Now showing items 153-172 of 204

• #### A Quadrature-Free Method for Simulation and Inversion of 1.5D Direct Current (DC) Borehole Measurements ﻿

(2016-12)
Resistivity inverse problems are routinely solved in order to characterize hydrocarbon bearing formations. They often require a large number of forward problems simulations. When considering a one dimensional (1D) planarly ...
• #### Quantities of interest for surface based resistivity geophysical measurements ﻿

(2015-12-31)
The objective of traditional goal-oriented strategies is to construct an optimal mesh that minimizes the problem size needed to achieve a user prescribed tolerance error for a given quantity of interest (QoI). Typical ...
• #### Rational approximation of P-wave kinematics — Part 1: Transversely isotropic media ﻿

(2020-09)
In seismic data processing and several wave propagation modeling algorithms, the phase velocity, group velocity, and traveltime equations are essential. To have these equations in explicit form, or to reduce algebraic ...
• #### Rational approximation of P-wave kinematics — Part 2: Orhorhombic media ﻿

(2020-09)
Orthorhombic anisotropy is a modern standard for 3D seismic studies in complex geologic settings. Several seismic data processing methods and wave propagation modeling algorithms in orthorhombic media rely on phase-velocity, ...
• #### Red refinements of simplices into congruent subsimplices ﻿

(2014-12-31)
We show that in dimensions higher than two, the popular "red refinement" technique, commonly used for simplicial mesh refinements and adaptivity in the finite element analysis and practice, never yields subsimplices which ...
• #### Refined Isogeometric Analysis for a Preconditioned Conjugate Gradient Solver ﻿

(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, ...
• #### Refined Isogeometric Analysis for fluid mechanics and electromagnetism ﻿

(2019-03)
Starting from a highly continuous isogeometric analysis discretization, we introduce hyperplanes that partition the domain into subdomains and reduce the continuity of the discretization spaces at these hyperplanes. As the ...
• #### Refined isogeometric analysis for generalized Hermitian eigenproblems ﻿

(2021-04)
We use refined isogeometric analysis (rIGA) to solve generalized Hermitian eigenproblems (Ku = λMu). rIGA conserves the desirable properties of maximum-continuity isogeometric analysis (IGA) while it reduces the solution ...
• #### Refined isogeometric analysis of quadratic eigenvalue problems ﻿

(2022-07-16)
Certain applications that analyze damping effects require the solution of quadratic eigenvalue problems (QEPs). We use refined isogeometric analysis (rIGA) to solve quadratic eigenproblems. rIGA discretization, while ...
• #### 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 ...
• #### Regions of prevalence in the coupled restricted three-body problems approximation ﻿

(2012-12-31)
This work concerns the role played by a couple of the planar circular restricted three-body problem in the approximation of the bicircular model. The comparison between the differential equations governing the dynamics ...
• #### Regular polygons on isochordal-viewed hedgehogs ﻿

(2022)
A curve $\alpha$ is called isochordal viewed if there is a smooth motion of a constant length chord with its endpoints along $\alpha$ such that their tangents to the curve at these points form a constant angle. In this ...
• #### Reparameterization of ruled surfaces: toward generating smooth jerk-minimized toolpaths for multi-axis flank CNC milling ﻿

(2020-05)
This paper presents a novel jerk minimization algorithm in the context of multi-axis flank CNC machining. The toolpath of the milling axis in a flank milling process, a ruled surface, is reparameterized by a B-spline ...
• #### Reproductive value, sensitivity, and nonlinearity: Population-management heuristics derived from classical demography ﻿

(2013-12-31)
In classical demographic theory, reproductive value and stable age distribution are proportional to the sensitivities of the asymptotic population size to changes in mortality and maternity, respectively. In this note we ...
• #### Rigorous computation of smooth branches of equilibria for the three dimensional Cahn-Hilliard equation ﻿

(2011-12-31)
In this paper, we propose a new general method to compute rigorously global smooth branches of equilibria of higher-dimensional partial differential equations. The theoretical framework is based on a combination of the ...
• #### Rigorous numerics for NLS: Bound states, spectra, and controllability ﻿

(2015-12-31)
In this paper it is demonstrated how rigorous numerics may be applied to the one-dimensional nonlinear Schrödinger equation (NLS); specifically, to determining bound-state solutions and establishing certain spectral ...
• #### Rigorous numerics for symmetric connecting orbits: Even homoclinics of the Gray-Scott equation ﻿

(2011-12-31)
In this paper we propose a rigorous numerical technique for the computation of symmetric connecting orbits for ordinary differential equations. The idea is to solve a projected boundary value problem (BVP) in a function ...
• #### Rigorous numerics in floquet theory: Computing stable and unstable bundles of periodic orbits ﻿

(2013-12-31)
In this paper, a rigorous method to compute Floquet normal forms of fundamental matrix solutions of nonautonomous linear differential equations with periodic coefficients is introduced. The Floquet normal form of a fundamental ...
• #### A Secondary Field Based hp-Finite Element Method for the Simulation of Magnetotelluric Measurements ﻿

(2015-12-31)
In some geophysical problems, it is sometimes possible to divide the subsurface resistivity distribution as a one dimensional (1D) contribution plus some two dimensional (2D) inhomogeneities. Assuming this scenario, we ...
• #### Semi-analytical response of acoustic logging measurements in frequency domain ﻿

(2015-12-31)
This work proposes a semi-analytical method for simulation of the acoustic response of multipole eccentered sources in a fluid-filled borehole. Assuming a geometry that is invariant with respect to the azimuthal and vertical ...