Browsing Computational Mathematics (CM) by Title
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On numerical regularity of the facetoface longestedge bisection algorithm for tetrahedral partitions
(Science of Computer Programming, 20141231)The finite element method usually requires regular or strongly regular families of partitions in order to get guaranteed a priori or a posteriori error estimates. In this paper we examine the recently invented longestedge ... 
On the application of isogeometric finite volume method in numerical analysis of wetsteam flow through turbine cascades
(Computers and Mathematics with Applications, 201910)The isogeometric finite volume analysis is utilized in this research to numerically simulate the twodimensional viscous wetsteam flow between stationary cascades of a steam turbine for the first time. In this approach, ... 
On the maximum angle condition for the conforming longestedge nsection algorithm for large values of n
(Computer Aided Geometric Design, 20151231)In this note we introduce the conforming longestedge $n$section algorithm and show that for $n \ge 4$ it produces a family of triangulations which does not satisfy the maximum angle condition. 
On the regularization of the collision solutions of the onecenter problem with weak forces
(Discrete and Continuous Dynamical Systems, 20111231)We study the possible regularization of collision solutions for one centre problems with a weak singularity. In the case of logarithmic singularities, we consider the method of regularization via smoothing of the potential. ... 
Onedimensional chaos in a system with dry friction: analytical approach
(Meccanica, 20151231)We introduce a new analytical method, which allows to find chaotic regimes in nonsmooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered. The corresponding ... 
Optimal quadrature rules for odddegree spline spaces and their application to tensorproductbased isogeometric analysis
(Computer Methods in Applied Mechanics and Engineering, 20160101)We introduce optimal quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. Using the homotopy continuation concept (Barton and Calo, 2016) that ... 
Optimally refined isogeometric analysis
(Procedia Computer Science, 201706)Performance of direct solvers strongly depends upon the employed discretization method. In particular, it is possible to improve the performance of solving Isogeometric Analysis (IGA) discretizations by introducing multiple ... 
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 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 ...