Browsing Computational Mathematics (CM) by Title
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Red refinements of simplices into congruent subsimplices
(Computers and Mathematics with Applications, 20141231)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 ... 
Reducing variability in the cost of energy of ocean energy arrays
(Renewable and Sustainable Energy Reviews, 201909)Variability in the predicted cost of energy of an ocean energy converter array is more substantial than for other forms of energy generation, due to the combined stochastic action of weather conditions and failures. If the ... 
Refined Isogeometric Analysis for a Preconditioned Conjugate Gradient Solver
(Computer Methods in Applied Mechanics and Engineering, 20180615)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: A SOLVERBASED DISCRETIZATION METHOD
(20180622)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 computeraided ... 
Regions of prevalence in the coupled restricted threebody problems approximation
(Communications in Nonlinear Science and Numerical Simulation, 20121231)This work concerns the role played by a couple of the planar circular restricted threebody problem in the approximation of the bicircular model. The comparison between the differential equations governing the dynamics ... 
Reproductive value, sensitivity, and nonlinearity: Populationmanagement heuristics derived from classical demography
(Theoretical Population Biology, 20131231)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 CahnHilliard equation
(Numerische Mathematik, 20111231)In this paper, we propose a new general method to compute rigorously global smooth branches of equilibria of higherdimensional partial differential equations. The theoretical framework is based on a combination of the ... 
Rigorous numerics for NLS: Bound states, spectra, and controllability
(Physica D: Nonlinear Phenomena, 20151231)In this paper it is demonstrated how rigorous numerics may be applied to the onedimensional nonlinear Schrödinger equation (NLS); specifically, to determining boundstate solutions and establishing certain spectral ... 
Rigorous numerics for symmetric connecting orbits: Even homoclinics of the GrayScott equation
(SIAM Journal on Mathematical Analysis, 20111231)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
(SIAM Journal on Applied Dynamical Systems, 20131231)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 ... 
Semianalytical response of acoustic logging measurements in frequency domain
(Computers and Mathematics with Applications, 20151231)This work proposes a semianalytical method for simulation of the acoustic response of multipole eccentered sources in a fluidfilled borehole. Assuming a geometry that is invariant with respect to the azimuthal and vertical ... 
Sensitivity study of boreholetosurface and crosswell electromagnetic measurements acquired with energized steel casing to water displacement in hydrocarbonbearing layers
(Geophysics, 20081231)We study the theoretical response of electromagnetically energized steel casing in the presence of subsurface variations of electrical resistivity. Casing is energized with a finitesize solenoid antenna located along the ... 
SimTek  an edXbased platform for Mathematical Multiphysics Simulation
(International Conference on MOOCs in Scandinavia, 20151231)[No abstract available] 
Simulation of DC duallaterolog measurements in complex formations: A Fourierseries approach with nonorthogonal coordinates and selfadapting finite elements
(Geophysics, 20091231)Dual laterolog (DLL) makes use of a galvanic conduction principle to focus electrical currents into rock formations, thereby minimizing shoulder and borehole effects in the measurement of formation resistivity. The tool ... 
Simulation of marine controlled source electromagnetic measurements using a parallel fourier hpfinite element method
(Computational Geosciences, 20111231)We introduce a new numerical method to simulate geophysical marine controlled source electromagnetic (CSEM) measurements for the case of 2D structures and finite 3D sources of electromagnetic (EM) excitation. The method ... 
Simulation of the HarshLab floating platform for offshore experimentation using FEniCSHPC
(Poster EUSKAMPUS IV Marine Energy Conference, 2017) 
Singular dynamics under a weak potential on a sphere
(Nonlinear Differential Equations and Applications, 20131231)We give a detailed analytical description of the global dynamics of a point mass moving on a sphere under the action of a logarithmic potential. We perform a McGeheetype blowup in order to cope with the singularity of ... 
Some discrete maximum principles arising for nonlinear elliptic finite element problems
(Computers and Mathematics with Applications, 20151231)The discrete maximum principle (DMP) is an important measure of the qualitative reliability of the applied numerical scheme for elliptic problems. This paper starts with formulating simple sufficient conditions for the ... 
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 ... 
A source time reversal method for seismicity induced by mining
(Inverse Problems and Imaging, 20170101)In this work, we present a modified TimeReversal Mirror (TRM) Method, called Source Time Reversal (STR), to find the spatial distribution of a seismic source induced by mining activity. This methodology is based on a known ...