A Spline-Trigonometric Galerkin Method and an Exponentially Convergent Boundary Integral Method
نویسندگان
چکیده
منابع مشابه
A convergent boundary integral method for three-dimensional water waves
We design a boundary integral method for time-dependent, threedimensional, doubly periodic water waves and prove that it converges with O(h3) accuracy, without restriction on amplitude. The moving surface is represented by grid points which are transported according to a computed velocity. An integral equation arising from potential theory is solved for the normal velocity. A new method is deve...
متن کاملGalerkin Boundary Integral Method for Evaluating Surface Derivatives
A Galerkin boundary integral procedure for evaluating the complete derivative, e.g., potential gradient or stress tensor, is presented. The expressions for these boundary derivatives involve hypersingular kernels, and the advantage of the Galerkin approach is that the integrals exist when a continuous surface interpolation is employed. As a consequence, nodal derivative values, at smooth surfac...
متن کاملA trigonometric Galerkin method for volume integral equations arising in TM grating scattering
Transverse magnetic (TM) scattering of an electromagnetic wave from a periodic dielectric diffraction grating can mathematically be described by a volume integral equation. This volume integral equation, however, in general fails to feature a weakly singular integral operator. Nevertheless, after a suitable periodization, the involved integral operator can be efficiently evaluated on trigonomet...
متن کاملA discontinuous-Galerkin-based immersed boundary method
A numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced. The proposed method is conceptually simple and free of userdefined parameters. Starting with a conforming finite element mesh, the key ingredient is to switch those elements intersected by the Dirichlet boundary to a discontinuous-Galerkin approximation and impo...
متن کاملBoundary temperature reconstruction in an inverse heat conduction problem using boundary integral equation method
In this paper, we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain. This problem consists of determining the temperature on the interior boundary curve from the Cauchy data (boundary temperature and heat flux) on the exterior boundary curve. To this end, the boundary integral equation method is used. Since the resulting system of linea...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1983
ISSN: 0025-5718
DOI: 10.2307/2007682