Spectral Processing of Tangential Vector Fields

2016 ◽  
Vol 36 (6) ◽  
pp. 338-353 ◽  
Author(s):  
Christopher Brandt ◽  
Leonardo Scandolo ◽  
Elmar Eisemann ◽  
Klaus Hildebrandt
Keyword(s):  
Vector Fields ◽  
Spectral Processing ◽  
Tangential Vector

scholarly journals Modeling Tangential Vector Fields on a Sphere

2018 ◽  
Vol 113 (524) ◽  
pp. 1625-1636 ◽  
Author(s):  
Minjie Fan ◽  
Debashis Paul ◽  
Thomas C. M. Lee ◽  
Tomoko Matsuo
Keyword(s):  
Vector Fields ◽  
Tangential Vector

scholarly journals Analysis of finite element methods for vector Laplacians on surfaces

2019 ◽  
Vol 40 (3) ◽  
pp. 1652-1701 ◽  
Author(s):  
Peter Hansbo ◽  
Mats G Larson ◽  
Karl Larsson
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Vector Fields ◽  
Optimal Order ◽  
Order Error ◽  
Optimal Order Error Estimates ◽  
Elastic Membranes ◽  
Tangential Vector ◽  
Higher Order Finite Elements ◽  
Lagrange Elements

Abstract We develop a finite element method for the vector Laplacian based on the covariant derivative of tangential vector fields on surfaces embedded in ${\mathbb{R}}^3$. Closely related operators arise in models of flow on surfaces as well as elastic membranes and shells. The method is based on standard continuous parametric Lagrange elements that describe a ${\mathbb{R}}^3$ vector field on the surface, and the tangent condition is weakly enforced using a penalization term. We derive error estimates that take into account the approximation of both the geometry of the surface and the solution to the partial differential equation. In particular, we note that to achieve optimal order error estimates, in both energy and $L^2$ norms, the normal approximation used in the penalization term must be of the same order as the approximation of the solution. This can be fulfilled either by using an improved normal in the penalization term, or by increasing the order of the geometry approximation. We also present numerical results using higher-order finite elements that verify our theoretical findings.

HODGE DECOMPOSITIONS ON THE BOUNDARY OF NONSMOOTH DOMAINS: THE MULTI-CONNECTED CASE

2001 ◽  
Vol 11 (09) ◽  
pp. 1491-1503 ◽  
Author(s):  
A. BUFFA
Keyword(s):  
Vector Fields ◽  
General Topology ◽  
Cohomology Space ◽  
Nonsmooth Domains ◽  
Connected Case ◽  
Tangential Vector

This paper concerns the characterization of tangential traces for the space H(curl, Ω), when Ω is a Lipschitz polyhedron in ℝ3 under general topology assumptions. Suitable spaces of tangential vector fields are introduced and characterized. Hodge decompositions are provided and they involve the first cohomology space of the boundary Γ. Such a space is characterized and a basis is furnished.

Cohomologies of Lie algebra of tangential vector fields. II

1970 ◽  
Vol 4 (2) ◽  
pp. 110-116 ◽  
Author(s):  
I. M. Gel'fand ◽  
D. B. Fuks
Keyword(s):  
Lie Algebra ◽  
Vector Fields ◽  
Tangential Vector

MODELING TANGENTIAL VECTOR FIELDS ON REGULAR SURFACES BY MEANS OF MIE POTENTIALS

2007 ◽  
Vol 05 (03) ◽  
pp. 417-449 ◽  
Author(s):  
WILLI FREEDEN ◽  
CARSTEN MAYER
Keyword(s):  
Vector Fields ◽  
Numerical Test ◽  
Scaling Functions ◽  
Refinement Equation ◽  
Regular Surface ◽  
Tangential Vector ◽  
Classical Potential ◽  
Classical Potential Theory ◽  
Complex Valued ◽  
Integration Rules

By means of the limit and jump relations of classical potential theory with respect to the vectorial Helmholtz equation, a wavelet approach is established on a regular surface. The multiscale procedure is constructed in such a way that the emerging scalar, vectorial and tensorial potential kernels act as scaling functions. Corresponding wavelets are defined via a canonical refinement equation. A tree algorithm for fast decomposition of a tangential complex-valued vector field given on a regular surface is developed based on numerical integration rules. Some numerical test examples conclude the paper.

Parallel Computation of Complex Antennas around the Coated Object Using Iterative Vector Fields Technique

2014 ◽  
Vol E97.C (7) ◽  
pp. 661-669
Author(s):  
Ying YAN ◽  
Xunwang ZHAO ◽  
Yu ZHANG ◽  
Changhong LIANG ◽  
Zhewang MA
Keyword(s):  
Parallel Computation ◽  
Vector Fields
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