Browsing Simulation of Wave Propagation by Title
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Offsets and front tire tracks to projective hedgehogs
(20220725)There are some known properties on curves of constant width and Zindler curves and their relationship with offsets and front tiretrack curves in convex geometry. In this work, a generalization of all these concepts and ... 
On Conforming Tetrahedralisations of Prismatic Partitions
(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. 
On continuous and discrete maximum principles for elliptic problems with the third boundary condition
(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
(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
(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 isoptics and isochordalviewed curves
(2021)In this paper, some results involving isoptic curves and constant $\phi$width curves are given for any closed curve. The nonconvex case, as well as nonsimple shapes with or without cusps are considered. Relating the ... 
On modifications of continuous and discrete maximum principles for reactiondiffusion problems
(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
(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
(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
(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 numerical solution of Fredholm and Hammerstein integral equations via Nystr\"{o}m method and Gaussian quadrature rules for splines
(202201)Nystr\"{o}m method is a standard numerical technique to solve Fredholm integral equations of the second kind where the integration of the kernel is approximated using a quadrature formula. Traditionally, the quadrature ... 
On quadrature rules for solving Partial Differential Equations using Neural Networks
(20220401)Neural Networks have been widely used to solve Partial Differential Equations. These methods require to approximate definite integrals using quadrature rules. Here, we illustrate via 1D numerical examples the quadrature ... 
On the application of isogeometric finite volume method in numerical analysis of wetsteam flow through turbine cascades
(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
(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
(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
(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
(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
(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 ... 
A Painless Automatic hpAdaptive Strategy for Elliptic Problems
(202001)In this work, we introduce a novel hpadaptive strategy. The main goal is to minimize the complexity and implementational efforts hence increasing the robustness of the algorithm while keeping close to optimal numerical ... 
Parallel refined Isogeometric Analysis in 3D
(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 ...