Imposing Dirichlet boundary conditions in hierarchical Cartesian meshes by means of stabilized Lagrange multipliers
Imposing Dirichlet boundary conditions in hierarchical Cartesian meshes by means of stabilized Lagrange multipliers
复制标题
通过稳定拉格朗日乘子在分层笛卡尔网格中施加狄利克雷边界条件
DOI：
10.1002/nme.4629
复制
发表时间：
2014
影响因子：
2.9
通讯作者：
J. García
中科院分区：
文献类型：
--
作者：
M. Valiente;J. A. Vitoria;E. Soriano;J. García
The use of Cartesian meshes independent of the geometry has some advantages over the traditional meshes used in the finite element method. The main advantage is that their use together with an appropriate hierarchical data structure reduces the computational cost of the finite element analysis. This improvement is based on the substitution of the traditional mesh generation process by an optimized procedure for intersecting the Cartesian mesh with the boundary of the domain and the use efficient solvers based on the hierarchical data structure. One major difficulty associated to the use of Cartesian grids is the fact that the mesh nodes do not, in general, lie over the boundary of the domain, increasing the difficulty to impose Dirichlet boundary conditions. In this paper, Dirichlet boundary conditions are imposed by means of the Lagrange multipliers technique. A new functional has been added to the initial formulation of the problem that has the effect of stabilizing the problem. The technique here presented allows for a simple definition of the Lagrange multipliers field that even allow us to directly condense the degrees of freedom of the Lagrange multipliers at element level. Copyright © 2014 John Wiley & Sons, Ltd.
