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Partition of Unity Methods
book

Partition of Unity Methods

by Stéphane P. A. Bordas, Alexander Menk, Sundararajan Natarajan
October 2023
Intermediate to advanced content levelIntermediate to advanced
368 pages
12h 57m
English
Wiley
Content preview from Partition of Unity Methods

9 Combined Extended Finite Element and Level Set Method (XFE-LSM) for Free Boundary Problems

Ravindra Duddu

Department of Civil and Environmental Engineering, Vanderbilt University, USA

As described in Chapter 3, it is convenient to represent embedded interfaces using a scalar level set function phi; however, if the interface is moving with some velocity ModifyingAbove v With right-arrow one needs to solve a first-order nonlinear partial differential equation (PDE) given by the level set evolution to determine its new location. The interface velocity ModifyingAbove v With right-arrow can be obtained by numerically solving the governing elliptic or parabolic PDEs associated with the physics of the problem; by using the extended finite element method (XFEM) to solve these PDEs, one can eliminate the need for the finite element mesh to coincide with the embedded interface. The level set method proposed in Osher and Sethian (1988) and Sethian (1999b) enables us to capture the motion of interface in a consistent and efficient way through fast marching techniques. An important point is that the interface velocity ModifyingAbove v With right-arrow is only defined for points that lie on the ...

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ISBN: 9780470667088Purchase Link