Open Access
Computer Methods in Applied Mechanics and Engineering
Reads0
Chats0
TLDR
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.read more
Citations
More filters
Book ChapterDOI
On-line, on-board evolution of robot controllers
TL;DR: A feasibility study into the evolution of robot controllers during the actual operation of robots (on-line), using only the computational resources within the robots themselves ( on-board) and the resulting algorithm is evaluated in a hybrid system.
Journal ArticleDOI
Subspace dynamic mode decomposition for stochastic Koopman analysis.
TL;DR: This paper proposes subspace DMD as an algorithm for the Koopman analysis of random dynamical systems with observation noise and investigates the empirical performance of sub space DMD with several dynamical Systems and shows its utility.
Journal ArticleDOI
Regional aerosol deposition in the human airways: The SimInhale benchmark case and a critical assessment of in silico methods
Pantelis Koullapis,Stavros C. Kassinos,J. Muela,Carlos David Pérez-Segarra,Joaquim Rigola,Oriol Lehmkuhl,Yan Cui,Martin Sommerfeld,Jakub Elcner,Miroslav Jicha,Igor Saveljic,Nenad Filipovic,Frantisek Lizal,Laura Nicolaou +13 more
TL;DR: In vitro deposition measurements have been conducted in a human‐based model of the upper airways, and several groups within MP1404 SimInhale have computed the same case using a variety of simulation and discretization approaches, and a critical discussion of the performance of the various simulation methods is provided.
Journal ArticleDOI
Non-linear Petrov–Galerkin methods for reduced order modelling of the Navier–Stokes equations using a mixed finite element pair
D. Xiao,D. Xiao,Fangxin Fang,Juan Du,Christopher C. Pain,Ionel Michael Navon,Andrew G. Buchan,Ahmed H. Elsheikh,G. Hu +8 more
TL;DR: In this article, a nonlinear Petrov-Galerkin approach was developed for proper orthogonal decomposition (POD) reduced order modelling of the Navier-Stokes equations, based on the use of the cosine rule between the advection direction in Cartesian space-time and the direction of the gradient of the solution.
Posted Content
Density and Level Set-XFEM Schemes for Topology Optimization of 3-D Structures
Carlos H. Villanueva,Kurt Maute +1 more
TL;DR: The numerical results demonstrate that the LSM–XFEM approach describes crisply the geometry and predicts the structural response with acceptable accuracy even on coarse meshes.
References
More filters
Book
An Introduction to Fluid Dynamics
TL;DR: The dynamique des : fluides Reference Record created on 2005-11-18 is updated on 2016-08-08 and shows improvements in the quality of the data over the past decade.
Book
A practical guide to splines
TL;DR: This book presents those parts of the theory which are especially useful in calculations and stresses the representation of splines as linear combinations of B-splines as well as specific approximation methods, interpolation, smoothing and least-squares approximation, the solution of an ordinary differential equation by collocation, curve fitting, and surface fitting.
Numerical solution of boundary value problems for ordinary differential equations
TL;DR: In this article, the Riccati method is used to solve boundary value problems for Ordinary Differential Equations and to solve nonlinear problems for BVPSs in the standard form.
Book
Numerical solution of boundary value problems for ordinary differential equations
TL;DR: This book discusses Consistency, Stability, and Convergence higher-Order One-Step Schemes Collocation Theory Acceleration Techniques Higher-Order ODEs Finite Element Methods and Initial Value Methods.
Related Papers (5)
An improved uniformly convergent scheme in space for 1D parabolic reaction-diffusion systems
C. Clavero,José Luis Gracia +1 more