Bifurcation points and bifurcated branches in fluids mechanics by high‐order mesh‐free geometric progression algorithms

2020 ◽  
Author(s):  
Mohammed Rammane ◽  
Said Mesmoudi ◽  
Abdeljalil Tri ◽  
Bouazza Braikat ◽  
Noureddine Damil
Keyword(s):  
High Order ◽  
Geometric Progression ◽  
Bifurcation Points ◽  
Mesh Free ◽  
Fluids Mechanics

Parametric Noise Reduction in a High-Order Nonlinear MEMS Resonator Utilizing Its Bifurcation Points

2017 ◽  
Vol 26 (6) ◽  
pp. 1189-1195 ◽  
Author(s):  
Guillermo Sobreviela ◽  
Chun Zhao ◽  
Milind Pandit ◽  
Cuong Do ◽  
Sijun Du ◽  
...  
Keyword(s):  
Noise Reduction ◽  
High Order ◽  
Bifurcation Points ◽  
Mems Resonator ◽  
Parametric Noise

Agglomeration-based physical frame dG discretizations: An attempt to be mesh free

2014 ◽  
Vol 24 (08) ◽  
pp. 1495-1539 ◽  
Author(s):  
Francesco Bassi ◽  
Lorenzo Botti ◽  
Alessandro Colombo
Keyword(s):  
Finite Element ◽  
Convergence Rates ◽  
Numerical Test ◽  
High Order ◽  
Test Cases ◽  
Computational Domain ◽  
Element Discretization ◽  
Mesh Free ◽  
Domain Boundaries ◽  
Coarse Grids

In this work we consider agglomeration-based physical frame discontinuous Galerkin (dG) discretization as an effective way to increase the flexibility of high-order finite element methods. The mesh free concept is pursued in the following (broad) sense: the computational domain is still discretized using a mesh but the computational grid should not be a constraint for the finite element discretization. In particular the discrete space choice, its convergence properties, and even the complexity of solving the global system of equations resulting from the dG discretization should not be influenced by the grid choice. Physical frame dG discretization allows to obtain mesh-independent h-convergence rates. Thanks to mesh agglomeration, high-order accurate discretizations can be performed on arbitrarily coarse grids, without resorting to very high-order approximations of domain boundaries. Agglomeration-based h-multigrid techniques are the obvious choice to obtain fast and grid-independent solvers. These features (attractive for any mesh free discretization) are demonstrated in practice with numerical test cases.

scholarly journals A new type of high-order elements based on the mesh-free interpolations

2016 ◽  
Vol 65 ◽  
pp. 63-71 ◽  
Author(s):  
Dean Hu ◽  
Yigang Wang ◽  
Haifei Zhan ◽  
Shuyao Long
Keyword(s):  
High Order ◽  
Mesh Free ◽  
New Type

scholarly journals Hermite integrator for high-order mesh-free schemes

2018 ◽  
Vol 71 (1) ◽  
Author(s):  
Satoko Yamamoto ◽  
Junichiro Makino
Keyword(s):  
High Order ◽  
Mesh Free

High order mesh-free method for frictional contact

2018 ◽  
Vol 94 ◽  
pp. 103-112 ◽  
Author(s):  
Youssef Belaasilia ◽  
Bouazza Braikat ◽  
Mohammad Jamal
Keyword(s):  
Frictional Contact ◽  
High Order ◽  
Mesh Free ◽  
Mesh Free Method

A high order mesh-free method for buckling and post-buckling analysis of shells

2019 ◽  
Vol 99 ◽  
pp. 89-99 ◽  
Author(s):  
Mustapha Fouaidi ◽  
Abdellah Hamdaoui ◽  
Mohammad Jamal ◽  
Bouazza Braikat
Keyword(s):  
Buckling Analysis ◽  
High Order ◽  
Mesh Free ◽  
Mesh Free Method ◽  
Post Buckling

Solving the incompressible fluid flows by a high‐order mesh‐free approach

2020 ◽  
Vol 92 (5) ◽  
pp. 422-435 ◽  
Author(s):  
Mohammed Rammane ◽  
Said Mesmoudi ◽  
Abdeljalil Tri ◽  
Bouazza Braikat ◽  
Noureddine Damil
Keyword(s):  
Incompressible Fluid ◽  
Fluid Flows ◽  
High Order ◽  
Mesh Free ◽  
Incompressible Fluid Flows

scholarly journals A High-Order HDG Method with Dubiner Basis for Elliptic Flow Problems

2020 ◽  
Vol 16 (32) ◽  
pp. 33-54
Author(s):  
Manuela Bastidas ◽  
Bibiana Lopez-Rodríguez ◽  
Mauricio Osorio
Keyword(s):  
Numerical Approximation ◽  
Discontinuous Solution ◽  
High Order ◽  
Flow Problems ◽  
Classic Problem ◽  
Hybridizable Discontinuous Galerkin ◽  
Macro Scale ◽  
Fluids Mechanics ◽  
Second Order Elliptic Equation ◽  
Theoretical Results

We propose a standard hybridizable discontinuous Galerkin (HDG) method to solve a classic problem in fluids mechanics: Darcy’s law. This model describes the behavior of a fluid trough a porous medium and it is relevant to the flow patterns on the macro scale. Here we present the theoretical results of existence and uniqueness of the weak and discontinuous solution of the second order elliptic equation, as well as the predicted convergence order of the HDG method. We highlight the use and implementation of Dubiner polynomial basis functions that allow us to develop a general and efficient high order numerical approximation. We also show some numerical examples that validate the theoretical results.

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