Simulation of Wave Propagation
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Adjoint-based formulation for computing derivatives with respect to bed boundary positions in resistivity geophysics
(Computational Geosciences, 2019-02)In inverse geophysical resistivity problems, it is common to optimize for specific resistivity values and bed boundary positions, as needed, for example, in geosteering applications. When using gradient-based inversion ... -
Parallel refined Isogeometric Analysis in 3D
(IEEE Transactions on Parallel and Distributed Systems, 2018-11)We study three-dimensional isogeometric analysis (IGA) and the solution of the resulting system of linear equations via a direct solver. IGA uses highly continuous $C^{p-1}$ basis functions, which provide multiple benefits ... -
Asymptotic Models for the Electric Potential across a Highly Conductive Casing
(Computers and Mathematics with Applications, 2018-07)We analyze a configuration that involves a steel-cased borehole, where the casing that covers the borehole is considered as a highly conductive thin layer. We develop an asymptotic method for deriving reduced problems ... -
On initialization of milling paths for 5-axis flank CNC machining of free-form surfaces with general milling tools
(Computer Aided Geometric Design (CAGD, Elsevier), 2019-03-27)We propose a path-planning algorithm for 5-axis flank CNC machining with general tools of varying curvature. Our approach generalizes the initialization strategy introduced for conical tools [Bo et al., 2017] to arbitrary ... -
A space-time DPG method for the wave equation in multiple dimensions
(RICAM book series, 2019)A space-time discontinuous Petrov–Galerkin (DPG) method for the linear wave equation is presented. This method is based on a weak formulation that uses a broken graph space. The well-posedness of this formulation is ... -
Fast inversion of logging-while-drilling resistivity measurements acquired in multiple wells
(Geophysics, 2016-10)This paper introduces a new method for the fast inversion of borehole resistivity measurements acquired in multiple wells using logging-while-drilling (LWD) instruments. There are two key novel contributions. First, we ... -
Finite element approximation of electromagnetic fields using nonfitting meshes for Geophysics
(SIAM Journal on Numerical Analysis, 2018-07)We analyze the use of nonfitting meshes for simulating the propagation of electromagnetic waves inside the earth with applications to borehole logging. We avoid the use of parameter homogenization and employ standard edge ... -
Time-Domain Goal-Oriented Adaptivity Using Pseudo-Dual Error Representations
(Computer Methods in Applied Mechanics and Engineering, 2017-12)Goal-oriented adaptive algorithms produce optimal grids to solve challenging engineering problems. Recently, a novel error representation using (unconventional) pseudo-dual problems for goal-oriented adaptivity in the ... -
Explicit-in-Time Goal-Oriented Adaptivity
(Computer Methods in Applied Mechanics and Engineering, 2019-04-15)Goal-oriented adaptivity is a powerful tool to accurately approximate physically relevant solution features for partial differential equations. In time dependent problems, we seek to represent the error in the quantity of ... -
Source time reversal (STR) method for linear elasticity
(Computers & Mathematics with Applications, 2018)We study the problem of source reconstruction for a linear elasticity problem applied to seismicity induced by mining. We assume the source is written as a variable separable function $\mathbf{f(x)}\>g(t)$ . We first present ... -
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 ...
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