Numerical approximations of singular source terms in differential equations

By Anna-Karin Tornberg, Björn Engquist. 2004

302 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/f962cbe7f5f094d0a14f4582f7d62157ba9ba4e4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Stanley J. Osher
2. Michael Y. Wang
3. Shengyin Wang
4. Zhilin Li
5. Frank Losasso
6. Ronald Fedkiw
7. Martin Burger
8. Anna-Karin Tornberg

In Electrical and Electronic Engineering

1. Stanley J. Osher
2. Shilpa Khatri
3. Martin Burger
4. G. Wei
5. Frank Losasso
6. Guo-Wei He
7. Zhilin Li
8. Xing Zhang

Citations in the corpus

• Spatially adaptive techniques for level set methods and incompressible flow (2006, background): “[95] recently discovered that level set methods can suffer from O(1) errors with the typical delta function approach, and thus caution should be exercised when following this methodology.”
• A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations (2009, methodology): “IB methods have been successfully applied to simulate stationary boundary problems, but non-physical force oscillations are produced by some variants of IB methods when dealing with moving boundaries.”
• A discontinuous‐Galerkin‐based immersed boundary method (2008, background): “The precise way to do it varies among authors, and not all of them are equivalent in terms of accuracy [38, 72, 71, 19, 45, 62].”
• Radial basis functions and level set method for structural topology optimization (2006, background): “It should be noted that a recent result in [33] has shown that the most common technique for the regularization of the Dirac delta function in level set methods is inconsistent, and may lead to O (1) errors.”
• An adaptive, formally second order accurate version of the immersed boundary method (2007, unknown): “[3,37].”
• High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources (2006, background): “Recently, Tornberg and Engquist [44] have proposed and analyzed a class of regularization methods for treating the singular source terms.”
• A survey on level set methods for inverse problems and optimal design (2005, methodology): “In order to ensure a reasonable accuracy it is important to choose appropriate functions w [54, 137, 138], or to use adaptive refinement (which can be based on standard a-posteriori estimation).”
• On the order of accuracy of the immersed boundary method: Higher order convergence rates for sufficiently smooth problems (2005, background): “In [32], Tornberg and Engquist examine the use of smoothed delta functions in the regularization of singular source terms in a variety of settings.”
• A numerical method for two phase flows with insoluble surfactants (2011, methodology): “[26], where x is a point in X and X(s) is a point along C.”