BALAY S., BUSCHELMAN K., EIJKHOUT V., GROPP W. D., KAUSHIK D., KNEPLEY M. G., MCINNES L. C., SMITH B. F., ZHANG H.: PETSc Users Manual. Tech. Rep. ANL-95/11 - Revision 2.1.5, Mathematics and Computer Science Division, Argonne National Laboratory, 2004. Available at http://wwwunix. mcs.anl.gov/petsc/petsc-2/. 6  Home/Search   Document Not in Database   Summary   Related Articles   Check

....deleted. Unfortunately, one cannot reasonably require 8 the presence of such features in other solver packages. The second solver package interfaced to SUMMA3d was PETSc, a flexible package for solving linear and nonlinear systems of equations with the capability of solving timedependent problems [1]. PETSc is a much more comprehensive, general package than BlockSolve95; it does not have some of the features that were taken advantage of in the interface of SUMAA3d to BlockSolve95. The interface points between the two packages are the PETSc matrix and vector objects, Mat and Vec, respectively. ....

Satish Balay, Lois Curfman McInnes, William D. Gropp, and Barry F. Smith. PETSc 2.0 users manual. ANL Report ANL-95/11, Argonne National Laboratory, Argonne, Ill., November 1995.

....[20] MPI is designed for achieving portable high performance communication in parallel applications. Numerous implementations of MPI have been realized in industry and academia, and MPI has successfully been used in many domains (e.g. scientific computing, visualization, and bioinformatics) [2, 5, 16, 23]. With the increasing popularity of clusters and MPI applications, the issue of reliability at the middleware and application layers has recently gained prominence. Clusters inherently increase the availability at hardware level with redundant and hot swappable components. However, this ....

S. Balay et al., PETSc Users Manual, tech. report ANL-95/11, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL., 1995.

....scalable, we expect to find the problem size which marks the turning point which validates the method. We return to the issue when considering the test case. 2. J The application layer The application level of our current effort is built upon pre existing nu merical packages such as PETSc (ref. [28]) or ScaLAPACK. We have relied upon the scalability of such libraries to more than account for the time required for the middleware to handle the user s data. It is the developer s burden to understand the application routines from such libraries at an intricate level so that accurate time ....

Balay, S., Gropp, W., Curlman McInnes, L., Smith, B.,PETSc Users Manual, rev. 2.1.0, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439

....[72] to a parallel environment has involved the goal of maximizing code re use. Some newer software systems [19] appear to view this goal as secondary and they provide some tools for the integration of alien modules. In contrast, software systems with a more coherent vision, such as PETSc [9] and PLAPACK [74] take a more uni ed view of the computational environment and present the 49 user with a library that has a more consistent interface. These libraries also avoid the pitfall of hiding parallelism in order to avoid added complexity. They expose levels of parallelism to the ....

Satish Balay, William Gropp, Lois Curfman McInnes, and Barry Smith. PETSc 2.0 users manual. Technical Report ANL-95/11, Argonne National Laboratory, Oct. 1996.

....created by the grid generation software GEOMPACK [19] Using GEOMPACK, the grids of different sizes are independently generated. The Krylov iterative solvers that we have employed are Generalised Minimal Residual (GMRES) 33] and BiConjugate Gradient (BCGS) 37] as provided by the PETSc library [8]. The well established and publicly available code AMG1R5 [38] has been used as a scalar AMG solver. The approximate AMG solving procedure consists of 1 V(1,1) multigrid cycle. The component wise AMG preconditioner, implemented in both parallel (AMG P) and successive (AMG S) versions, has been ....

Balay S, Gropp W, McInnes LC, Smith B. PETSc 2.0 Users Manual. ANL-95/11--Revision 2.0.28. Argonne National Laboratory. 1999.

....dynamic grid refinement that provides the user with all data structures and operations necessary to work on dynamically 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 ....

S. Balay, W. Gropp, L. Curfman McInnes, B. Smith. PETSc 2.0 - User Manual. Tech. Rep. ANL-95/11 - Revision 2.0.22, Argonne National Laboratory, 1995.

....matrix A resulting from one step of Newton s method is non symmetric and indefinite. The specific example uses q = 500, 1, and solves to a relative convergence of 10 Gamma10 . Outer iterations are generated from the Transpose Free Quasi Minimal Residual algorithm (TFQMR) 5] using PETSc [3] and each of the preconditioners is generated using the PETSc shell option to ensure consistency. Results were obtained for four different discretizations resulting in 61, 121, 221, and 441 degrees of freedom (DOFs) Table 1 shows convergence statistics for this example as a function of problem ....

S. Balay, W. Gropp, L. C. McInnes, and B Smith. PETSc 2.0 Users Manual. Argonne National Laboratory, Argonne, Il., anl-95/11 - revision 2.0.17 edition, 1995.

....the package, particular attention is paid to the linear algebra layer and interfaces to it. The COOOL package (Deng, Gouveia, and Scales [8] is another collection of C classes and includes implementations of a wide variety of algorithms and algorithm components. The PETSc project (Balay et al. [1]) focuses on the development of software components for large scale linear algebra, allowing data structure independent implementation of solvers for partial di#erential equations and nonlinear equations, on serial and parallel architectures. Although PETSc is implemented chiefly in C, its follows ....

S. Balay, W. Gropp, L. Curfman McInnes, and B. Smith. PETSc Users Manual. Mathematics and Computer Science Division, Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, Ill. 60439, April 2001.

.... on a serial nite element code (FEAP [9] and a parallel graph partitioner (ParMetis [14] and our solver Prometheus (Prometheus is freely available in a publicly domain library [16] Prometheus can be further decomposed into three parts: General unstructured multigrid support built on PETSc [5] (Epimetheus in Figure 8) Non nested geometric multigrid method (Prometheus in Figure 8) Aggregation multigrid methods (Atlas in Figure 8) Athena reads a large at nite element mesh input le in parallel, uses ParMetis to partition the nite element graph, and then constructs a complete ....

S. Balay, W. D. Gropp, L. C. McInnes, and B. F. Smith. PETSc 2.0 users manual. Technical report, Argonne National Laboratory, 1996.

.... on a serial nite element code (FEAP [18] and a parallel graph partitioner (ParMetis [28] and our solver Prometheus (Prometheus is freely available in a public domain library [32] Prometheus can be further decomposed into three parts: 1) general unstructured multigrid support built on PETSc [5]; 2) the non nested geometric multigrid method; and 3) the aggregation multigrid methods. The system reads a large at nite element mesh input le in parallel, uses ParMetis to partition the nite element graph, and then constructs a complete nite element problem on each processor. These ....

S. Balay, W. D. Gropp, L. C. McInnes, and B. F. Smith. PETSc 2.0 users manual. Technical report, Argonne National Laboratory, 1996. 16

....flows, we utilize a matrix free GMRES, which consistently accounts for the viscous terms within the matrix vector product. In this case, only the pre conditioner suffers from neglecting the viscous terms. The infrastructure related to the Newton Krylov method in this paper is based on the PETSc [59] library of Argonne National Laboratory. For further details of the numerical method we refer to [60] 61] 5.2 Validation of the Basic Scheme In the following, various test cases are considered using regular, non adaptive structured grids in order to validate the basic finite volume scheme. ....

S. Balay, W. Gropp, L.C. McInnes, B.F. Smith, PETSc 2.0 Users Manual, Tech. Rep. ANL-95/11 - Revision 2.0.28, Argonne National Laboratory, 2000, http://www-fp.mcs.anl.gov/petsc/

....parallel implementation allowing the tackeling of larger grid sizes. For our application we employed the software PETSc 2. 0 (Portable and Extensible Toolkit for Scientific Computing) developed and maintained at the Mathematics and Computer Science Division of the Argonne National Laboratory, see Balay et al. 1998). PETSc is a set of routines designed to solve large scale computational problems in a parallel environment. The software is written in C and can be linked to C, C or Fortran programs. We used a computing platform constituted by a 32 PC LINUX cluster. The individual machines are Pentium II that ....

Balay, S., W. D. Gropp, L. Curfman McInnes and B. F. Smith (1998). PETSc 2.0 Users Manual. Technical Report ANL 95/11. Argonne National Laboratory.

.... a similar F90 package for the Telluride effort (and eventually other applications) In addition, although there are numerous other high quality packages for iteratively solving systems of linear equations in other languages, such as ITPACK [7] and NSPCG [6] in F77, AZTEC 2 [4] and PETSc 3 [1] in C, and Diffpack 4 in C , we knew of no such effort in F90. So development of JTpack90 5 began with JTpack77 6 as a starting point, driven by the needs of Telluride 7 . 2 Overview of JTpack90 2.1 Design Goals Although JTpack90 is a tool driven by the needs of a particular ....

S. Balay, W. Gropp, L. C. McInnes, and B. Smith, PETSc 2.0 users manual, Tech. Rep. ANL-95/11, Argonne National Laboratory, Oct 1996.

....general solvers that suit our purposes. The library contains components able to manipulate parallel sparse matrices and solve large scale systems using preconditioned Krylov subspace methods. The different components of PETSc are illustrated in Figures 2 and 3, reprinted from the users manual (Balay et al. 1998)) The development of compilers for distributed memory computers is slow paced and has, so far, provided limited functionality in dealing with sparse matrices and the algorithms in which they are used. High Performance Fortran (HPF) compilers, for example, have not yet come to maturity and are ....

Balay, S., Gropp, W.D., Curfman McInnes, L. and Smith, B.F., (1998). PETSc 2.0 Users Manual. ANL 95/11, Argonne National Laboratory, http://www.mcs.anl. gov/petsc/petsc.html.

....old ) where superscript new denotes new iterates and old denotes old iterates. F (T ) and J(T ) are obtained by a second order finite volume method which leads to a set of large sparse linear system and it can be solved by means of a standard domain decomposition software package such as PETSc [BGMS97] More processors may be used to achieve a secondary level of parallelism for the Newton s iterative scheme, which are separately controlled by di#erent hosts assigned to each of the subproblems. Therefore the inverse welding problem has two levels of parallelism. One level being the di#erential ....

S. Balay, W. Gropp, L.C. McInnes, and B. Smith. PETSc 2.0 User Manual. Argonne National Laboratory, http://www.mcs.anl.gov/petsc/, 1997.

....BLAS (Basic Linear Algebra Subroutines) routines, and the BLACS communications libraries were then installed. SCALAPACK (Scalable Linear Algebra Package) 17] which is a parallel version of the LAPACK libraries was also installed. PETSc (Portable, Extensible Toolkit for Scientific Computation)[18] was also included among the installed software since it provides tools for scientific computing, visualization, and profiling. 5.2 Processing Nodes The installation of the processing nodes was trivial. The Linux CD was installed into the processing node an a Redhat Linux KickStart Script was ....

S. Balay, W. Gropp, L. McInnes, B. Smith. 2000. PETSc 2.0 Users Manual, ANL-95/11 - Revision 2.0.28, Argonne National Laboratory.

....undertaking to develop and generally support only a very limited class of applications. Users with non mainstream needs can find frameworks to be too restrictive and limited. Middle ground between these two extremes can be found in the many parallel utility libraries for linear algebra (e.g. [15, 1]) partitioning (e.g. 6, 16] and other common kernel operations. Although we personally prefer this library approach to parallel software development, it is not without its problems. A key challenge for the developers of parallel libraries is the design of easy to use and efficient interfaces. ....

S. Balay, W. D. Gropp, L. Curfman McInnes, and B. F. Smith, PETSc 2.0 users manual, Tech. Rep. ANL-95/11 - Revision 2.0.29, Argonne National Laboratory, 2000. http://www-fp.mcs.anl.gov/petsc/.

.... these concepts, a three dimensional unstructured grid incompressible Euler code from NASA (as an example of a traditional procedural software written in FORTRAN77 but doing memory allocation in ANSI C) has been parallelized with Portable Extensible Toolkit for Scientific Computing (PETSc) library [4] (designed from object oriented principles but written in ANSI C) for distributed memory architectures. We have tuned this code for execution time and memory. Even on one processor, the PETSc ported parallel code runs about 8 times faster than the legacy code on a medium sized data set ....

....(making maintenance easy) has become obvious especially since C implementations can provide speed and efficiency competitive with native FORTRAN codes [9] One even does not need OOP language to implement the OOD principles. The Portable Extensible Toolkit for Scientific Computing (PETSc [4]) is one excellent example a data structure neutral parallel library written in ANSI C. PETSc is designed around several components (e.g. Vec (vectors) Mat (matrices, both dense and sparse) and supports abstraction, encapsulation, modularity, polymorphism, and limited inheritance. Each ....

Satish Balay, William Gropp, Lois Curfman McInnes, and Barry Smith. PETSc 2.0 users manual. Technical Report ANL-95/11, Mathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL 60439, 1995. (see http://www.mcs.anl.gov/petsc/petsc.html).

.... discuss the effective parallel implementation of the components of multigrids as they are all standard linear algebraic operations with sparse matrices and dense vectors e.g. matrix vector products, matrix triple products, dot products, etc and are implemented by our numeric libraries PETSc [4]. We, however, do need to be concerned with some algorithmic issues for the efficient application of multigrid solvers on large scale problems on typical parallel machines of today. In particular, on large problems the coarsest grids have so few equation per processor that one must agglomerate ....

....graph, then constructs a fully valid serial finite element problem to provide a well specified serial finite element problem on each processor. ffl Epimetheus is an algebraic multigrid solver infrastructure that provides a solver to Athena, a driver for Prometheus, an interface to PETSc [4], and numerical primitives not provided by PETSc (e.g. the sparse matrix triple product) ffl Prometheus is our restriction operator constructor and is the implantation of the coarse algorithms discussed in this paper. Athena, Epimetheus, and Prometheus are implemented with about 30,000 lines of ....

[Article contains additional citation context not shown here]

S. Balay, W.D. Gropp, L. C. McInnes, and B.F. Smith. PETSc 2.0 users manual. Technical report, Argonne National Laboratory, 1996.

....numerical experiments on an IBM SP with 80, 120 Mhz, Power2 processors at Argonne National Laboratory. An extended version of the Finite Element Analysis Program (FEAP) 11] is used to generate out test problems and produce our graphics. We use ParMetis [9] to calculate our partitions, and PETSC [2] for our parallel programming and development environment. Our code is implemented in C , FEAP is implemented in FORTRAN, PETSc and ParMetis are implemented in C. We want to show that our complexity analysis is indicative of the actual behavior of the algorithm with real (imperfect) mesh ....

S. Balay, W.D. Gropp, L. C. McInnes, and B.F. Smith. PETSc 2.0 users manual. Technical report, Argonne National Laboratory, 1996.

....parts: Athena, a parallel finite element program built on a serial finite element code (FEAP [9] and a parallel mesh partitioner (ParMetis [16] and our solver Prometheus. Prometheus can be further decomposed into two parts: Epimetheus, general unstructured multigrid support (built on PETSc [3]) and our particular multigrid algorithm Prometheus (whose sole responsibility is to construct the restriction operators between each grid) Prometheus and Epimetheus are not implemented separately and constitute the publicly available library [19] Athena reads a large flat finite element ....

S. Balay, W.D. Gropp, L. C. McInnes, and B.F. Smith. PETSc 2.0 users manual. Technical report, Argonne National Laboratory, 1996.

....1) Athena, a parallel nite element program built on a serial nite element code (FEAP [14] and a parallel graph partitioner (ParMetis [20] and 2) our solver Prometheus. Prometheus can be further decomposed into three parts: 1) Epimetheus, general unstructured multigrid support (built on PETSc [3]) 2) the geometric multigrid method Prometheus; and 3) the algebraic multigrid method Atlas. Prometheus, Atlas, and Epimetheus are available as a publicly domain library called Prometheus [23] Athena reads a large at nite element mesh input le in parallel (ie, each processor seeks and ....

S. Balay, W. D. Gropp, L. C. McInnes, and B. F. Smith. PETSc 2.0 users manual. Technical report, Argonne National Laboratory, 1996.

....(see Figure 3) This is called compressed row storage format for unrolling. Using such a matrix format, we expected to save the execution time because of the effect of unrolling. cval[12] f0,1,0,0,1,2,1,2,3,2,3,0g; indices aval[12] fa; b; 0; c; d; e; f; g; h; i; j; 0g; elements nsize[4]=f2,3,3,2g; the number of elements of each row csize=3; fixed size Fig. 3. Compressed row storage format for unrolling Before executing the main iteration, the actual time of the matrix by vector product was measured. With this information, we can select the best matrix storage ....

....on distributed memory machines because the synchronization is needed only once. In case of using CGS, lines 8 11 in the Figure 1 are replaced as shown in Figure 5. CGS has less in computational error than MGS. Therefore, our library provides iterative refinement Gram Schmidt orthogonalization [4] (see Figure 6) 1: for k=0,1, Delta Delta Delta,i 2: hk;i = w; vk ) 3: end 4: for k=0,1, Delta Delta Delta,i 5: w = w Gamma hk;i vk 6: end Fig. 5. Classical Gram Schmidt orthogonalization 1: for k=0,1, Delta Delta Delta,i 2: hk;i = w; vk ) 3: end 4: for k=0,1, Delta Delta ....

[Article contains additional citation context not shown here]

S.Balay, W.D.Gropp, L.C.McInnes, B.F.Smith: PETSc 2.0 Users Manual. ANL95 /11 - Revision 2.0.24, Argonne National Laboratory (1999).

....an inexact version of the well known conjugate gradient (CG) method along with several preconditioners on a multi processor SGI Power Challenge machine at the Computer Center of the University of Hamburg. We used the software package PETSc (Portable Extensible Toolkit for Scienti c Computing) [4, 5], which is based on the message passing standard MPI [26] Among the class of iterative Krylov subspace solvers (cf. e.g. 23] the CG method is nearly optimal for the class of matrices B k considered here (sparse, symmetric, positive de nite) Inexact refers to the stopping criterion rtol ....

S. Balay, W.D. Gropp, L.C. McInnes, and B.F. Smith, \PETSc 2.0 users manual," Tech. Rep. ANL-95/11 - Revision 2.0.22, Argonne National Laboratory, 1998.

....project, distributed data types are created collectively, but may be manipulated collectively (using, for example, PETSc vector routines) as well as individually. PETSc vectors are linear arrays that primarily support irregular grid graph computations. Collective vector routines (such as VecAXPY [6], which is the equivalent of an overwriting DAXPY) are implemented atomically, like HPF s FORALL. Individual elements can also be assigned values (VecSetValues) but since this incurs the overhead of a function call and possibly communication, such assignments are best grouped together. PETSc ....

....One of the most useful and common operations on distributed variables is copy faces, which fetches values from neighboring processors and stores them in the ghost point locations. This facilitates standard stencil operations without the need for frequent remote data accesses. As in PETSc [6], support is provided for so called box and star shaped difference stencils. This controls whether or not corner ghost points need to be copied. However, rather than making this an attribute of the distributed variable, it is specified at the time of the copy faces operation, as is the update of ....

S. Balay, W.D. Gropp, L. Curfman McInnes, B.F. Smith, PETSc 2.0 Users manual , Report ANL--95/11 - Revision 2.0.17, Argonne National Laboratory, Argonne, IL 60439, 1997

....algorithms is often slow due to the investment necessary to switch solvers. Increasingly, more modern solver libraries have adopted object oriented techniques that make them easier and more extensible to use. The object oriented solver libraries in widest use within the DOE are the PETSc library [2], and the ISIS library [7] Although there are several other object oriented libraries in the wider community, in this paper we will concentrate on these two libraries as representative of the state of the art. The core object models for both libraries are similar. The model consists of base ....

S. Balay, W. Gropp, L. C. McInnes, and B. Smith, Petsc 2.0 user's manual, Tech. Rep. ANL95 /11, Argonne National Laboratory, Nov. 1995.

....Cross and Olof B. Widlund c fl1999 DDM.org ALGORITHMS FOR METAL CUTTING PROBLEMS 323 FORTRAN and its parallel version uses MPI (Message Passing Interface) calls. One implicit algorithm is implemented by coupling the state of the art PETSc (Portable, Extensible Toolkit for Scientific Computation) [BGLS] software with in house software in order to solve the subproblems. The second implicit algorithm is implemented completely within PETSc. PETSc uses MPI as the underlying communication library. Finally, a 2D example is used to test the algorithms and various comparisons are made. The dimensionless ....

Balay S., Gropp W., L.C.McInnes, and Smith B.PETSc 2.0 User Manual. Argonne National Laboratory. http://www.mcs.anl.gov/petsc/.

....presents the rationales behind our design. For the solution of the linear system, SIFFEA currently employs the linear solves in PETSc, which includes a variety of iterative solvers and rich functionality for managing matrices and vectors. For more information about PETSc, readers are referred to [4]. 4.1 Element Matrix and Vector Solving a boundary value problem using FEM includes two distinct transformations of its mathematical formulation: the dioeerential equation is rst transformed into an integral form (a.k.a. weak form) and then the integral form is transformed into a matrix and ....

Balay, S., Gropp, W. D., McInnes, L. C., and Smith, B. F. PETSc 2.0 users manual. Tech. Rep. ANL-95/11, Argonne National Laboratory, 1998.

....this, we have adopted an object based approach to programming. This object based approach has already been popularized for high performance parallel computing by libraries like the Toolbox being developed at Mississippi State University [3] the PETSc library at Argonne National Laboratory [2], and the Message Passing Interface [8] The PLAPACK infrastructure uses a data distribution that starts by partitioning the vectors associated with the linear algebra problem and assigning the subvectors to This project was sponsored in part by the Parallel Research on Invariant Subspace ....

Satish Balay, William Gropp, Lois Curfman McInnes, and Barry Smith. PETSc 2.0 users manual. Technical Report ANL-95/11, Argonne National Laboratory, Oct. 1996.

....onto the local subspaces, defined in (39) 40) ii) Conjugate gradient method applied to the additive two level operator T as2 = T 0 J X i=1 T i ; where the T 0 the projection onto the coarse space V 0 . Our results have been obtained on a SUN Ultra1, using the PETSc 2. 0 library ; see [4]. The independence of the condition number on the diameter h of the fine mesh is observed, once the number of subdomains and the relative overlap ffi =H are fixed; the results are not presented here. We have first considered a unit cube Omega Gamma Tables 1 and 2 show the estimated condition ....

Satish Balay, William Gropp, Lois Curfman McInnes, and Barry F. Smith. PETSc Users' Manual. Technical Report ANL-95/11, Mathematics and Computer Science Division, Argonne National Laboratory, 1995.

....Given the problem size, the finite element simulation was executed on 8 processors of the IBM SP. Figure 6 shows an example of the temperature distribution of a rotating disk as modeled by FIFEA. FIFEA makes extensive use of the PETSc (Portable, Extensible, Toolkit for Scientific computation) [Balay et al. 1995] to do linear algebra and to manipulate sparse matrices and vectors. FIFEA and PETSc use the MPI library [Gropp et al. 1994] for communication between the IBM SP processors. One IBM SP processors sends and receives results to and from the SGI Onyx using the CAVEcomm library [Disz et al. 1995] ....

Balay, S., Gropp, W., Curfman McInnes, L., and Smith, B. 1995. PETSc 2.0 Users Manual. Technical Report ANL-95/11. Argonne National Laboratory.

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S. Balay, W. D. Gropp, L. C. McInnes, and B. F. Smith. PETSc 2.0 users manual. Technical report, Argonne National Laboratory, 1996.

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S. Balay, W.D. Gropp, L. C. McInnes, and B.F. Smith. PETSc 2.0 users manual. Technical report, Argonne National Laboratory, 1996. 19

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S. Balay, W. D. Gropp, L. C. McInnes, B. F. Smith, PETSc users manual, Tech. Rep. ANL-95/11 - Revision 2.1.1, Argonne National Laboratory (2001).

.... by transforming the linear system (6) into the equivalent form B 1 = B 1 f (u ) 7) through the action of a preconditioner, B, whose inverse action approximates that of the Jacobian (see, e.g. 2] We implement the pseudo transient Newton Krylov solvers using PETSc [3,4], a suite of software for the scalable solution of PDE based applications. The software design, which incorporates a hierarchy of data and algorithmic components, facilitates experimentation and the development of novel algorithms. For example, we implemented the adaptive linear solvers discussed ....

Balay S, Buschelman K, Gropp W, Kaushik D, Knepley M, McInnes LC, Smith B, Zhang H. PETSc users manual. Tech. Rep. ANL-95/11 -- Revision 2.1.3, Argonne National Laboratory, 2002 (see www.mcs.anl.gov/petsc).

....and introduction to the fields of Scientific Computing, Computer Science, and Applied Mathematics. I would like to express my gratitude to the following ffl Professor Taylor for providing and maintaining FEAP, without which this work would have been grossly inferior [36] ffl The PETSc team [10]: Satish Balay, William Gropp, Lois Curfman McInnes, and Barry Smith for providing a great product, without which this work would have been grossly inferior. And I especially want to thank Barry Smith for his tireless support of PETSc, for his concise theory manual Domain Decomposition [78] and ....

....experiments on an IBM SP with 80, 120 Mhz, Power2 (P2SC) processors at Argonne National Laboratory. An extended version of the Finite Element Analysis Program (FEAP) 36] is used to generate out test problems and produce 68 our graphics. We use ParMetis [53] to calculate our partitions, and PETSc [10] for our parallel programming and development environment. Our code is implemented in C , FEAP is implemented in FORTRAN, PETSc and ParMetis are implemented in C. We want to show that our complexity analysis is indicative of the actual behavior of the algorithm with real (imperfect) mesh ....

[Article contains additional citation context not shown here]

S. Balay, W.D. Gropp, L. C. McInnes, and B.F. Smith. PETSc 2.0 users manual. Technical report, Argonne National Laboratory, 1996.

....performance possibilities of an application code written using PETSc by presenting results for a three dimensional, fully implicit Euler simulation. This article is not intended as a users guide or introduction to the use of PETSc; for that information we refer readers to the PETSc users manual [BGMS95]. Rather, this article discusses in some technical detail several specific aspects that are important in the design of PETSc. In fact, users of PETSc do not have to understand the technical details discussed here in order to use PETSc effectively. 2 The Message Passing Model for Programming ....

....Both support the use of any of the linear solvers in a truncated Newton algorithm. Recently, we have added support for using backward Euler timestepping schemes. We plan to include additional higher order timestepping schemes in the future. All the solvers are introduced in the PETSc users manual [BGMS95]. 5.5 Object Oriented Features of PETSc This article has touched on several object oriented features of PETSc without providing a complete overview of the object oriented design. In this section we focus on how object oriented techniques are used to organize the overall software package. ....

Satish Balay, William Gropp, Lois Curfman McInnes, and Barry Smith. PETSc 2.0 users manual. Technical Report ANL-95/11, Argonne National Laboratory, November 1995.

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BALAY S., BUSCHELMAN K., EIJKHOUT V., GROPP W. D., KAUSHIK D., KNEPLEY M. G., MCINNES L. C., SMITH B. F., ZHANG H.: PETSc Users Manual. Tech. Rep. ANL-95/11 - Revision 2.1.5, Mathematics and Computer Science Division, Argonne National Laboratory, 2004. Available at http://wwwunix. mcs.anl.gov/petsc/petsc-2/. 6

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S. Balay, W.D. Gropp, L. C. McInnes, and B.F. Smith. PETSc 2.0 users manual. Technical report, Argonne National Laboratory, 1996.

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S. Balay, W.D. Gropp, L. C. McInnes, and B.F. Smith. PETSc 2.0 users manual. Technical report, Argonne National Laboratory, 1996.

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Satish Balay, William Groopp, Lois Curfman McInnes, and Barry Smith. PETSc 2.0 users manual. Technical Report ANL-95/11 -- Revision 2.0.15, Mathematics and Computer Science Division, Argonne National Laboratory, 1996.

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L. M. S. Balay, W. Gropp and B. Smith. PETSc users manual. Argonne National Laboratory, 2001.

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L. M. S. Balay, W. Gropp and B. Smith. PETSc users manual. Argonne National Laboratory, 2001.

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Balay, S., McInnes, L. C., Gropp, W. D. & Smith, B. F. 1995. PETSc 2.0 users manual. ANL Report ANL-95/11, Argonne National Laboratory, Argonne, Ill., November.

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S. Balay, W. Gropp, L. McInnes, B. Smith. 2000. PETSc 2.0 Users Manual, ANL95 /11 - Revision 2.0.28, Argonne National Laboratory.

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S. Balay, W. D. Gropp, L. C. McInnes, and B. F. Smith, PETSc 2.0 users manual, tech. report, Argonne National Laboratory, 1996.

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S. Balay, W. D. Gropp, L. C. McInnes, and B. F. Smith, PETSc 2.0 users manual, tech. report, Argonne National Laboratory, 1996.

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S. Balay, W. D. Gropp, L. C. McInnes, and B. F. Smith, PETSc 2.0 users manual, tech. rep., Argonne National Laboratory, 1996.

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S. Balay, W. Gropp, L. Curfman McInnes, and B. Smith, PETSc Users Manual, Report ANL-95/11 (Revision 2.1.0), Argonne National Laboratory, IL (2001).

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S. Balay, W. Gropp , L. Curfman McInnes, and B. Smith, PETSc 2.0 Users Manual, Technical Report ANL-95/11, Argonne National Laboratory, 1995.

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