Now showing items 78-97 of 204

• #### Gauss-Galerkin quadrature rules for quadratic and cubic spline spaces and their application to isogeometric analysis ﻿

(2016-07-01)
We introduce Gaussian quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. By definition, these spaces are of even degrees. The optimal quadrature ...
• #### Gaussian quadrature for $C^1$ cubic Clough-Tocher macro-triangles ﻿

(2018-10-31)
A numerical integration rule for multivariate cubic polynomials over n-dimensional simplices was designed by Hammer and Stroud [14]. The quadrature rule requires n + 2 quadrature points: the barycentre of the simplex and ...
• #### Gaussian quadrature rules for $C^1$ quintic splines with uniform knot vectors ﻿

(2017-03-22)
We provide explicit quadrature rules for spaces of $C^1$ quintic splines with uniform knot sequences over finite domains. The quadrature nodes and weights are derived via an explicit recursion that avoids numerical solvers. ...
• #### Generalization of the Pythagorean Eigenvalue Error Theorem and its Application to Isogeometric Analysis ﻿

(2018-10-13)
This chapter studies the effect of the quadrature on the isogeometric analysis of the wave propagation and structural vibration problems. The dispersion error of the isogeometric elements is minimized by optimally blending ...
• #### Generalization of the Zlámal condition for simplicial finite elements in ℝ d ﻿

(2011-12-31)
The famous Zlámal's minimum angle condition has been widely used for construction of a regular family of triangulations (containing nondegenerating triangles) as well as in convergence proofs for the finite element method ...
• #### A Geometric Toolbox for Tetrahedral Finite Element Partitions ﻿

(2011-12-31)
In this work we present a survey of some geometric results on tetrahedral partitions and their refinements in a unified manner. They can be used for mesh generation and adaptivity in practical calculations by the finite ...
• #### Geometry and tool motion planning for curvature adapted CNC machining ﻿

(2021)
CNC machining is the leading subtractive manufacturing technology. Although it is in use since decades, it is far from fully solved and still a rich source for challenging problems in geometric computing. We demonstrate ...
• #### Global Time-Renormalization of the Gravitational N-body Problem ﻿

(2021-01-01)
This work considers the gravitational N-body problem and introduces global time-renormalization functions that allow the efficient numerical integration with fixed time-steps. First, a lower bound of the radius of convergence ...
• #### Goal-oriented adaptivity for a conforming residual minimization method in a dual discontinuous Galerkin norm ﻿

(2021-03)
We propose a goal-oriented mesh-adaptive algorithm for a finite element method stabilized via residual minimization on dual discontinuous-Galerkin norms. By solving a saddle-point problem, this residual minimization delivers ...
• #### Goal-Oriented Adaptivity using Unconventional Error Representations ﻿

(2017-09)
In Goal-Oriented Adaptivity (GOA), the error in a Quantity of Interest (QoI) is represented using global error functions of the direct and adjoint problems. This error representation is subsequently bounded above by ...
• #### Goal-oriented adaptivity using unconventional error representations for the 1D Helmholtz equation ﻿

(2015-12-31)
In this work, the error of a given output functional is represented using bilinear forms that are different from those given by the adjoint problem. These representations can be employed to design novel h, p, and hp ...
• #### Goal-oriented adaptivity using unconventional error representations for the multi-dimensional Helmholtz equation ﻿

(2017-06-27)
In goal‐oriented adaptivity, the error in the quantity of interest is represented using the error functions of the direct and adjoint problems. This error representation is subsequently bounded above by element‐wise error ...
• #### Goal-Oriented p-Adaptivity using Unconventional Error Representations for a 1D Steady State Convection-Diffusion Problem ﻿

(2017)
This work proposes the use of an alternative error representation for Goal-Oriented Adaptivity (GOA) in context of steady state convection dominated diffusion problems. It introduces an arbitrary operator for the computation ...
• #### High-accuracy adaptive modeling of the energy distribution of a meniscus-shaped cell culture in a Petri dish ﻿

(2015-12-31)
Cylindrical Petri dishes embedded in a rectangular waveguide and exposed to a polarized electromagnetic wave are often used to grow cell cultures. To guarantee the success of these cultures, it is necessary to enforce that ...
• #### High-frequency analysis of the efficiency of a local approximate DtN2 boundary condition for prolate spheroidal-shaped boundaries ﻿

(2010-12-31)
The performance of the second-order local approximate DtN boundary condition suggested in [4] is investigated analytically when employed for solving high-frequency exterior Helmholtz problems with elongated scatterers. ...
• #### Highly-accurate 5-axis flank CNC machining with conical tools ﻿

(2018-04)
A new method for $5$-axis flank computer numerically controlled (CNC) machining using a predefined set of tappered ball-end-mill tools (aka conical) cutters is proposed. The space of lines that admit tangential motion of ...
• #### $hp$-Adaptive Simulation and Inversion of Magnetotelluric Measurements ﻿

(2015-12-18)
The magnetotelluric (MT) method is a passive exploration technique that aims at esti- mating the resistivity distribution of the Earth’s subsurface, and therefore at providing an image of it. This process is divided into ...
• #### A hybrid method for inversion of 3D DC resistivity logging measurements ﻿

(2014-12-31)
This paper focuses on the application of hp hierarchic genetic strategy (hp-HGS) for solution of a challenging problem, the inversion of 3D direct current (DC) resistivity logging measurements. The problem under consideration ...
• #### Hypersingular integral equations over a disc: Convergence of a spectral method and connection with Tranter's method ﻿

(2014-12-31)
Two-dimensional hypersingular equations over a disc are considered. A spectral method is developed, using Fourier series in the azimuthal direction and orthogonal polynomials in the radial direction. The method is proved ...
• #### ICCS 2017 Workshop on Agent-Based Simulations, Adaptive Algorithms and Solvers ﻿

(2017)
This workshop seeks to integrate results from different domains of computer science, computational science, and mathematics. We welcome simulation papers, either hard simulations using finite element or finite difference ...