Browsing Computational Mathematics (CM) by Title
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On Adomian Based Numerical Schemes for Euler and NavierStokes Equations, and Application to Aeroacoustic Propagation
(20180312)In this thesis, an Adomian Based Scheme (ABS) for the compressible NavierStokes equations is constructed, resulting in a new multiderivative type scheme not found in the context of fluid dynamics. Moreover, this scheme ... 
On Conforming Tetrahedralisations of Prismatic Partitions
(Springer Proceedings in Mathematics and Statistics, 20131231)We present an algorithm for conform (facetoface) subdividing prismatic partitions into tetrahedra. This algorithm can be used in the finite element calculations and analysis. © Springer Science+Business Media New York 2013. 
On continuous and discrete maximum principles for elliptic problems with the third boundary condition
(Applied Mathematics and Computation, 20131231)In this work, we present and discuss some continuous and discrete maximum principles for linear elliptic problems of the second order with the third boundary condition (almost never addressed to in the available literature ... 
On global and local mesh refinements by a generalized conforming bisection algorithm
(Journal of Computational and Applied Mathematics, 20101231)We examine a generalized conforming bisection (GCB)algorithm which allows both global and local nested refinements of the triangulations without generating hanging nodes. It is based on the notion of a mesh density function ... 
On initialization of milling paths for 5axis flank CNC machining of freeform surfaces with general milling tools
(Computer Aided Geometric Design (CAGD, Elsevier), 20190327)We propose a pathplanning algorithm for 5axis flank CNC machining with general tools of varying curvature. Our approach generalizes the initialization strategy introduced for conical tools [Bo et al., 2017] to arbitrary ... 
On intermediatescale opensea experiments on floating offshore structures: Feasibility and application on a spar support for offshore wind turbines
(Marine Structures, 20180628)Experimental investigation of floating structures represents the most direct way for achieving their dynamic identification and it is particularly valuable for relatively new concepts, such as floating supports for offshore ... 
On modifications of continuous and discrete maximum principles for reactiondiffusion problems
(Advances in Applied Mathematics and Mechanics, 20111231)In this work, we present and discuss some modifications, in the form of twosided estimation (and also for arbitrary source functions instead of usual signconditions), of continuous and discrete maximum principles for the ... 
On nonobtuse refinements of tetrahedral finite element meshes
(Proceedings of International Conference MASCOT2012 / ISGG2012, Las Palmas, Spain, 2014, 20141231)It is known that piecewise linear continuous finite element (FE) approximations on nonobtuse tetrahedral FE meshes guarantee the validity of discrete analogues of various maximum principles for a wide class of elliptic ... 
On numerical quadrature for $C^1$ quadratic PowellSabin 6split macrotriangles
(Journal of Computational and Applied Mathematics, 20180801)The quadrature rule of Hammer and Stroud [16] for cubic polynomials has been shown to be exact for a larger space of functions, namely the $C^1$ cubic CloughTocher spline space over a macrotriangle if and only if the ... 
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 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, ...