Browsing Computational Mathematics (CM) by Title
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Parallel refined Isogeometric Analysis in 3D
(IEEE Transactions on Parallel and Distributed Systems, 201811)We study threedimensional isogeometric analysis (IGA) and the solution of the resulting system of linear equations via a direct solver. IGA uses highly continuous $C^{p1}$ basis functions, which provide multiple benefits ... 
Parameterization of Invariant Manifolds for Periodic Orbits I: Efficient Numerics via the Floquet Normal Form
(SIAM Journal on Applied Dynamical Systems, 20151231)We present an efficient numerical method for computing FourierTaylor expansions of (un)stable manifolds associated with hyperbolic periodic orbits. Three features of the method are that (1) we obtain accurate representation ... 
A partition of unity finite element method for computational diffusion MRI
(Journal of Computational Physics, 2018)The Bloch–Torrey equation describes the evolution of the spin (usually water proton) magnetization under the influence of applied magnetic field gradients and is commonly used in numerical simulations for diffusion MRI ... 
Performance of a multifrontal parallel direct solver for hpfinite element method
(Proceedings of the IASTED International Conference on Advances in Computer Science and Engineering, ACSE 2009, 20091231)In this paper we present the performance of our parallel multifrontal direct solver when applied to solve linear systems of equations resulting from discretizations of a hp Finite Element Method (hpFEM). The hpFEM ... 
PetIGAMF: A multifield highperformance toolbox for structurepreserving Bsplines spaces
(Journal of Computational Science, 201701)We describe a highperformance solution framework for isogeometric discrete differential forms based on Bsplines: PetIGAMF. Built on top of PetIGA, an opensource library we have built and developed over the last decade, ... 
Portable simulation framework for diffusion MRI
(Journal of Magnetic Resonance, 20190923)The numerical simulation of the diffusion MRI signal arising from complex tissue microstructures is helpful for understanding and interpreting imaging data as well as for designing and optimizing MRI sequences. The ... 
Quantities of interest for surface based resistivity geophysical measurements
(Procedia Computer Science, 20151231)The objective of traditional goaloriented 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 ... 
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 ... 
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 ...