Computational Mathematics (CM)
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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 ... -
A C0 interior penalty discontinuous Galerkin method for fourth‐order total variation flow I: Derivation of the method and numerical results
(NMPDE:Numerical Methods For Partial Differential Equations, 2019-02-23)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 ... -
A C 0 interior penalty discontinuous Galerkin Method for fourth-order total variation flow. II: Existence and uniqueness
(NMPDE:Numerical Methods For Partial Differential Equations, 2019-02-25)We prove the existence and uniqueness of a solution of a C0 Interior Penalty Discontinuous Galerkin (C0 IPDG) method for the numerical solution of a fourth‐order total variation flow problem that has been developed in part ... -
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 ... -
Normal lubrication force between spherical particles immersed in a shear-thickening fluid
(Physics of Fluids, 2018-12-07)In this work, the inverse bi-viscous model [Physics of Fluids 29, 103104 (2017)] is used to describe a shear-thickening fluid. An analytical velocity profile in a planar Poiseuille flow is utilized to calculate an approximate ... -
Apparent slip mechanism between two spheres based on solvent rheology: Theory and implication for the shear thinning of non-Brownian suspensions
(Physical Review Fluids, 2018-12-10)Analytical results for the apparent slip between two spheres in a simple biviscous model of a shear thinning fluid are presented. Velocity profiles and apparent slip lengths along the surfaces are analyzed in order to ... -
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 ... -
Nonlinear computations of heave motions for a generic Wave Energy Converter
(In Vittorio Bucci Alberto Marinò (Eds.), Technology and Science for the Ships of the Future, Proceedings of NAV 2018: 19th International Conference on Ship and Maritime Research, IOS Press BV, 2018)A bench-marking activity of numerical methods for analysis of Wave Energy Converters (WEC) was proposed under the Ocean Energy Systems (OES) International Energy Agency (IEA) Task 10 in 2015. The purpose of the benchmark ... -
Finite Element Simulations of Two-phase Flow and Floating Bodies Using FEniCS-HPC
(13th World Congress in Computational Mechanics WCCM, New York, USA, 2018-07)We present a variational multiscale stabilized finite element method to solve the variable density incompressible Navier-Stokes equations for the simulation of two-phase flow. We introduce a level-set method based on the ... -
Adaptive Direct FEM Simulation with Unicorn/FEniCS-HPC for CS1
(5th International Workshop on High Order CFD Methods, 2018-01-01) -
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 ...
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