Simulation of Wave Propagation
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Fast One-dimensional Finite Element Approximation of Geophysical Measurements
(2018)There exist a wide variety of geophysical prospection methods. In this work, we focus on resistivity methods. We categorize these resistivity prospection methods according to their acquisition location as (a) on the surface, ... -
Gaussian quadrature for $C^1$ cubic Clough-Tocher macro-triangles
(Journal of Computational and Applied Mathematics, 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 ... -
Generalization of the Pythagorean Eigenvalue Error Theorem and its Application to Isogeometric Analysis
(Numerical Methods for PDEs, 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 ... -
A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements
(Geosciences, 2018-06-14)In some geological formations, borehole resistivity measurements can be simulated using a sequence of 1D models. By considering a 1D layered media, we can reduce the dimensionality of the problem from 3D to 1.5D via a ... -
Goal-oriented adaptivity using unconventional error representations for the multi-dimensional Helmholtz equation
(International Journal for Numerical Methods in Engineering, 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 ... -
Refined Isogeometric Analysis for a Preconditioned Conjugate Gradient Solver
(Computer Methods in Applied Mechanics and Engineering, 2018-06-15)Starting from a highly continuous Isogeometric Analysis (IGA) discretization, refined Isogeometric Analysis (rIGA) introduces $C^0$ hyperplanes that act as separators for the direct LU factorization solver. As a result, ... -
On numerical quadrature for $C^1$ quadratic Powell-Sabin 6-split macro-triangles
(Journal of Computational and Applied Mathematics, 2018-08-01)The quadrature rule of Hammer and Stroud [16] for cubic polynomials has been shown to be exact for a larger space of functions, namely the $C^1$ cubic Clough-Tocher spline space over a macro-triangle if and only if the ... -
REFINED ISOGEOMETRIC ANALYSIS: A SOLVER-BASED DISCRETIZATION METHOD
(2018-06-22)Isogeometric analysis (IGA) is a computational approach frequently employed nowadays to study problems governed by partial differential equations (PDEs). This approach defines the geometry using conventional computer-aided ... -
Efficient quadrature rules for subdivision surfaces in isogeometric analysis
(Computer Methods in Applied Mechanics and Engineering, 2018-10)We introduce a new approach to numerical quadrature on geometries defined by subdivision surfaces based on quad meshes in the context of isogeometric analysis. Starting with a sparse control mesh, the subdivision process ... -
Fast 2.5D Finite Element Simulations of Borehole Resistivity Measurements
(Computational Geosciences, 2018-05-29)We develop a rapid 2.5-dimensional (2.5D) finite element method for simulation of borehole resistivity measurements in transversely isotropic (TI) media. The method combines arbitrary high-order $H^1$ - and $H$ (curl)-conforming ... -
Finite Element Simulations of Logging-While-Drilling and Extra-Deep Azimuthal Resistivity Measurements using Non-Fitting Grids
(Computational Geosciences, 2018-04-27)We propose a discretization technique using non-fitting grids to simulate magnetic field-based resistivity logging measurements. Non-fitting grids are convenient because they are simpler to generate and handle than fitting ... -
Highly-accurate 5-axis flank CNC machining with conical tools
(The International Journal of Advanced Manufacturing Technology, 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 ... -
Super Abrasive Machining of Integral Rotary Components Using Grinding Flank Tools
(Metals, 2018-01-01)Manufacturing techniques that are applied to turbomachinery components represent a challenge in the aeronautic sector. These components require high resistant super-alloys in order to satisfy the extreme working conditions ... -
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 ... -
Dispersion-minimizing quadrature rules for $C^1$ quadratic isogeometric analysis
(Computer Methods in Applied Mechanics and Engineering, 2017-09-20)We develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrations that minimize the discrete dispersion error of the approximation. The rules are optimal in the sense that they only ... -
Goal-Oriented p-Adaptivity using Unconventional Error Representations for a 1D Steady State Convection-Diffusion Problem
(Procedia Computer Science, 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 ... -
ICCS 2017 Workshop on Agent-Based Simulations, Adaptive Algorithms and Solvers
(Procedia Computer Science, 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 ... -
Optimally refined isogeometric analysis
(Procedia Computer Science, 2017-06)Performance of direct solvers strongly depends upon the employed discretization method. In particular, it is possible to improve the performance of solving Isogeometric Analysis (IGA) discretizations by introducing multiple ... -
Automatic fitting of conical envelopes to free-form surfaces for flank CNC machining
(Computer Aided Design, 2017-10)We propose a new algorithm to detect patches of free-form surfaces that can be well approximated by envelopes of a rotational cone under a rigid body motion. These conical envelopes are a preferable choice from the ... -
Necking in 2D incompressible polyconvex materials: theoretical framework and numerical simulations
(Quarterly Journal of Mechanics and Applied Mathematics, 2017-06-15)We show examples of 2D incompressible isotropic homogeneous hyperelastic materials with a poly-convex stored-energy function that present necking. The construction of the stored-energy function of amaterial satisfying all ...
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