Hans Petter Langtangen

How do scientists develop and use scientific software

New knowledge in science and engineering relies increasingly on results produced by scientific software. Therefore, knowing how scientists develop and use software in their research is critical to assessing the necessity for improving current development practices and to making decisions about the future allocation of resources. To that end, this paper presents the results of a survey conducted online in October-December 2008 which received almost 2000 responses. Our main conclusions are that (1) the knowledge required to develop and use scientific software is primarily acquired from peers and through self-study, rather than from formal education and training; (2) the number of scientists using supercomputers is small compared to the number using desktop or intermediate computers; (3) most scientists rely primarily on software with a large user base; (4) while many scientists believe that software testing is important, a smaller number believe they have sufficient understanding about testing concepts; and (5) that there is a tendency for scientists to rank standard software engineering concepts higher if they work in large software development projects and teams, but that there is no uniform trend of association between rank of importance of software engineering concepts and project/team size.

Modern software tools for scientific computing

The purpose of this text is to survey recent advances in the development of software tools for scientific computing. It emphasizes the design of large software codes, computational efficiency, object-oriented programming, reliability of numerical software and parallel computing.

A Comprehensive Set of Tools for Solving Partial Differential Equations; Diffpack

This chapter presents an overview of the functionality in Diffpack, which is a software environment for the numerical solution of partial differential equations. Examples on how object-oriented programming techniques are applied for software design and implementation are provided. In addition, we present a collection of sample Diffpack applications.

Numerical methods for incompressible viscous flow.

Abstract We present an overview of the most common numerical solution strategies for the incompressible Navier–Stokes equations, including fully implicit formulations, artificial compressibility methods, penalty formulations, and operator splitting methods (pressure/velocity correction, projection methods). A unified framework that explains popular operator splitting methods as special cases of a fully implicit approach is also presented and can be used for constructing new and improved solution strategies. The exposition is mostly neutral to the spatial discretization technique, but we cover the need for staggered grids or mixed finite elements and outline some alternative stabilization techniques that allow using standard grids. Emphasis is put on showing the close relationship between (seemingly) different and competing solution approaches for incompressible viscous flow.

Direct numerical simulation of transitional flow in a patient-specific intracranial aneurysm

In experiments turbulence has previously been shown to occur in intracranial aneurysms. The effects of turbulence induced oscillatory wall stresses could be of great importance in understanding aneurysm rupture. To investigate the effects of turbulence on blood flow in an intracranial aneurysm, we performed a high resolution computational fluid dynamics (CFD) simulation in a patient specific middle cerebral artery (MCA) aneurysm using a realistic, pulsatile inflow velocity. The flow showed transition to turbulence just after peak systole, before relaminarization occurred during diastole. The turbulent structures greatly affected both the frequency of change of wall shear stress (WSS) direction and WSS magnitude, which reached a maximum value of 41.5Pa. The recorded frequencies were predominantly in the range of 1-500Hz. The current study confirms, through properly resolved CFD simulations that turbulence can occur in intracranial aneurysms.

A unified finite element model for the injection molding process

Abstract The paper presents a simulation model for the injection molding process. A 2D Hele–Shaw approximation is adopted for the polymer flow between two flat plates, whereas the moving polymer–air front is handled by a level-set-like method. The 3D heat equation is solved using finite elements in the flow plane, a spectral method in the perpendicular direction, and finite differences in time. A domain imbedding technique enables simplified treatment of complex mold geometries. Local mesh refinement is applied to improve the numerical accuracy in the vicinity of the polymer–air front. The main advantage of the model is that a common 2D finite element mesh can be used for all the equations. Using object-oriented programming, the compound simulator is efficiently implemented as an assembly of separate simulators for each partial differential equation (PDE) in the model. A case study regarding a simplified model problem, which contains the principal physical effects in the injection molding process, is discussed. We also present simulation results for a more engineering-oriented example concerning the filling of a mold for a computer keyboard.

Object-oriented design of preconditioned iterative methods in diffpack

As modern programming methodologies migrate from computer science to scientific computing, developers of numerical software are faced with new possibilities and challenges. Based on experiences from an ongoing project that develops C11 software for the solution of partial differential equations, this article has its focus on object-oriented design of iterative solvers for linear systems of equations. Special attention is paid to possible conflicts that have to be resolved in order to achieve a very flexible, yet efficient, code.

Computational models for weakly dispersive nonlinear water waves

Abstract Numerical methods for the two- and three-dimensional Boussinesq equations governing weakly nonlinear and dispersive water waves are presented and investigated. Convenient handling of grids adapted to the geometry or bottom topography is enabled by finite element discretization in space. Staggered finite difference schemes are used for the temporal discretization, resulting in only two linear systems to be solved during each time step. Efficient iterative solution of linear systems is discussed. By introducing correction terms in the equations, a fourth-order, two-level temporal scheme can be obtained. Combined with (bi-) quadratic finite elements, the truncation errors of this scheme can be made of the same order as the neglected perturbation terms in the analytical model, provided that the element size is of the same order as the characteristic depth. We present analysis of the proposed schemes in terms of numerical dispersion relations. Verification of the schemes and their implementations is performed for standing waves in a closed basin with constant depth. More challenging applications cover plane incoming waves on a curved beach and earthquake induced waves over a shallow seamount. In the latter example we demonstrate a significantly increased computational efficiency when using higher-order schemes and bathymetry-adapted finite element grids.

Unified framework for finite element assembly

At the heart of any finite element simulation is the assembly of matrices and vectors from discrete variational forms. We propose a general interface between problem-specific and general-purpose components of finite element programs. This interface is called Unified Form-assembly Code (UFC). A wide range of finite element problems is covered, including mixed finite elements and discontinuous Galerkin methods. We discuss how the UFC interface enables implementations of variational form evaluation to be independent of mesh and linear algebra components. UFC does not depend on any external libraries, and is released into the public domain.

An efficient probabilistic finite element method for stochastic groundwater flow

We present an efficient numerical method for solving stochastic porous media flow problems. Single-phase flow with a random conductivity field is considered in a standard first-order perturbation expansion framework. The numerical scheme, based on finite element techniques, is computationally more efficient than traditional approaches because one can work with a much coarser finite element mesh. This is achieved by avoiding the common finite element representation of the conductivity field. Computations with the random conductivity field only arise in integrals of the log conductivity covariance function. The method is demonstrated in several two- and three-dimensional flow situations and compared to analytical solutions and Monte Carlo simulations. Provided that the integrals involving the covariance of the log conductivity are computed by higher-order Gaussian quadrature rules, excellent results can be obtained with characteristic element sizes equal to about five correlation lengths of the log conductivity field. Investigations of the validity of the proposed first-order method are performed by comparing nonlinear Monte Carlo results with linear solutions. In box-shaped domains the log conductivity standard deviation σY may be as large as 1.5, while the head variance is considerably influenced by nonlinear effects as σY approaches unity in more general domains.