A Nitsche-based domain decomposition method for hypersingular integral equations

نویسندگان

  • Franz Chouly
  • Norbert Heuer
چکیده

We introduce and analyze a Nitsche-based domain decomposition method for the solution of hypersingular integral equations. This method allows for discretizations with non-matching grids without the necessity of a Lagrangian multiplier, as opposed to the traditional mortar method. We prove its almost quasi-optimal convergence and underline the theory by a numerical experiment.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Domain Decomposition Algorithms for an Indefinite Hypersingular Integral Equation in Three Dimensions

In this paper we report on a non-overlapping and an overlapping domain decomposition method as preconditioners for the boundary element approximation of an indefinite hypersingular integral equation on a surface. The equation arises from an integral reformulation of the Neumann screen problem with the Helmholtz equation in the exterior of a screen in R. It is well-known that the linear algebrai...

متن کامل

Preconditioners for pseudodifferential equations on the sphere with radial basis functions

In a previous paper a preconditioning strategy based on overlapping domain decomposition was applied to the Galerkin approximation of elliptic partial differential equations on the sphere. In this paper the methods are extended to more general pseudodifferential equations on the sphere, using as before spherical radial basis functions for the approximation space, and again preconditioning the i...

متن کامل

Approximations of hypersingular integral equations by the quadrature method

A numerical method is proposed and investigated for the hypersingular integral equations defined in Banach spaces. The hypersingular integral equations belong to a wider class of singular integral equations having much more stronger singularities. The proposed approximation method is an extension beyond the quadrature method. Moreover an error estimates theory is introduced for the hypersingula...

متن کامل

Hypersingular Integral Equations in Banach Spaces by the Quadrature Method

Abstract A new numerical method is introduced and investigated for the hypersingular integral equations defined in Banach spaces. The hypersingular integral equations belong to a wider class of singular integral equations having much more stronger singularities.The proposed approximation method is an extension beyond the quadrature method. Beyond the above, an error estimates theory is proposed...

متن کامل

Modified homotopy perturbation method for solving hypersingular integral equations of the first kind

Modified homotopy perturbation method (HPM) was used to solve the hypersingular integral equations (HSIEs) of the first kind on the interval [-1,1] with the assumption that the kernel of the hypersingular integral is constant on the diagonal of the domain. Existence of inverse of hypersingular integral operator leads to the convergence of HPM in certain cases. Modified HPM and its norm converge...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Numerische Mathematik

دوره 121  شماره 

صفحات  -

تاریخ انتشار 2012