Browsing Computational Mathematics (CM) by Title
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A C 0 interior penalty discontinuous Galerkin Method for fourthorder total variation flow. II: Existence and uniqueness
(NMPDE:Numerical Methods For Partial Differential Equations, 20190225)We prove the existence and uniqueness of a solution of a C0 Interior Penalty Discontinuous Galerkin (C0 IPDG) method for the numerical solution of a fourth‐order total variation flow problem that has been developed in part ... 
A C0 interior penalty discontinuous Galerkin method for fourth‐order total variation flow I: Derivation of the method and numerical results
(NMPDE:Numerical Methods For Partial Differential Equations, 20190223)We consider the numerical solution of a fourth‐order total variation flow problem representing surface relaxation below the roughening temperature. Based on a regularization and scaling of the nonlinear fourth‐order parabolic ... 
Computation of slat noise sources using adaptive FEM and lighthill's analogy
(19th AIAA/CEAS Aeroacoustics Conference, 20131231)This is a summary of preliminary results from simulations with the 30P30N highlift device. We used the General Galerkin finite element method (G2), where no explicit subgrid model is used, and where the computational mesh ... 
Computational cost estimates for parallel shared memory isogeometric multifrontal solvers
(Computers and Mathematics with Applications, 20141231)In this paper we present computational cost estimates for parallel shared memory isogeometric multifrontal solvers. The estimates show that the ideal isogeometric shared memory parallel direct solver scales as $\mathcal{O}( ... 
Computational cost of isogeometric multifrontal solvers on parallel distributed memory machines
(Computer Methods in Applied Mechanics and Engineering, 20151231)This paper derives theoretical estimates of the computational cost for isogeometric multifrontal direct solver executed on parallel distributed memory machines. We show theoretically that for the $C^{p1}$ global continuity ... 
Computational fixedpoint theory for differential delay equations with multiple time lags
(Journal of Differential Equations, 20121231)We introduce a general computational fixedpoint method to prove existence of periodic solutions of differential delay equations with multiple time lags. The idea of such a method is to compute numerical approximations of ... 
Control of distributed parameter systems modelled by parabolic variational inequalities of the obstacle type
(2019)We will investigate the numerical solution of the control problem modelled by parabolic variational inequalities. The general point of view adopted in this work has its roots in the work by R. Glowinski. The optimal control ... 
Dimensionally adaptive hpfinite element simulation and inversion of 2D magnetotelluric measurements
(Journal of Computational Science, 20160901)Magnetotelluric (MT) problems often contain different subdomains where the conductivity of the media depends upon one, two, or three spatial variables. Traditionally, when a MT problem incorporates a threedimensional (3D) ... 
Direct FEM large scale computation of turbulent multiphase flow in urban water systems and marine energy
(Proceesings of ECCOMAS Congress 2016 VII European Congress on Computational Methods in Applied Sciences and Engineering, 20161130)HighReynolds number turbulent incompressible multiphase flow represents a large class of engineering problems of key relevance to society. Here we describe our work on modeling two such problems: 1. The Consorcio de Aguas ... 
Direct finite element simulation of turbulent flow for marine based renewable energy
(Companion paper to F. Wendt, et. al. International energy agency ocean energy systems task 10 wave energy converter modeling verification and validation. In 12th European Wave and Tidal Energy Conference, 2017., 2017)In this article we present a computational framework for simulation of turbulent flow in marine based renewable energy applications. In particular, we focus on floating structures and rotating turbines. This work is an ... 
Direct solvers performance on hadapted grids
(Computers and Mathematics with Applications, 20151231)We analyse the performance of direct solvers when applied to a system of linear equations arising from an $h$adapted, $C^0$ finite element space. Theoretical estimates are derived for typical $h$refinement patterns arising ... 
Discontinuous highorder finitevolume/finiteelement method for inviscid compressible flows
(53rd AIAA Aerospace Sciences Meeting (2015), 20151231)The discontinuous, hybrid controlvolume/finiteelement method merges the desirable conservative properties and intuitive physical formulation of the finitevolume technique, with the capability of local arbitrary highorder ... 
Discrete maximum principles for nonlinear parabolic PDE systems
(IMA Journal of Numerical Analysis, 20121231)Discrete maximum principles (DMPs) are established for finite element approximations of systems of nonlinear parabolic partial differential equations with mixed boundary and interface conditions. The results are based on ... 
Discrete nonnegativity for nonlinear cooperative parabolic PDE systems with nonmonotone coupling
(Mathematics and Computers in Simulation, 20131231)Discrete nonnegativity principles are established for finite element approximations of nonlinear parabolic PDE systems with mixed boundary conditions. Previous results of the authors are extended such that diagonal dominance ... 
Dispersionminimizing quadrature rules for $C^1$ quadratic isogeometric analysis
(Computer Methods in Applied Mechanics and Engineering, 20170920)We develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrations that minimize the discrete dispersion error of the approximation. The rules are optimal in the sense that they only ... 
Editors' preface for the topical issue "Advances in Numerical Analysis and Numerical Linear Algebra"
(Central European Journal of Mathematics, 20121231)[No abstract available] 
Editors' preface for the topical issue "Numerical Methods for LargeScale Scientific Computing, I"
(Central European Journal of Mathematics, 20131231)[No abstract available] 
Editors' preface for the topical issue "Numerical Methods for LargeScale Scientific Computing, II"
(Central European Journal of Mathematics, 20131231)[No abstract available] 
Efficient mass and stiffness matrix assembly via weighted Gaussian quadrature rules for Bsplines
(Journal of Computational and Applied Mathematics, 20191214)Calabr{\`o} et al. [10] changed the paradigm of the mass and stiffness computation from the traditional elementwise assembly to a rowwise concept, showing that the latter one offers integration that may be orders of ... 
Efficient quadrature rules for subdivision surfaces in isogeometric analysis
(Computer Methods in Applied Mechanics and Engineering, 201810)We introduce a new approach to numerical quadrature on geometries defined by subdivision surfaces based on quad meshes in the context of isogeometric analysis. Starting with a sparse control mesh, the subdivision process ...