A subdivision scheme for unstructured quadrilateral meshes with improved convergence rate for isogeometric analysis

2019 ◽  
Vol 106 ◽  
pp. 101043
Author(s):  
Yue Ma ◽  
Weiyin Ma
Keyword(s):  
Convergence Rate ◽  
Isogeometric Analysis ◽  
Subdivision Scheme ◽  
Quadrilateral Meshes

A New Plate Formulation Based on Triangular Isogeometric Analysis

2018 ◽  
Author(s):  
Mehrdad Zareh ◽  
Xiaoping Qian
Keyword(s):  
Convergence Rate ◽  
Isogeometric Analysis ◽  
Complex Geometry ◽  
Plate Theory ◽  
Necessary Condition ◽  
Local Refinement ◽  
Geometric Models ◽  
Plate Elements ◽  
Element Technique ◽  
C1 Continuity

This paper presents application of rational triangular Bezier splines (rTBS) for developing Kirchhoff-Love plate elements in the context of isogeometric analysis. Triangular isogeometric analysis can provide the C1 continuity over the mesh including elements interfaces, a necessary condition in finite elements formulation based on Kirchhoff-Love shell and plate theory. Using rTBS and macro-element technique, we develop Kirchhoff-Love plate elements, investigate the convergence rate and apply the method on complex geometry. Obtained results demonstrate that the optimal convergence rate is achievable; moreover, this method is applicable to represent thin geometric models of complex topology or thin geometric models in which efficient local refinement is required.

scholarly journals A New Approach to Increase the Flexibility of Curves and Regular Surfaces Produced by 4-Point Ternary Subdivision Scheme

2020 ◽  
Vol 2020 ◽  
pp. 1-17 ◽  
Author(s):  
Rabia Hameed ◽  
Ghulam Mustafa ◽  
Amina Liaqat ◽  
Dumitru Baleanu ◽  
Faheem Khan ◽  
...  
Keyword(s):  
Tensor Product ◽  
Numerical Experiments ◽  
Subdivision Scheme ◽  
Shape Parameters ◽  
New Approach ◽  
Quadrilateral Meshes ◽  
Displacement Vectors ◽  
Approximating Subdivision Scheme ◽  
Interpolatory Subdivision

In this article, we present a new subdivision scheme by using an interpolatory subdivision scheme and an approximating subdivision scheme. The construction of the subdivision scheme is based on translation of points of the 4-point interpolatory subdivision scheme to the new position according to three displacement vectors containing two shape parameters. We first study the characteristics of the new subdivision scheme analytically and then present numerical experiments to justify these analytical characteristics geometrically. We also extend the new derived scheme into its bivariate/tensor product version. This bivariate scheme is applicable on quadrilateral meshes to produce smooth limiting surfaces up to C 3 continuity.

BDDC PRECONDITIONERS FOR ISOGEOMETRIC ANALYSIS

2013 ◽  
Vol 23 (06) ◽  
pp. 1099-1142 ◽  
Author(s):  
L. BEIRÃO DA VEIGA ◽  
D. CHO ◽  
L. F. PAVARINO ◽  
S. SCACCHI
Keyword(s):  
Convergence Rate ◽  
Domain Decomposition ◽  
Elliptic Problem ◽  
Isogeometric Analysis ◽  
Numerical Experiments ◽  
Three Dimensional ◽  
Parallel Computers ◽  
Basis Functions ◽  
Polynomial Degree ◽  
Balancing Domain Decomposition

A Balancing Domain Decomposition by Constraints (BDDC) preconditioner for Isogeometric Analysis of scalar elliptic problems is constructed and analyzed by introducing appropriate discrete norms. A main result of this work is the proof that the proposed isogeometric BDDC preconditioner is scalable in the number of subdomains and quasi-optimal in the ratio of subdomain and element sizes. Another main result is the numerical validation of the theoretical convergence rate estimates by carrying out several two- and three-dimensional tests on serial and parallel computers. These numerical experiments also illustrate the preconditioner performance with respect to the polynomial degree and the regularity of the NURBS basis functions, as well as its robustness with respect to discontinuities of the coefficient of the elliptic problem across subdomain boundaries.

Convergence of Finite Fifference Method for Parabolic Problem

2003 ◽  
Vol 3 (1) ◽  
pp. 45-58 ◽  
Author(s):  
Dejan Bojović
Keyword(s):  
Convergence Rate ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Parabolic Problem ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Variable Coefficients ◽  
Rate Estimate ◽  
Convergence Rate Estimate ◽  
Initial Boundary Value

Abstract In this paper we consider the first initial boundary-value problem for the heat equation with variable coefficients in a domain (0; 1)x(0; 1)x(0; T]. We assume that the solution of the problem and the coefficients of the equation belong to the corresponding anisotropic Sobolev spaces. Convergence rate estimate which is consistent with the smoothness of the data is obtained.

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