Browsing Computational Mathematics (CM) by Title
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The maximum angle condition is not necessary for convergence of the finite element method
(Numerische Mathematik, 20121231)We show that the famous maximum angle condition in the finite element analysis is not necessary to achieve the optimal convergence rate when simplicial finite elements are used to solve elliptic problems. This condition ... 
The Modellers' Halting Foray into Ecological Theory: Or, What is This Thing Called 'Growth Rate'?
(Acta Biotheoretica, 20151231)This discussion paper describes the attempt of an imagined group of nonecologists ("Modellers" ) to determine the population growth rate from field data. The Modellers wrestle with the multiple definitions of the growth ... 
Timeresolved Adaptive Direct FEM Simulation of Highlift Aircraft Configurations
(Numerical simulation of the aerodynamics of highlift configurations, 20170801)Our simulation methodology is referred to as Direct FEM Simulation (DFS), or General Galerkin (G2) and uses a finite element method (FEM) with piecewise linear approximation in space and time, and with numerical stabilization ... 
Timeresolved adaptive FEM simulation of the DLRF11 aircraft model at high Reynolds number
(52nd AIAA Aerospace Sciences Meeting  AIAA Science and Technology Forum and Exposition, SciTech 2014, 20141231)We present a timeresolved, adaptive finite element method for aerodynamics, together with the results from the HiLiftPW2 workshop, where this method is used to compute the ow past a DLRF11 aircraft model at realistic ... 
Towards a parameterfree method for high Reynolds number turbulent flow simulation based on adaptive finite element approximation
(Computer Methods in Applied Mechanics and Engineering, 20150501)This article is a review of our work towards a parameterfree method for simulation of turbulent flow at high Reynolds numbers. In a series of papers we have developed a model for turbulent flow in the form of weak solutions ... 
Towards efficient 5axis flank CNC machining of freeform surfaces via fitting envelopes of surfaces of revolution
(ComputerAided Design, 20160630)We introduce a new method that approximates freeform surfaces by envelopes of oneparameter motions of surfaces of revolution. In the context of 5axis computer numerically controlled (CNC) machining, we propose a flank ... 
Towards HPCEmbedded Case Study: Kalray and MessagePassing on NoC
(Scalable Computing, 2017)Today one of the most important challenges in HPC is the development of computers with a low power consumption. In this context, recently, new embedded manycore systems have emerged. One of them is Kalray. Unlike other ... 
Towards optimal advection using stretchmaximizing stream surfaces
(Computer Aided Geometric Design, 20170301)We investigate a class of stream surfaces that expand in time as much as possible. Given a vector field, we look for seed curves that locally propagate in time in a stretchmaximizing manner, i.e., curves that infinitesimally ... 
Towards the development of adaptive finite element methods for internal flow aeroacoustics
(19th AIAA/CEAS Aeroacoustics Conference, 20131231)We report the latest results obtained in the development of an adaptive finite element method for computational aeroacoustics (CAA). The new methodology is based on the General Galerkin (G2) method, which has been successfully ... 
Unified modeling language description of the objectoriented multiscale adaptive finite element method for stepandflash imprint lithography simulations
(IOP Conference Series: Materials Science and Engineering, 20141231)In the first part of the paper we present the multiscale simulation of the StepandFlash Imprint Lithography (SFIL), a modern patterning process. The simulation utilizes the hp adaptive Finite Element Method (hpFEM) ... 
Unstructured, curved elements for the twodimensional high order discontinuous controlvolume/finiteelement method
(International Journal for Numerical Methods in Engineering, 20141231)Quadrilateral and triangular elements with curved edges are developed in the framework of spectral, discontinuous, hybrid controlvolume/finiteelement method for elliptic problems. In order to accommodate hybrid meshes, ... 
The value of continuity: Refined isogeometric analysis and fast direct solvers
(Computer Methods in Applied Mechanics and Engineering, 20160923)We propose the use of highly continuous finite element spaces interconnected with low continuity hyperplanes to maximize the performance of direct solvers. Starting from a highly continuous Isogeometric Analysis (IGA) ... 
Variational multiscale stabilization for compressible flow
(Computer Methods in Applied Mechanics and Engineering, 2018)This paper presents a variational multiscale stabilization for the finite element numerical solution of the Euler and NavierStokes equations of compressible flow. All the components of the dual operator are considered in ...