, can be used to explore the transition between propagation regimes over many orders of magnitude in time.
985 citations
TL;DR: Recently, Frumkin pointed out that none of the well-known algorithms that transform an integer matrix into Smith or Hermite normal form is known to be polynomially bounded in its runn...
Abstract: Recently, Frumkin [9] pointed out that none of the well-known algorithms that transform an integer matrix into Smith [16] or Hermite [12] normal form is known to be polynomially bounded in its runn...
506 citations
TL;DR: In this article, it is shown that a complete set of orthonormal polynomials in N variables can be obtained by using products of such polynomial in a single variahle.
Abstract: I t is well known that a complete set of orthonormal polynomials in N variables can be obtained by using products of such polynomials in a single variahle. Such a procedure lacks symmetry, and there is sometimes an advantage to be gained by expressing the polynomials in tensor invariant notation. The -\--vector z,(i = 1, 2, . . . , X ) is denoted by x. The second order tensor (dyad) X , X , is denoted by x'. Similarly, xn is used for the n-th order tensor x,,xi2 x,, . For the scalar product I t is convenient to introduce a special notation.
488 citations
TL;DR: The HWENO finite volume methodology is more suitable to serve as limiters for the Runge-Kutta discontinuous Galerkin (RKDG) methods, than the original WENO infinite volume methodology.
480 citations
1 Jan 1996
Abstract: 1. Introduction 2. Introduction to spectral methods via orthogonal functions 3. Introduction to PS methods via finite differences 4. Key properties of PS approximations 5. PS variations/enhancements 6. PS methods in polar and spherical geometries 7. Comparisons of computational cost - FD vs. PS methods 8. Some application areas for spectral methods Appendices.
443 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 17 |
| 2024 | 20 |
| 2023 | 33 |
| 2022 | 92 |
| 2021 | 60 |
| 2020 | 59 |