Langtangen, H.P. Computational Partial Differential Equations - Numerical Methods and Diffpack Programming. Lecture Notes in Computational Science and Engineering 2, Springer-Verlag, 1999.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....elliptic partial differential equations based on a block partitioning of the problem domain. The package is written in Algol 68, and makes full use of the language s support for operator overloading. One of the key features of this system is its features for problem specification. DIFFPACK [16] written in C , DIFFPACK is a comprehensive package for the numerical solution of partial differential equations using the Finite Element method. DIFFPACK supports parallelism in the sense that there are parallel implementations of the underlying linear algebra routines written using MPI. ....

Langtangen, H.P. Computational Partial Differential Equations - Numerical Methods and Diffpack Programming. Lecture Notes in Computational Science and Engineering 2, Springer-Verlag, 1999.

.... Various applications of OOP to engineering problems can be found in [4] 9] Diffpack is an example of a C based object oriented environment developed to address the modeling of continuum systems governed by partial differential equations (PDEs) using both finite differences and finite elements [10]. Basic finite element operations (e.g. finite element definition, integration rules, assembly of the stiffness matrix and load vectors, application of essential and natural boundary conditions, definition of continuum fields over finite elementgrids,etc. have been introduced in Diffpack using ....

....and reusability. In the presentwork, wehave used the widely used Diffpack library of classes for analysis of systems governed by partial differential equations, so as to concentrate only on the implementation of the particular physical mechanisms in the form of classes [10]. Depending on the type of process examined, a common approach to OOP implementation is by partitioning the original problem in various subproblems based on physical and or mathematical arguments. Examples of both of these cases will be shown later in this paper. For each subproblem defined, ....

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H. P. Langtangen. Computational Partial Differential Equations - Numerical Methods and Diffpack Programming. Springer-Verlag, New York, 1999.

....This is not the first object oriented design 14 N. S. Nedialkov, K. R. Jackson of an ODE solver. The Godess [Ols97] and TIDE [Hoh93b] a successor of CODE [Hoh93a] packages offer generic ODE solvers that implements traditional methods for IVPs for ODEs. Another successful package is Diffpack [Lan99] which is devised for solving partial differential equations. In [Lan99] there is also an example of how to construct an object oriented ODE solver. In this section, we briefly review some object oriented concepts supported in C . We use them in the discussion of the choice of programming ....

....of an ODE solver. The Godess [Ols97] and TIDE [Hoh93b] a successor of CODE [Hoh93a] packages offer generic ODE solvers that implements traditional methods for IVPs for ODEs. Another successful package is Diffpack [Lan99] which is devised for solving partial differential equations. In [Lan99] there is also an example of how to construct an object oriented ODE solver. In this section, we briefly review some object oriented concepts supported in C . We use them in the discussion of the choice of programming language (x1.8) and in the description of VNODE (x1.9) A reader familiar ....

H. P. Langtangen. Computational Partial Differential Equations -- Numerical Methods and Diffpack Programming. Springer-Verlag, 1999.

....of object oriented (O O) programming techniques in developing PDE software has shown its many advantages. The C programming language, which is a foremost representative in this respect, has inherent features that are well suited for the complicated process of numerical PDE solution. We refer to [BN94, Lan99] for an introduction to this topic. The most attractive features of C are modularity, polymorphism and inheritance. So extensive code reuse is a direct advantage of O O programming. The possibility of a modular implementation of mathematical abstractions gives rise to an application independent ....

....interface of PDE simulators. The application programmer needs only to concentrate on critical numerics, at a high abstraction level if desired. Therefore reliable, flexible and extensible simulators can be developed in an efficient way. Diffpack is an O O scientific computing environment (see [Lan99, Dif]) The design of Diffpack has taken numerical efficiency into consideration by confining OO techniques to high level administrative tasks, while using low level C codes and carefully constructed for loops in CPU intensive numerics. The C Diffpack libraries contain, among other things, ....

Langtangen H. P. (1999) Computational Partial Differential Equations -- Numerical Methods and Diffpack Programming. Springer-Verlag.

....are being developed continually. Our goals are to create a laboratory for quickly prototyping new algorithmic innovations, and to provide efficient software on serial and parallel platforms. Object oriented techniques have been applied to iterative solvers such as those found in Diffpack [LAN99, DIF] and PETSc [BGM 97, PET] How1 Department of Computer Science, Old Dominion University, Norfolk VA 23529 0162 USA. fdobrian,kumfert,potheng cs.odu.edu. 2 ICASE, NASA Langley Research Center, Hampton VA 23681 2199 USA. pothen icase.edu 2 F. Dobrian, G. Kumfert and A. Pothen ever, the ....

H. P. Langtangen. Computational Partial Differential Equations: Numerical Methods and Diffpack Programming. Springer-Verlag, 1999.

....is easy to explain. Linear systems solvers (often just called linear solvers) require work of the order of n ff , where n is the number of unknowns in the system and ff 1. If ff 1, which is the common case for Gaussian elimination, classical iterations, and conjugate gradient like methods [2], the solution of linear systems will dominate over the work required to set up the system (which is proportional to n) In 70s and 80s, researchers constructed so called multi level methods having the nice property that ff = 1. These methods are characterized by employing a hierarchy of grids, ....

....the (complicated) multigrid algorithm in an existing Diffpack finite element solver and how flexible this implementation is. The required background for reading the report is knowledge of typical finite element solvers in Diffpack, like the Poisson1, Poisson2, and Elasticity1 solvers from [2]. Furthermore, the reader must know the basics of multigrid algorithms, e.g. from [2, app. C.4.2] In particular, we will use mathematical symbols from [2, app. C.4.2] In any implementation of the multigrid method one needs the following operations and data structures: ffl a hierarchy of grids ....

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H. P. Langtangen. Computational Partial Differential Equations -- Numerical Methods and Diffpack Programming. Lecture Notes in Computational Science and Engineering. Springer-Verlag, 1999.

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