libMesh : a C++ library for parallel adaptive mesh refinement/coarsening simulations

Gropp W, Lusk E, Doss N, Skjellum A (1996) MPICH: A high-performance, portable implementation of the MPI message passing interface standard. Parallel Comput 22(6):789–828

Carey GF (1997) Computational grids: generation, adaptation, and solution strategies. Taylor & Francis, London

Barth W, Kirk B (2003) PC cluster construction: lessons learned and friendly advice. Shortcourse on cluster computing and adaptive finite element methods, The University of Western Australia, Perth

Becker EB, Carey GF, Oden JT (1981) Finite elements—an introduction, vol 1. Prentice Hall, Englewood cliffs

Flaherty JE, Paslow PJ, Shephard MS, Vasilakis JD (eds) (1989) Adaptive methods for partial differential equations. SIAM, Philadelphia

Babuska I, Zienkiewicz OC, Gago J, Oliviera ERA (1986) Accuracy estimates and adaptive refinements in finite element computations. Wiley, London

Babuska I, Rheinboldt WC (1982) Computational error estimates and adaptive processes for some nonlinear structural problems. Comput Methods Appl Mech Eng 34:895–937

Carey GF, Anderson M, Carnes B, Kirk B (2004) Some aspects of adaptive grid technology related to boundary and interior layers. J Comput Appl Math 166(1):55–86, ISSN 0377-0427, http://dx.doi.org/10.1016/j.cam.2003.09.036

Barth W, Carey GF, Kirk B, McLay R (2000) Parallel distributed solution of viscous flow with heat transfer on workstation clusters. in high performance computing 2000 proceedings, Washington

Gamma E, Helm R, Johnson R, Vlissides J (1995) Design patterns: elements of reusable object-oriented software. Addison-Wesley, Reading

Carey GF, McLay R (1995) Multi-level preconditioners for the parallel PCG package, copper Mtn. Conference on multigrid methods. In: Proceedings of the copper mountain conference on multigrid methods, Copper Mountain, CO

Carey GF (1976) A mesh refinement scheme for finite element computations. Comput Methods Appl Mech Eng 7:93–105

Carey GF (1976) An analysis of finite element equations and mesh subdivision. Comput Methods Appl Mech Eng 9:165–179

Carey GF, Finlayson BA (1975) Orthogonal collocation on finite elements. J Chem Eng Sci 30:587–596

Bank RE (1998) PLTMG: A software package for solving elliptic partial differential equations, Users’ Guide 8.0, Software, environments and tools, vol 5. SIAM, Philadelphia

Plaza A, Carey GF (2000) Local refinement of simplicial grids based on the skeleton. Appl Numerical Math 32:195–218

Plaza A, Padrón MA, Carey GF (2000) A 3D refinement/derefinement algorithm for solving evolution problems. Appl Numerical Math 32:401–418

Carey GF, Kabaila A, Utku M (1982) On penalty methods for interelement constraints. Comput Methods Appl Mech Eng 30:151–171

Bangerth W, Rannacher R (2003) Adaptive finite element methods for differential equations. Birkhäuser Verlag, Basel

Eriksson K, Estep D, Hansbo P, Johnson C (1996) Adaptive finite elements. Springer, Berlin Heidelberg New York

Estep D, Larson M, Williams R (2000) Estimating the error of numerical solutions of systems of nonlinear reaction–diffusion equations. Mem Am Math Soc 696:1–109

Estep D, Holst M, Mikulencak D (2002) Accounting for stability: a posteriori estimates based on residuals and variational analysis. Commun Numerical Methods Eng 8:15–30

Estep D, Holst M, Larson M (2005) Generalized Green’s functions and the effective domain of influence. SIAM J Sci Comput 26:1314–1339

Kelly DW, Gago JP, Zienkiewicz OC, Babuska I (1983) A posteriori error analysis and adaptive processes in the finite element method: part I. Error analysis. Int J Num Meth Eng 19:1593–1619

Zienkiewicz OC, Zhu JZ (1987) A simple error estimator and adaptive procedure for practical engineering analysis. Int J Numerical Methods Eng 24:337–357

Wahlbin LB (1995) Superconvergence in Galerkin finite element methods. Springer, Berlin Heidelberg New York

Carey V (2005) A posteriori error estimation for the finite element method via local averaging. Ph.D. thesis, Center for Applied Mathematics Deptartment, Cornell University

Stewart JR, Edwards HC (2004) A framework approach for developing parallel adaptive multiphysics applications. Finite Elem Anal Des 40(12):1599–1617, ISSN 0168-874X, http://dx.doi.org/10.1016/j.finel.2003.10.006

Bangerth W (2000) Using modern features of C++ for adaptive finite element methods: dimension-independent programming in deal.II. In: Deville M, Owens R (eds) Proceedings of the 16th IMACS World Congress 2000, Lausanne, Switzerland, 2000, Document Sessions/118-1

Budge K, Peery J (1996) Experiences developing ALEGRA: a C++ coupled Physics Framework. In: Henderson ME, Anderson CR, Lyons SL (eds) Object oriented methods for interoperable scientific and engineering computing

Barton JJ, Nackman LR (1994) Scientific and engineering C++: an introduction with advanced techniques and examples. Addison-Wesley, Reading

Bastian P, et al (1997) UG – A flexible software toolbox for solving partial differential equations. Comput Vis Sci 1:27–40

Devloo PRB, Longhin GC (2002) Object oriented design philosophy for scientific computing. Math Model Numerical Anal 36:793–807

Demkowicz L, Rachowicz W, Devloo PRB (2002) A fully automatic hp-adaptivity. J Sci Comput17:127–155

Free software foundation (1999) GNU lesser general public license. http://www.gnu.org/licenses/lgpl.html

Imamura M (2002) Using Doxygen: A quick guide to getting started and using the Doxygen inline documentation system for documenting source code. Tech. rep., Linux Users Group at Georgia Tech

Meyers RJ, Tautges TJ, Tuchinsky PM (1998) The hex-tet hex-dominant meshing algorithm as implemented in CUBIT. In: Proceedings of the 7th International Meshing Roundtable, 151–158

Shewchuk JR (1996) Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator. In: Lin MC, Manocha D (eds) Applied computational geometry: towards geometric engineering, vol. 1148 of lecture notes in computer science, 203–222, Springer, from the First ACM Workshop on Applied Computational Geometry

Si H (2005) TetGen—a quality tetrahedral mesh generator and three-dimensional Delaunay triangulator. Weierstrass Institute for Applied Analysis and Stochastics, Berlin

Karypis G, Kumar V (1995) METIS unstructured graph partitioning and sparse matrix order. Technical report, University of Minnesota, Department of Computer Science

Karypis G, Kumar V (1998) A parallel algorithm for multilevel graph partitioning and sparse matrix reordering. Parallel Distrib Comput 48:71–95

Devine K, Boman E, Heaphy R, Hendrickson B, Vaughan C (2002) Zoltan data management services for parallel dynamic applications. Comput Sci Eng 4(2):90–97

Skalický T (1996) LASPack Reference Manual. Dresden University of Technology

Balay S, Eijkhout V, Gropp WD, McInnes LC, Smith BF (1997) Efficient management of parallelism in object oriented numerical software libraries. In: Arge E ,Bruaset AM, Langtangen HP (eds) Modern software tools in scientific computing, 163–202, Birkhäuser Press

Hernandez V, Roman JE, Vidal V (2005) SLEPc: a scalable and flexible toolkit for the solution of eigenvalue problems. ACM Trans Math Softw 31(3):351–362

Iqbal S, Carey GF (2005) Performance analysis of dynamic load balancing algorithms with variable number of processors. J Parallel Distrib Comput 65(8):934–948

Balay S, Buschelman K, Eijkhout V, Gropp W, Kaushik D, Knepley M, McInnes LC, Smith B, Zhang H (2005) PETSc users manual. Argonne National Laboratory, Mathematics and Computer Science Division, 2.3.0 edn

Gresho PM, Sani RL (1998) Incompressible flow and the finite element method. Wiley, London

Clough R, Tocher J (1965) Finite element stiffness matrices for analysis of plates in blending. In: Proceedings of conference on matrix methods in structural analysis

Ciarlet PJ (1978) The finite element method for elliptic problems. North-Holland, Amsterdam

Dreyer D, Petersen S, von Estorff O (2006) Effectiveness and robustness of improved infinite elements for exterior acoustics. Comput Methods Appl Mech Eng 195(29–32):3591–3607

Dreyer D, von Estorff O (2003) Improved conditioning of infinite elements for exterior acoustics. Int J Numerical Methods Eng 58(6):933–953

Marichalar JJ, Rochelle WC, Kirk BS, Campbell CH (2006) BLIMPK/Streamline Surface Catalytic Heating Predictions on the Space Shuttle Orbiter, 44th AIAA Aerospace Sciences Meeting and Exhibit, AIAA Paper 2006-180

Valenciano J, Chaplain MAJ (2004) An explicit subparametric spectral element method of lines applied to a tumor angiogenesis system of partial differential equations. Math Model Methods Appl Sci 14:165–187

Carey G, Barth W, Woods JA, Kirk BS, Anderson ML, Chow S, Bangerth W (2004) Modelling error and constitutive relations in simulation of flow and transport. Int J Numerical Methods Fluids 46:1211–1236

Peterson JW, Carey GF, Knezevic DJ, Murray BT (accepted Mar. 2006) Adaptive finite element methodology for tumor angiogenesis modeling. Int J Numer Meth Eng

Simedrea P, Antiga L, Steinman DA (2006) Towards a new framework for simulating magnetic resonance imaging. In: First Canadian student conference on biomedical computing, http://cscbc2006.cs.queensu.ca/assets/documents/Papers/paper108.pdf

Schindler M, Talkner P, Hänggi P (2005) Computing stationary free-surface shapes in microfluidics. submitted to J Fluid Mech http://arxiv.org/pdf/physics/0511217

Petersen S, Dreyer D, von Estorff O (2006) Assessment of finite and spectral element shape functions for efficient iterative simulations of interior acoustics. Comput Methods Appl Mech Eng (in press)

Brinkmeier M, Nackenhorst U, Petersen S, von Estorff O (2006) A numerical model for the simulation of tire rolling noise. J Sound Vib (submitted)

Lu S, Holst MJ, Bank RE, McCulloch AD, Michailova A (2005) 3D model of synchronous calcium signaling in ventricular myocyte, biophysical society annual meeting abstract issue