20 research outputs found
A simple approach to the numerical simulation with trimmed CAD surfaces
In this work a novel method for the analysis with trimmed CAD surfaces is
presented. The method involves an additional mapping step and the attraction
stems from its sim- plicity and ease of implementation into existing Finite
Element (FEM) or Boundary Element (BEM) software. The method is first verified
with classical test examples in structural mechanics. Then two practical
applications are presented one using the FEM, the other the BEM, that show the
applicability of the method.Comment: 20 pages and 16 figure
Fast Isogeometric Boundary Element Method based on Independent Field Approximation
An isogeometric boundary element method for problems in elasticity is
presented, which is based on an independent approximation for the geometry,
traction and displacement field. This enables a flexible choice of refinement
strategies, permits an efficient evaluation of geometry related information, a
mixed collocation scheme which deals with discontinuous tractions along
non-smooth boundaries and a significant reduction of the right hand side of the
system of equations for common boundary conditions. All these benefits are
achieved without any loss of accuracy compared to conventional isogeometric
formulations. The system matrices are approximated by means of hierarchical
matrices to reduce the computational complexity for large scale analysis. For
the required geometrical bisection of the domain, a strategy for the evaluation
of bounding boxes containing the supports of NURBS basis functions is
presented. The versatility and accuracy of the proposed methodology is
demonstrated by convergence studies showing optimal rates and real world
examples in two and three dimensions.Comment: 32 pages, 27 figure
Fast immersed boundary method based on weighted quadrature
Combining sum factorization, weighted quadrature, and row-based assembly
enables efficient higher-order computations for tensor product splines. We aim
to transfer these concepts to immersed boundary methods, which perform
simulations on a regular background mesh cut by a boundary representation that
defines the domain of interest. Therefore, we present a novel concept to divide
the support of cut basis functions to obtain regular parts suited for sum
factorization. These regions require special discontinuous weighted quadrature
rules, while Gauss-like quadrature rules integrate the remaining support. Two
linear elasticity benchmark problems confirm the derived estimate for the
computational costs of the different integration routines and their
combination. Although the presence of cut elements reduces the speed-up, its
contribution to the overall computation time declines with h-refinement