Browsing Computational Mathematics (CM) by Title
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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 for fluid mechanics and electromagnetism
(Computer Methods in Applied Mechanics and Engineering, 201903)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: 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 ... 
Reparameterization of ruled surfaces: toward generating smooth jerkminimized toolpaths for multiaxis flank CNC milling
(ComputerAided Design, 202005)This paper presents a novel jerk minimization algorithm in the context of multiaxis flank CNC machining. The toolpath of the milling axis in a flank milling process, a ruled surface, is reparameterized by a Bspline ... 
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 ... 
Shearthickening of a noncolloidal suspension with a viscoelastic matrix
(Journal of Fluid Mechanics, 2019)In this work we study the rheology of a noncolloidal suspension of rigid spherical particles interacting with a viscoelastic matrix. Threedimensional numerical simulations under shear flow are performed using 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 ... 
Snapshots location for Reduced Order Models: An approach based on Proper Orthogonal Decomposition and Mesh Adaptivity Techniques
(20190628)Solving Partial Differential Equations (PDE), is a key issue in science and engineering since they are widely used in many real problem modelling including fluid mechanics, acoustics, heat and mass transfer ...etc. Exact ... 
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 ...