A. M. Bruaset and H. P. Langtangen, Object-oriented design of preconditioned iterative methods in Di#pack, ACM Trans. Math. Software (1997), pp. 50--80.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....23681 2199. Email: pothen cs.odu.edu, pothen icase.edu.URL: www.cs.odu.edu pothen. 1 In this paper we present the design of our sequential solver. Work on a parallel version using the message passing model is in progress. Object oriented packages for iterative methods are described in [1, 2]. 2. Overview of the problem. Graph theory provides useful tools for computing the solution of sparse systems. Corresponding to a symmetric matrix A is its undirected adjacency graph G(A) Each vertex in the graph corresponds to a column (or row) in the matrix and each edge to a symmetric pair of ....

A. M. Bruaset and H. P. Langtangen, Object-oriented design of preconditioned iterative methods in Di#pack, ACM Trans. Math. Software (1997), pp. 50--80.

....to read, maintain, and adapt to other applications or move to other computer platforms. Cogito [44] is a system of software tools, written in Fortran 90 with an object oriented design, for PDE solvers on composite grids. A number of projects with similar goals exist, see for example Diffpack [6], PETSc [3] and Overture [5] These are C C implementations. Even though Fortran 90 is not a fully object oriented language it gives support for object oriented programming through the type, module and interface concepts [23, 28] The partitioning module for composite grids will be a part of ....

....classes communicate through fixed interfaces with simple data structures, indicated with arrows in the figure. These data structures are encapsulated in communication objects, cgdata, griddata, laplmatrix, weights, and part array. A similar approach using communication objects is also taken in [6]. A PDE is solved by applying mathematical numerical operations on the grid functions, i.e. Dplus, Add, Scale, etc. If a distribution is attached, the operations are parallelized and the details with message passing are hidden within the class. Consequently the high level solver becomes ....

A.M. Bruaset, H.P. Langtangen, Object-Oriented Design of Preconditioned Iterative methods in Diffpack, ACM Transactions on Mathematical Software, vol 23, no 1:50-80, March 1997.

....refined computational grids. The standardization of numerical operations on sparse matrices has received a lot of interest [8, 3] Moreover, var ious tools are now available [2, 12] and a number of papers have recently outlined the convenience of object oriented methods for PDE solvers [14, 5]. However, to the best of our knowledge, the software environment proposed in this paper is the first that brings together a support for adaptive meshing, an object oriented interface implemented in Fortran 90, and a communication layer based on MPI. The paper is organized as follows. In Section ....

A. M. Bruaset, H. P. Langtangen. Object-oriented design of preconditioned iterative methods in diffpack. ACM. Trans. Math. Softw., 23: 50-80, Mar. 1997.

....of Chow and Heroux [5] who focus on preconditioning of iterative solvers for linear systems and describe a C package for that allows implementation of block preconditioners in a way that is independent of the storage scheme for the submatrix blocks. The Di#pack code of Bruaset and Langtangen [4] is a C object oriented implementation of iterative solvers for sparse linear systems. 1.3. Outline of This Paper Section 2 of this paper describes the primal dual interior point algorithms that are the basis of OOQP. The layered structure of the code and its major classes are outlined in ....

....These algorithms have proved to be the most e#ective methods for linear programming problems and in our experience are just as e#ective for QP. Mehrotra s algorithm is outlined below. Algorithm MPC (Mehrotra Predictor Corrector) Given starting point (x, y, z, s) with (z, s) 0, parameter # # [2, 4]; repeat Set = z T s mC ; Solve for (#x a# , #y a# , #z a# , #s a# ) # # # # Q A T C T 0 A 0 0 0 C 0 0 I 0 0 S Z # # # # # # # # #x a# #y a# #z a# #s a# # # # # = # # # # r Q r A r C ZSe # # # # , 5) where S = diag(s 1 , s 2 , ....

A. M. Bruaset and H. P. Langtangen. Object-oriented design of preconditioned iterative methods in Di#pack. ACM Transactions on Mathematical Software, 23(1):50--80, 1997.

....for declaring attributes and methods is a relaxed Java like syntax. Library References LAPACK [37, 38, 32, 60] SparseLib and IML [30, 78, 31, 85, 53] Paladin [48, 49] JLAPACK [14, 15, 26] OwlPack [20, 19, 18, 24] MTL and ITL [80, 81, 83, 79, 82, 59, 58] PMLP [11, 12, 51] Di pack [17, 75] ISIS [2, 27] Sparspak or Sparspak90 [45] Oblio and Spindle [29, 28, 57] JAMA [68] Jampack [88, 25] BPKIT [21, 22, 23] Table 2: Object oriented linear algebra libraries. 3.1 Initial Analysis A matrix isatwo dimensional container of numbers. The dimensions of a matrix are the number of ....

A. M. Bruaset and H. P. Langatangen. Object-oriented design of preconditioned iterative methods in Dipack. ACM Transactions on Mathematical Software, 23(1):50-80, 1997. 249

....computing community. Most of the time advanced translates to object orientedness, but other paradigms, such as generic programming, are also used. Currently, iterative solvers are the main targets for the new software techniques, PETSc (written in C) 10] and Diffpack (written in C ) [4]) being well known examples. Less has been done to improve the design of direct solvers. Oblio s sister, Spindle ( 5] handles ordering algorithms (Oblio has only factorization and solve algorithms) We are aware of only one other sparse direct solver package that uses object oriented design: ....

A. M. Bruaset and H. P. Langtangen. Object-oriented design of preconditioned iterative methods in Diffpack. ACM Transactions on Mathematical Software, pages 50--80, 1997.

....algorithm must not be aware of its internal representation. In practice, sparse matrix algorithms must take advantage of the storage format as an essential optimization. This is often done in object oriented libraries like Diffpack and PETSc by data structure neutral programming (see [BL97] and [BGM 97] respectively) This is accomplished by providing an abstract base class for a matrix or vector, and deriving concrete implementations for each data layout: compressed sparse row, compressed column major, AIJ (row index, column index, value) triples, blocked compressed sparse, etc. ....

A. M. Bruaset and H. P. Langtangen. Object-oriented design of preconditioned iterative methods in DIFFPACK. ACM Transactions on Mathematical Software, 23:50--80, 1997.

....just interfaces in a base class and we want to let derived classes implement a proper behavior. In this paper we present the design of our sequential solver. Work on a parallel version using the message passing model is in progress. Object oriented packages for iterative methods are described in [1, 2]. 2 Overview of the problem Graph theory provides useful tools for computing the solution of sparse systems. Corresponding to a symmetric matrix A is an undirected graph G(A) Each vertex in the graph corresponds to a column (or row) in the matrix and each edge to a symmetric pair of off diagonal ....

A. M. Bruaset and H. P. Langtangen. Object-oriented design of preconditioned iterative methods in Diffpack. ACM Trans. Math. Software, pages 50--80, 1997.

....compilers. BPKIT also has an interface for Fortran 77 users. 4 Delta E. Chow and M. A. Heroux BPKIT is available at http: www.cs.umn.edu chow bpkit.html. Other C efforts in the numerical solution of linear equations include LAPACK [Dongarra et al. 1993] for dense systems, and Diffpack [Bruaset and Langtangen 1997], ISIS [Clay 1997] SparseLib and IML [Dongarra et al. 1994] for sparse systems. It is also possible to use an object oriented style in other languages [Eijkhout 1996; Machiels and Deville 1997; Smith et al. 1995] In Section 2, we discuss various issues that arise when designing interfaces ....

Bruaset, A. M. and Langtangen, H. P. 1997. Object-oriented design of preconditioned iterative methods in Diffpack. ACM Trans. Math. Softw. 23, 50--80.

....abstract data types and object oriented programming are important mechanisms for achieving the necessary degree of modularity. In fact, the Diffpack code for the described framework was realized as a high level, compact combination of existing C classes. We refer to [ABL97, BL97, ABC 97, BL96] and the references therein for information about object oriented numerics, the efficiency of C for scientific computing, the design of Diffpack and examples on Diffpack applications. It should be mentioned that objectoriented implementations of domain decomposition and multilevel strategies ....

....be reused in our framework. The preconditioner can either be a matrix or an action. In case of an action, the preconditioner can, e.g. call a linear solver for the same or a related PDE problem. Linear solvers can utilize convergence monitors in order to control the degree of solution accuracy [BL96] At its present stage of development, Diffpack offers relatively simple nonlinear solvers, like Newton s method or the Picard iteration. This type of algorithm requires the programmer to define and solve a linear (sub)system. Operators can be defined in terms of coefficient matrices arising from ....

[Article contains additional citation context not shown here]

Bruaset A. M. and Langtangen H. P. (1996) Object-oriented design of preconditioned iterative methods. To appear in ACM Trans. Math. Software .

....our model problems. Both our model problems are inde nite and symmetric problems, i.e. having both positive and negative eigenvalues, and we must use a method that can handle such situations 1 . Di pack already has appropriate solvers for symmetric and inde nite systems: Symmlq and MinRes (see [8]) The basic operations in the Krylov solvers are matrixvector product, vector addition and inner products, which all are of O(n) operations (as we have very sparse matrices) The memory requirement is O(n) entries of memory, since we only need to store the matrix and some vectors. ....

A. M. Bruaset and H. P. Langtangen. Object-oriented design of preconditioned iterative methods in Dipack. Transactions on Mathematical Software, 23:50-80, 1997.

....course, Diffpack supports preconditioning techniques in connection with iterative solvers. Examples on preconditioning techniques offered by Diffpack are matrix splitting and incomplete LU factorizations. Information about the linear algebra features in Diffpack can be found in a separate report [3]. 14 On some Unix systems the awk utility, which is used by Gnuplot, requires parenthesis in regular expressions to be surrounded by brackets: 17 In Chapter 3 the reader was introduced to some simple graphics available in Diffpack. The model problem was the wave equation in one space ....

A. M. Bruaset and H. P. Langtangen. Object-oriented design of preconditioned iterative methods in Diffpack. To appear in Transactions on Mathematical Software, pages ???-- ???, 1996?

....storage details are inherent parts of the matrix representation and the programmer does not need to be concerned with this when using the matrix object. Refining this approach, the dense and sparse matrix formats could be organized together with other matrix implementations as a class hierarchy [6,7]. Introducing a common base class that defines a generic interface to matrix operations, the user would then be able to dynamically switch between different storage schemes without changes to the application code, see Figure 1.1. At this point, it is appropriate to discuss how the extension from ....

....comprehensive treatment of computational efficiency So far we have outlined a possible object oriented design of dense matrices and looked briefly at its extension to sparse matrix structures. A more detailed discussion on matrix and vector implementations in the framework of OOP can be found in [6, 7]. In particular, these papers deal with hierarchical implementations of multiple storage schemes, as well as the use of templates, i.e. parameterization with respect to the data type used for the matrix entries. For other discussions and alternative views of objectoriented linear algebra tools, ....

[Article contains additional citation context not shown here]

A. M. Bruaset and H. P. Langtangen. Object-oriented design of preconditioned iterative methods in Diffpack. To appear in ACM Trans. Math. Software, 1996.

....In this chapter we will address important issues concerning the design of such a toolkit within the framework of object oriented programming (OOP) see [2, 4, 12] and references therein. To a large extent, we discuss possible solutions that have been implemented in C as part of Diffpack [7,8,10]. This package is intended for the numerical solution of partial differential equations, mainly by use of finite element methods. However, being a part of a much wider research program, subsets of this linear algebra package are also extensively used in other projects, e.g. related to scattered ....

....of methods for the solution of linear systems. However, we will not go into detail about the different algorithms or their implementation. More information on relevant methods can be found in [5, 6] and references therein. Object oriented design of such solvers is treated more thoroughly in [7, 13]. Linear solvers can in general be divided into two categories: Direct and iterative methods. Regardless of the chosen algorithm, a clearly layered design as indicated by the Matrix and Vector hierarchies is vital to obtain a high overall performance. The core operations that turn out to be ....

A. M. Bruaset and H. P. Langtangen. Object-oriented design of preconditioned iterative methods in Diffpack. To appear in ACM Transactions on Mathematical Software, 1996.

....of the linear system in the Tf2 simulations; averaged CPU time (in seconds) measured on HP and number of iterations at each time level. The stopping criterion Sc2(10 Gamma10 ) is used by the iterative methods. 5. 3 Efficiency of the linear algebra in Diffpack The linear algebra tools (see [6]) in Diffpack have a carefully designed structure. By utilizing the object oriented programming (OOP) techniques, Diffpack offers the users with a rich collection of solution methods, preconditioners and stopping criteria. The users are able to make flexible combinations at run time and the ....

A. M. Bruaset and H. P. Langtangen, Object-oriented design of preconditioned iterative methods, Report no. STF33 A94036, Diffpack report, 1994.

....abstract data types and object oriented programming are important mechanisms for achieving the necessary degree of modularity. In fact, the Dioepack code for the described framework was realized as a high level, compact combination of existing C classes. We refer to [ABL96, BL96a, ABC 96, BL96b] and the references therein for information about object oriented numerics, the eOEciency of C for scienti c computing, the design of Dioepack and examples on Dioepack applications. It should be mentioned that objectoriented implementations of domain decomposition and multilevel strategies have ....

....possibly a preconditioner. The preconditioner can either be a matrix or an action. In case of an action, the preconditioner can, e.g. call a linear solver for the same or a related PDE problem. Linear solvers can utilize convergence monitors in order to control the degree of solution accuracy [BL96b] At its present stage of development, Dioepack ooeers relatively simple nonlinear solvers, like Newton s method or the Picard iteration. This type of algorithms requires the programmer to de ne and solve a linear (sub )system. Operators can be de ned in terms of coeOEcient matrices arising from ....

[Article contains additional citation context not shown here]

Bruaset A. M. and Langtangen H. P. (1996) Object-oriented design of preconditioned iterative methods. To appear in ACM Trans. Math. Software.

No context found.

A. M. Bruaset and H. P. Langtangen, Object-oriented design of preconditioned iterative methods in Dipack, ACM Transactions on Mathematical Software, (1997), pp. 50-80.

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