Overlapping Schwarz methods in H(curl) on polyhedral domains
نویسندگان
چکیده
We consider domain decomposition preconditioners for the linear algebraic equations which result from finite element discretization of problems involving the bilinear form α(·, ·) + (curl ·, curl ·) defined on a polyhedral domain Ω. Here (·, ·) denotes the inner product in (L(Ω)) and α is a positive number. We use Nedelec’s curl-conforming finite elements to discretize the problem. Both additive and multiplicative overlapping Schwarz preconditioners are studied. Our results are uniform with respect to the mesh size and α under standard assumptions concerning the overlapping subdomains.
منابع مشابه
Fast Solvers and Schwarz Preconditioners for Spectral Nédélec Elements for a Model Problem in H(curl)
1 1. Introduction. In this paper, we present fast solvers and overlapping additive Schwarz methods for spectral Nédélec element discretizations for a model problem in H(curl). Results of numerical experiments in two dimensions and arguments for a theoretical condition number bound in two and three dimensions are presented. We first show the derivation of the model problem in the implicit time d...
متن کاملTwo-level Overlapping Schwarz Method for H(curl) in 2d for Irregular Subdomains
A bound is obtained for the condition number of a two-level overlapping Schwarz algorithm for problems posed in H(curl) in 2D, where the subdomains are only assumed to be uniform in the sense of Peter Jones. The coarse space is based on energy minimization and its dimension equals the number of subdomain edges. Local direct solvers over overlapping subdomains are also used. The bound is indepen...
متن کاملFachrichtung 6 . 1 – Mathematik Preprint Nr . 323 Characterization of trace spaces of H ( curl , Ω ) on curvilinear Lipschitz polyhedral domains Ω
متن کامل
Domain Decomposition Preconditioners for Spectral Nédélec Elements in Two and Three Dimensions
In this paper, we present several domain decomposition preconditioners for high-order Spectral Nédélec element discretizations for a Maxwell model problem in H(curl), in particular overlapping Schwarz preconditioners and Balancing Neumann-Neumann preconditioners. For an efficient and fast implementation of these preconditioners, fast matrix-vector products and direct solvers for problems posed ...
متن کاملA Two-level Overlapping Schwarz Method for H(curl) in Two Dimensions with Irregular Subdomains
A bound is obtained for the condition number of a two-level overlapping Schwarz algorithm for problems posed in H(curl) in two dimensions, where the subdomains are only assumed to be uniform in the sense of Peter Jones. The coarse space is based on energy minimization and its dimension equals the number of interior subdomain edges. Local direct solvers are used on the overlapping subdomains. Ou...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Num. Math.
دوره 10 شماره
صفحات -
تاریخ انتشار 2002