Computational Mathematics (CM)
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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 ... -
Numerical simulation of the von Kármán sodium dynamo experiment
(Journal of Fluid Mechanics, 2018-09-03)We present hydrodynamic and magnetohydrodynamic (MHD) simulations of liquid sodium flows in the von Kármán sodium (VKS) set-up. The counter-rotating impellers made of soft iron that were used in the successful 2006 experiment ... -
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 ... -
Variational multiscale stabilization for compressible flow
(Computer Methods in Applied Mechanics and Engineering, 2018)This paper presents a variational multiscale stabilization for the finite element numerical solution of the Euler and Navier-Stokes equations of compressible flow. All the components of the dual operator are considered in ... -
On intermediate-scale open-sea experiments on floating offshore structures: Feasibility and application on a spar support for offshore wind turbines
(Marine Structures, 2018-06-28)Experimental investigation of floating structures represents the most direct way for achieving their dynamic identification and it is particularly valuable for relatively new concepts, such as floating supports for offshore ... -
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 ... -
A $C^0$ INTERIOR PENALTY DISCONTINUOUS GALERKIN METHOD FOR FOURTH ORDER TOTAL VARIATION FLOW
(Journal of Mathematical analysis and applications, 2017)We consider the numerical solution of a fourth order total variation flow problem representing surface relaxation below the roughening temperature. Based on a regularization and scaling of the nonlinear fourth order parabolic ... -
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 ... -
On Adomian Based Numerical Schemes for Euler and Navier-Stokes Equations, and Application to Aeroacoustic Propagation
(2018-03-12)In this thesis, an Adomian Based Scheme (ABS) for the compressible Navier-Stokes equations is constructed, resulting in a new multiderivative type scheme not found in the context of fluid dynamics. Moreover, this scheme ... -
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 ... -
Time-resolved Adaptive Direct FEM Simulation of High-lift Aircraft Configurations
(Numerical simulation of the aerodynamics of high-lift configurations, 2017-08-01)Our simulation methodology is referred to as Direct FEM Simulation (DFS), or General Galerkin (G2) and uses a finite element method (FEM) with piecewise linear approximation in space and time, and with numerical stabilization ... -
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 ...
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