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Object oriented design philosophy for scientific computing

Philippe R. B. Devloo, Gustavo C. Longhin (2002)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This contribution gives an overview of current research in applying object oriented programming to scientific computing at the computational mechanics laboratory (LABMEC) at the school of civil engineering – UNICAMP. The main goal of applying object oriented programming to scientific computing is to implement increasingly complex algorithms in a structured manner and to hide the complexity behind a simple user interface. The following areas are current topics of research and documented within the...

Object oriented design philosophy for scientific computing

Philippe R.B. Devloo, Gustavo C. Longhin (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This contribution gives an overview of current research in applying object oriented programming to scientific computing at the computational mechanics laboratory (LABMEC) at the school of civil engineering – UNICAMP. The main goal of applying object oriented programming to scientific computing is to implement increasingly complex algorithms in a structured manner and to hide the complexity behind a simple user interface. The following areas are current topics of research and documented within the...

Observations Regarding Algorithms Required for Robust CFD Codes

F. T. Johnson, D. S. Kamenetskiy, R. G. Melvin, V. Venkatakrishnan, L. B. Wigton, D. P. Young, S. R. Allmaras, J. E. Bussoletti, C. L. Hilmes (2011)

Mathematical Modelling of Natural Phenomena

Over the last three decades Computational Fluid Dynamics (CFD) has gradually joined the wind tunnel and flight test as a primary flow analysis tool for aerodynamic designers. CFD has had its most favorable impact on the aerodynamic design of the high-speed cruise configuration of a transport. This success has raised expectations among aerodynamicists that the applicability of CFD can be extended to the full flight envelope. However, the complex nature...

On FE-grid relocation in solving unilateral boundary value problems by FEM

Jaroslav Haslinger, Pekka Neittaanmäki, Kimmo Salmenjoki (1992)

Applications of Mathematics

We consider FE-grid optimization in elliptic unilateral boundary value problems. The criterion used in grid optimization is the total potential energy of the system. It is shown that minimization of this cost functional means a decrease of the discretization error or a better approximation of the unilateral boundary conditions. Design sensitivity analysis is given with respect to the movement of nodal points. Numerical results for the Dirichlet-Signorini problem for the Laplace equation and the...

On interpolation error on degenerating prismatic elements

Ali Khademi, Sergey Korotov, Jon Eivind Vatne (2018)

Applications of Mathematics

We propose an analogue of the maximum angle condition (commonly used in finite element analysis for triangular and tetrahedral meshes) for the case of prismatic elements. Under this condition, prisms in the meshes may degenerate in certain ways, violating the so-called inscribed ball condition presented by P. G. Ciarlet (1978), but the interpolation error remains of the order O ( h ) in the H 1 -norm for sufficiently smooth functions.

On Synge-type angle condition for d -simplices

Antti Hannukainen, Sergey Korotov, Michal Křížek (2017)

Applications of Mathematics

The maximum angle condition of J. L. Synge was originally introduced in interpolation theory and further used in finite element analysis and applications for triangular and later also for tetrahedral finite element meshes. In this paper we present some of its generalizations to higher-dimensional simplicial elements. In particular, we prove optimal interpolation properties of linear simplicial elements in ℝ d that degenerate in some way.

On the inf-sup condition for higher order mixed FEM on meshes with hanging nodes

Vincent Heuveline, Friedhelm Schieweck (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider higher order mixed finite element methods for the incompressible Stokes or Navier-Stokes equations with Qr-elements for the velocity and discontinuous P r - 1 -elements for the pressure where the order r can vary from element to element between 2 and a fixed bound r * . We prove the inf-sup condition uniformly with respect to the meshwidth h on general quadrilateral and hexahedral meshes with hanging nodes.

On the numerical performance of a sharp a posteriori error estimator for some nonlinear elliptic problems

Balázs Kovács (2014)

Applications of Mathematics

Karátson and Korotov developed a sharp upper global a posteriori error estimator for a large class of nonlinear problems of elliptic type, see J. Karátson, S. Korotov (2009). The goal of this paper is to check its numerical performance, and to demonstrate the efficiency and accuracy of this estimator on the base of quasilinear elliptic equations of the second order. The focus will be on the technical and numerical aspects and on the components of the error estimation, especially on the adequate...

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