Hadamard regularization in BIE

In summary, the conversation discusses the implementation of a hypersingular boundary integral equation and the numerical evaluation of a Hadamard integral using the traction (dual) boundary element method. The speaker is seeking suggestions for articles or online sources about the regularization method for their implementation. Two potential sources mentioned are books on Google that discuss the Hadamard finite part integral and its regularization.
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I'm working with a hypersingular boundary integral equation and its numerical implementation (the traction (dual) boundary element method equation). This involves numerical evaluation of a Hadamard integral and I'm collecting whatever material I can find about the regularization method itself, since I'll be writing the implementation got to cover all possible bases (so far I'm going by a couple of papers by Blanchet, Mantic, Bureau, Guiggani). Any suggestions on good articles / online sources I should look at ?
 
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What is Hadamard regularization in BIE?

Hadamard regularization in BIE (boundary integral equation) is a technique used to solve boundary value problems in mathematical physics. It is a method of regularizing the coefficients in the integral equations, making them more well-conditioned and improving the accuracy of the solution.

How does Hadamard regularization work?

Hadamard regularization works by rewriting the boundary integral equations in a new form, where the coefficients are modified by a regularization parameter. This parameter is chosen to balance the accuracy and stability of the solution. The resulting equations are then solved using numerical methods.

What are the advantages of using Hadamard regularization in BIE?

Hadamard regularization can improve the accuracy of solutions to boundary value problems, particularly for problems with singularities or non-smooth boundaries. It also helps to reduce the effects of round-off and discretization errors, making the solution more stable.

Are there any drawbacks to using Hadamard regularization?

One potential drawback of Hadamard regularization is that it adds an extra parameter that needs to be chosen carefully. If the parameter is chosen poorly, it can lead to inaccurate or unstable solutions. Additionally, the regularization process can increase the computational cost of solving the boundary integral equations.

In what applications is Hadamard regularization commonly used?

Hadamard regularization in BIE is commonly used in a variety of applications, including electromagnetics, fluid dynamics, and heat transfer. It is particularly useful for problems involving complicated geometries or singularities, where traditional numerical methods may struggle to produce accurate solutions.

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