Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume II frontiers: Three dimensional Elliptic and Maxwell problems with applications

Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume II Frontiers: Three Dimensional Elliptic and Maxwell Problems with Applications

Volumn , Issue , 2007, Pages 1-417

  Demkowicz, Leszek ^a   Kurtz, Jason ^a   Pardo, David ^a   Paszenski, Maciek ^a   Rachowicz, Waldemar ^a   Zdunek, Adam ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85055930486     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Book

References (183)

1. M. Abramowitz and I.A. Stegun, editors. Handbook of Mathematical Functions, with Formulas, Graphs and Mathematical Tables, volume 55. National Bureau of Standards, Washington, D.C., (for sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C., 20402), 1966. Fifth printing, with corrections.
2. M. Ainsworth. A hierarchical domain decomposition preconditioner for hp finite element approximation on locally refined meshes. SIAM J. Sci. Comput. 17(6):1395–1414, 1996.
3. M. Ainsworth. A posteriori error estimation for fully discrete hierarchic models of elliptic boundary value problems on thin domains. Numer. Math. 80:325–363, 1998.
4. M. Ainsworth and M. Arnold. Construction and analysis of optimal hierarchic models of boundary value problems on thin circular and spherical geometries. SIAM J. Sci. Comput. 22:673–703, 2000.
5. M. Ainsworth and M. Arnold. Computable error bounds for some simple dimensionally reduced models on thin domains. IMA J. on Numer. Anal. 21:81– 105, 2001.
6. M. Ainsworth and J. Coyle. Conditioning of hierarchic p-version Nédélec element on meshes of curvilinear quadrilaterals and hexahedra. SIAM J. on Numer. Anal. 41(2):731–750, 2003.
7. M. Ainsworth and J. Coyle. Hierarchic finite element bases on unstructured tetrahedral meshes. Int. J. Num. Meth. Eng., 58(14):2103–2130, December 2003.
8. M. Ainsworth and L. Demkowicz. Explicit polynomial preserving trace liftings on a triangle. Math. Nachr. in print. see also ICES Report 03–47.
9. M. Ainsworth and J.T. Oden. A procedure for a posteriori error estimation for hp finite element methods. Comput. Methods Appl. Mech. Engrg. 101:73–96, 1992.
10. M. Ainsworth and J.T. Oden. A Posteriori Error Estimation in Finite Element Analysis. Wiley & Sons, New York, 2000.
11. P.R. Amestoy, I.S. Duff, J. Koster, and J.Y. L’Excellent. A fully asynchronous multifrontal solver using distributed dynamic scheduling. SIAM J. Matrix Analysis and Applications, 23(1):15–41, 2001.
12. P.R. Amestoy, I.S. Duff, and J.Y. L’Excellent. Multifrontal parallel distributed symmetric and unsymmetric solvers. Comput. Methods Appl. Mech. Engrg. 184: 501–520, 2000.
13. P.R. Amestoy, A. Guermouche, J.-Y. L’Excellent, and S. Pralet. Hybrid scheduling for the parallel solution of linear systems. Parallel Comput. 32(2):136–156, 2006.
14. H.T. Anastassiu and J.L. Volakis. The modal matching technique for electromagnetic scattering by cylindrical waveguide with canonical terminations. In IEEE AP-S International Symposium, volume 3, pages 26–29, 1995.
15. H.T. Anastassiu, J.L. Volakis, D.C. Ross, and D. Andersh. Electromagnetic scattering form simple jet engine models. IEEE Trans. Antennas Propagat. 44(3):420– 421, March 1996.
16. B.I. Anderson. Modeling and Inversion Methods for the Interpretation of Resistivity Logging Tool Response. Ph.D. thesis, Delft University of Technology, 2001.
17. D.N. Arnold, R.S. Falk, and R. Winther. Multigrid in H(div) and H(curl). Numer. Math. 85(2):197–217, 2000.
18. D.N. Arnold, B. Boffi, and R.S. Falk. Quadrilateral H(di v) finite element. I.A.N.-C.N.R, 1283:1–23, 2002.
19. D.N. Arnold and R.S. Falk. A uniformly accurate finite element method for the Reissner–Mindlin plate. SIAM J. Numer. Anal. 21:1276–1290, 1989.
20. I. Babuška and W.C. Rheinboldt. A posteriori error estimates for the finite element method. Int. J. Num. Meth. Eng. 12, 1978.
21. I. Babuška and Th. Strouboulis. The Finite Element Method and its Reliability. Clarendon Press, Oxford, 2001.
22. I. Babuška and I. Li. The hp version of the finite element method in the plate modeling problem. Comm. Appl. Numer. Methods. 8:17–26, 1992.
23. I. Babuška and L. Li. Hierarchic modeling of plates. Comput. Struct. 40:419–430, 1991.
24. I. Babuška and L. Li. The problem of plate modeling: Theoretical and computational results. Comput. Methods Appl. Mech. Engrg. 100:249–273, 1992.
25. I. Babuška and Ch. Schwab. A posteriori error estimation for hierarchic models of elliptic boundary value problems on thin domains. SIAM J. Numer. Anal. 33:221–246, 1996.
26. C. Balanis. Advanced Engineering Electromagnetics. Wiley, 1989.
27. K. Banaś. A model for parallel adaptive finite element software. Proc. Fifteen Int. Conf. on Domain Decomposition Methods. Freie Universitat Berlin, July 21–25, 2003.
28. R. Barrett, M. Berry, T.F. Chan, J. Demmel, J.M. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, and H. Van der Vost. Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods. SIAM, Philadelphia, 1994.
29. Y. Basar, U. Hanskotter, O. Kintzel, and Ch. Schwab. Simulation of large deformations in shell structures by the p-version of the finite element method. In Proc. of First MIT Conference on Computational and Solid Mechanics, pages 1–4. Elsevier Science Ltd., 2001.
30. P. Bastian, K. Birken, K. Johannsen, S. Lang, N. Neuss, and H. Rentz-Reichert UG—a flexible software toolbox for solving partial differential equations. Comput. Visual. Sci. 1(1):27–40, 1997.
31. A.C. Bauer and A.K. Patra. Robust and efficient domain decomposition preconditioners for adaptive hp finite element approximations of linear elasticity with and without discontinuous coefficients. Int. J. Num. Meth. Eng. 59(3):337–364, 2004.
32. R. Becker and R. Rannacher. Weighted a posteriori error control in FE methods. In Hans Georg et al. Bock, editor, ENUMAT 97. Proceedings of the 2nd European Conference on Numerical Mathematics and Advanced Applications, Heidelberg, Sep. 28– Oct. 3, 1997, pages 621–637, Singapore, 1998. World Scientific.
33. J.P. Bérenger. A perfectly matched layer for the absorption of electromagnetic waves. J. Comput. Phys. 114:185–200, 1994.
34. D. Boffi, M. Dauge, M. Costabel, and L. Demkowicz. Discrete compactness for the hp version of rectangular edge finite elements. SIAM J. Numer. Anal. 44(3):979–1004, 2006.
35. G. Booch, J. Rumbaugh, and I. Jacobson. The Unified Modeling Language User Guide. Addison-Wesley Professional, 1st edition, 1998.
36. J.H. Bramble. Multigrid methods. Pitman Research Notes in Mathematics Series. 294. Harlow: Longman Scientific & Technical. viii, 161 p., 1993.
37. J.H. Bramble and X. Zhang. Uniform convergence of the multigrid V-cycle for an anisotropic problem. Math. Comput. 70(234):453–470, 2001.
38. R.J. Burkholder, P.H. Pathak, and H.T. Chou. New ray and physical optics based methods for modeling duct propagation in the hybrid analysis of EM scattering by jet inlets. Technical Report Final Report 729526-1, The Ohio State University, ElectroScience Laboratory, Department of Electrical Engineering, 1320 Kinnear Road, Columbus, Ohio 43212, March 1995.
39. X. Cai and O.B. Widlund. Domain decomposition algorithms for indefinite elliptic problems. SIAM J. Sci. Stat. Comput. 13(1):243–258, 1992.
40. W. Cao and L. Demkowicz. Optimal error estimate for the projection based interpolation in three dimensions. Comput. Math. Appl. 50:359–366, 2005.
41. W. Cecot, L. Demkowicz, and W. Rachowicz. A two-dimensional infinite element for Maxwell’s equations. Comput. Methods Appl. Mech. Engrg. 188:625–643, 2000.
42. W. Cecot, L. Demkowicz, and W. Rachowicz. An hp-adaptive finite element method for electromagnetics. Part 3: A three-dimensional infinite element for Maxwell’s equations. Int. J. Num. Meth. Eng., 57:899–921, 2003.
43. CGNS (CFD General Notation System). http://www.cgns.org.
44. K.K. Chan, S.K. Wong, and E.S. Riseborough. Radar cross section modeling and measurements of inlets and cylinders with skew blades. IEEE Trans Antennas Propagat. 54(10):2930–2939, October 2006.
45. W.C. Chew and W.H. Weedon. A 3D perfectly matched medium from modified Maxwell’s equations with stretched coordinates. Microwave and Optical Technology Letters. 7(13):599–604, 1994.
46. J.R. Cho and J.T. Oden. A priori modeling error estimates of hierarchical models for elasticity problems for plate-and shell-like structures. Math. Comput. Modelling. 23:117–133, 1996.
47. J.R. Cho and J.T. Oden. A priori modeling error estimates of hierarchical models for elasticity problems for plate-and shell-like structures. Comput. Methods Appl. Mech. Engrg. 132:135–177, 1996.
48. 1, H(curl), and H(div) spaces on a cube. IRMAR Rennes, Technical Report 2007/15, Submitted to Math. Comp.
49. G. Crabtree, W. Huegle, and D. Salisbury. RCS compact range test results for a set of simple engine face models. Technical Report TM94226, GE Aircraft Engines, Cincinnati, Ohio, November 1994.
50. The Cubit geometry and mesh generation toolkit. http://sass1693.sandia.gov/cubit/cubit.html.
51. L. Demkowicz. A posteriori error analysis for steady-state Maxwell’s equations. In P. Ladavéze and J.T. Oden, editors, Advances in Adaptive Computational Methods in Mechanics. Elsevier, 1998.
52. L. Demkowicz. Edge finite elements of variable order for Maxwell’s equations. In D. Hecht, U. van Rienen, M. Günther, editors, Scientific Computing in Electrical Engineering, Lecture Notes in Computational Science and Engineering 18, pages 15–34. Springer-Verlag, Berlin, 2000. (Proceedings of the 3rd International Workshop, August 20–23, Warnemünde, Germany).
53. L. Demkowicz. Projection based interpolation. In Transactions on Structural Mechanics and Materials. Cracow University of Technology Publications, Cracow, 2004. Monograph 302, A special issue in honor of 70th Birthday of Prof. Gwidon Szefer, see also ICES Report 04-03.
54. L. Demkowicz. Fully automatic hp-adaptivity for Maxwell’s equations. Comput. Methods Appl. Mech. Engrg. 194:605–624, 2005.
55. L. Demkowicz. Polynomial exact sequences and projection-based interpolation with applications to Maxwell equations. In D. Boffi and L. Gastaldi, editors, Mixed Finite Elements, Compatibility Conditions and Applications, Lecture Notes in Mathematics. Springer-Verlag, 2007. See also ICES Report 06–12.
56. L. Demkowicz and I. Babuška. p interpolation error estimates for edge finite elements of variable order in two dimensions. SIAM J. Numer. Anal. 41(4):1195– 1208, 2003.
57. 1, H(curl), and H(div)-conforming projection-based interpolation in three dimensions. Quasi-optimal p-interpolation estimates. Comput. Methods Appl. Mech. Engrg. 194:267–296, 2005.
58. L. Demkowicz, K. Gerdes, Ch. Schwab, A. Bajer, and T. Walsh. HP90: A general and flexible Fortran 90 hp-FE code. Comput. Vis. Sci., 1:145–163, 1998.
59. L. Demkowicz, P. Monk, L. Vardapetyan, and W. Rachowicz. De Rham diagram for hp finite element spaces. Comput. Math. Appl. 39(7-8):29–38, 2000.
60. L. Demkowicz and M. Pal. An infinite element for Maxwell’s equations. Comput. Methods Appl. Mech. Engrg. 164:77–94, 1998.
61. L. Demkowicz, D. Pardo, and W. Rachowicz. 3D hp-adaptive finite element package (3Dhp90). Version 2.0. Technical Report 24, TICAM, 2002.
62. L. Demkowicz and J. Shen. A few new (?) facts about infinite elements. Comput. Methods Appl. Mech. Engrg. 2005.
63. L. Demkowicz and L. Vardapetyan. Modeling of electromagnetic absorp-tion/scattering problems using hp-adaptive finite elements. Comput. Methods Appl. Mech. Engrg. 152(1-2):103–124, 1998.
64. A. Düster, H. Bröker, and E. Rank. The p-version of the finite element method for three-dimensional curved thin walled structures. Int. J. Numer. Eng., 52:673–703, 2001.
65. J. Edlund. A Parallel, Iterative Method of Moments and Physical Optics Hybrid Solver for Arbitrary Surfaces. Ph.D. thesis, Department of Information Technology, Up-psala University, Licentiate Thesis 2001-01, 2001.
66. ∞ Collocation. Dissertation, The University of Texas, 1997.
67. H.C. Edwards. SIERRA framework version 3: Core services theory and design. Technical report, SAND2002-3616, Albuquerque, NM: Sandia National Laboratories, 2002.
68. H.C. Edwards and J.R. Stewart. SIERRA, A Software Environment for Developing Complex Multiphysics Applications. Computational Fluid and Solid Mechanics Proc. First MIT Conf., 2001.
69. H.C. Edwards, J.R. Stewart, and J.D. Zepper. Mathematical Abstractions of the SIERRA Computational Mechanics Framework. Proc. Fifth World Congress Comp. Mech. Vienna Austria, 2002.
70. Electromagnetic code consortium. http://www.arl.hpc.mil/PET/cta/cea/emcc/emcc.html.
71. F. Brezzi and M. Fortin Mixed and Hybrid Finite Element Methods. Springer-Verlag, New York, 1991.
72. I. Foster. Designing and Building Parallel Programs. http://www-unix.mcs.anl. gov/dbpp/, 1995.
73. L. Garcia, D. Pardo, and L. Demkowicz. A two-dimensional self-adaptive hp finite element method for the characterization of waveguide discontinuities. Part I: Energy-norm based automatic hp-adaptivity. Comput. Methods Appl. Mech. Engrg. 2007. accepted.
74. General electromagnetic solvers project.
75. P. Geng, T.J. Oden, and R.A. Van de Geijn. A parallel multifrontal algorithm and its implementation. Comput. Methods Appl. Mech. Engrg. 149:289–301, 1997.
76. J. Gopalakrishnan and L. Demkowicz. Quasioptimality of some spectral mixed methods. J. Comput. Appl. Math. 167(1), May 2004.
77. J. Gopalakrishnan, L.E. García-Castillo, and L. Demkowicz. Nédélec spaces in affine ccordinates. Comput. Math. Appl. 49:1285–1294, 2005.
78. J. Gopalakrishnan and J.E. Pasciak. Overlapping Schwarz preconditioners for indefinite time harmonic Maxwell equations. Math. Comput. 72(241):1–15, 2003.
79. J. Gopalakrishnan, J.E. Pasciak, and L. Demkowicz. Analysis of a multigrid algorithm for time harmonic Maxwell equations. SIAM J. Numer. Anal. 42(1): 90–108, 2004.
80. W.J. Gordon and C.A. Hall. Transfinite element methods: Blending function interpolation over arbitrary curved element domain. Numer. Math. 21:109–129, 1973.
81. V. Gradinaru and R. Hiptmair. Whitney elements on pyramids. ETNA, 8:154– 168, 1999. Also: Report 113, SFB 382, Universität Tübingen, March 1999.
82. R. Hiptmair. Multigrid method for Maxwell’s equations. SIAM J. Numer. Anal. 36(1):204–225, 1998.
83. http://www.cs.sandia.gov/Zoltan/. Zoltan: Data-management services for parallel applications, 2004.
84. Y.-S. Hwang, B. Moon, S.D. Sharma, R. Ponnusamy, R. Das, and J.H. Saltz. Runtime and language support for compiling adaptive irregular programs on distributed memory machines. Software—Practice and Experience, 25(6):597–621, 1995.
85. ICEM CFD Hexa. http://www-berkeley.ansys.com/hexa/index.html.
86. F. Ihlenburg. Finite Element Analysis of Acoustic Scattering. Springer-Verlag, New York, 1998.
87. B.M. Irons. A frontal solution program for finite element analysis. J. Numer. Methods Eng. 2:5–32, 1970.
88. Ch. Jhurani and L. Demkowicz. Dimensional reduction for a lattice-like mass-spring polymer model using hp-adaptivity. Comput. Methods Mater Sci. 6(3–4), 2006.
89. J. Jin. Electromagnetic scattering from large, deep, and arbitrarily-shaped open cavities. Electromagnetics, 18:3–34, 1998.
90. T. Joffrain, E.S. Quintana-Orti, and R. van de Geijn. Updating an LU factorization and its application to scalable out-of-core. SIAM J. Sci. Comput. 2006. submitted.
91. D.S. Jones. Acoustic and Electromagnetic Waves. Clarendon Press, Oxford, 1989.
92. G.E. Karniadakis and S.J. Sherwin. Spectral/hp Element Methods for CFD. Oxford University Press, 1999.
93. A.A. Kaufman. The electrical field in a borehole with casing. Geophys. 55(1):29– 38, 1990.
94. M.S. Khaira, G.L. Miller, and T.J. Sheffler. Nested dissection: A survey and comparison of various nested dissection algorithms. Technical report, CMU-CS-92-106R, Computer Science Department, Carnegie Mellon University, 1992.
95. N.W. Kolkunov. Foundation of Solving Elastic Shells. Izdatielstwo Wyzszaja Szkola, Moscow, second edition, 1972.
96. J. Kurtz. Fully Automatic hp-Adaptivity for Acoustic and Electromagnetic Scattering in Three Dimensions. Ph.D. thesis, The University of Texas at Austin, Austin, TX 78712, February 2007. Computational and Applied Mathematics.
97. J. Kurtz and L. Demkowicz. A fully automatic hp-adaptivity for elliptic PDEs in three dimensions. Comput. Methods Appl. Mech. Engrg. 2007. Special Issue in Honor of 80th Birthday of Prof. Ivo Babu˘ska, in print.
98. P. Ladevéze and D. Leguillon. Error estimate procedure in the Finite Element Method and applications. SIAM J. Numer. Anal. 20:1491–1506, 1983.
99. P. Ladevéze and E.A.W. Maunder. A general method for recovering equilibrating element tractions. Comput. Methods Appl. Mech. Engrg. 137:111–151, 1996.
100. A. Laszloffy, J. Long, and A.K. Patra. Simple data management, scheduling and solution strategies for managing the irregularities in parallel adaptive hp finite element simulations. Parallel Comput. 26:1765–1788, 2000.
101. P.D. Ledger, K. Morgan, O. Hassan, and N.P. Weatherill. Arbitrary order edge elements for electromagnetic scattering simulations using hybrid meshes and a PML. Int. J. Num. Meth. 55:339–358, 2002.
102. Ch.S. Lee and Sh.W. Lee. RCS of a coated circular waveguide terminated by a perfect conductor. IEEE Trans. Antennas Propagat. 35(4):391–398, April 1987.
103. L.Li. Discretization of the Timoshenko beam problem by the p and hp versions of the finite element method. Numer. Math. 57:413–420, 1990.
104. J.R. Lovell. Finite element methods in resistivity logging. Ph.D. thesis, Delft University of Technology, 1993.
105. A. Majda. Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, volume 53 of Applied Mathematical Sciences. Springer-Verlag, New York, 1984.
106. J. Meixner and W. Andrzejewski. Strenge theorie der beugung ebener elektro-magnetischer wellen and der vollkommen leitenden kreissheibe und and der kreisformingen offnung im vollkommend leitenden ebenen schirm. Ann. Physik. 7:157–168, 1950.
107. J.M. Melenk, K. Gerdes, and C. Schwab. Fully discrete hp finite elements: fast quadrature. Comput. Meth. Appl. Mech. Engrg. 190:4339–4364, 2001.
108. J. Merlin, S. Baden, S. Fink, and B. Chapman. Multiple Data Parallelism with HPF and KeLP. Elsevier Science, preprint, 1998.
109. Ch. Michler, L. Demkowicz, J. Kurtz, and D. Pardo. Improving the performance of perfectly matched layers by means of hp-adaptivity. Numer. Meth. Part. D. E. 2007. Published online in Wiley Inter Science, DOI 10.1002/num. 20252.
110. P. Monk. On the p-and hp-extension of Nédélec’s curl-conforming elements. J. Comput. Appl. Math. 53:117–137, 1994.
111. P. Monk. Finite Element Methods for Maxwell’s Equations. Numerical Mathematics and Scientific Computation. Oxford University Press, 2003.
112. MUMPS: a multifrontal massively parallel sparse direct solver. http://www.enseeiht.fr/lima/apo/MUMPS/.
113. L.A. Muth, R.C. Wittmann, and B.M. Kent. Interlaboratory comparisons in radar cross section measurment assurance. In AMTA 97, 19th Meeting & Symposium, pages 297–302, Historic Boston Park Plaza Hotel, Boston, Massachusetts, November 1997.
114. N. Nigam and J. Phillips. Higher-order finite elements on pyramids. in preparation.
115. 3 . Numer. Math. 35:315–341, 1980.
116. 3 . Numer. Math. 50:57–81, 1986.
117. NetCDF (network common data form). http://my.unidata.ucar.edu/software/netcdf/index.html.
118. National Institute of Standards and Technology. Electromagnetics division. Metrology for Radar Cross Section systems.
119. F. Obelleiro-Basteiro, J.L. Rodriguez, and R.J. Burkholder. An iterative physical optics approach for analyzing the electromagnetic scattering by large open-ended cavities. IEEE Trans. Antennas Propagat. 43(4):356–361, April 1995.
120. J.T. Oden and S. Prudhomme. Goal-oriented error estimation and adaptivity for the Finite Element Method. Comput. Math. Appl. 41:735–756, 2001.
121. J.T. Oden and J.R. Cho. Adaptive hpq-finite element methods of hierarchical models for plate-and shell-like structures. Comput. Methods Appl. Mech. Engrg. 236:317–345, 1996.
122. J.T. Oden and L.F. Demkowicz. Applied Functional Analysis for Science and Engineering. CRC Press, Boca Raton, 1996.
123. J.T. Oden, W. Wu, and M. Ainsworth. Three step hp adaptive strategy for the incompressible Navier–Stokes equations. In J.E. Flaherty and I. Babu˘ska, editors, Modeling, Mesh Generation and Adaptive Numerical Methods for Partial Differential Equations. IMA Minnesota, 1995.
124. M. Paraschivoiu, J. Perare, and A.T. Patera. A posteriori finite element bounds for linear functional outputs of elliptic partial differential equations. Comput. Methods Appl. Mech. Engrg, 150:289–312, 1997.
125. D. Pardo. Integration of hp-adaptivity with a two grid solver: applications to electromagnetics. Ph.D. thesis, The University of Texas at Austin, April 2004.
126. D. Pardo and L. Demkowicz. Integration of hp-adaptivity with a two grid solver for elliptic problems. Comput. Methods Appl. Mech. Engrg. 195, 2006.
127. D. Pardo, L. Demkowicz, and J. Gopalakrishnan. Integration of hp-adaptivity and a two grid solver for electromagnetic problems. Comput. Methods Appl. Mech. Engrg. 195:2533–2573, 2006.
128. D. Pardo, L. Demkowicz, C. Torres-Verdin, and C. Michler. PML Enhanced with a Self-Adaptive Goal-Oriented hp Finite-Element Method and Applications to Through-Casing Borehole Resistivity Measurements. Submitted to IEEE Transactions on Antennas and Propagation (TAP AP0604-0392). Preprint available at: www.ices.utexas.edu/%7Epardo, 2006.
129. D. Pardo, L. Demkowicz, C. Torres-Verdin, and M. Paszynski. A goal oriented hp-adaptive finite element strategy with electromagnetic applications. Part II: Electrodynamics. Comput. Methods Appl. Mech. Engrg. Vol. 196, No. 37–40, pp. 3585–3597, 2007.
130. D. Pardo, L. Demkowicz, C. Torres-Verdin, and M. Paszynski. Simulation of resistivity logging-while-drilling (LWD) measurements using a self-adaptive goal-oriented hp-finite element method. SIAM J. Appl. Math. 66:2085–2106, 2006.
131. D. Pardo, L. Demkowicz, C. Torres-Verdin, and L. Tabarovsky. A goal-oriented hp-adaptive finite element method with electromagnetic applications. Part I: Electrostatics. Int. J. Numer. Methods Eng. 65:1269–1309, 2006.
132. D. Pardo, L. Garcia, and L. Demkowicz. A two-dimensional self-adaptive hp finite element method for the characterization of waveguide discontinuities. Part II: Goal-oriented hp-adaptivity. Comput. Methods Appl. Mech. Engrg. 2007, accepted.
133. D. Pardo, M. Paszyński, and C. Torres-Verdin. Fast numerical simulations of 3D DC borehole resistivity measurements with a parallel self-adaptive goal-oriented finite element formulation. Technical report, Sixth Annual Report of Joint Industry Research Consortium on Formation Evaluation, The University of Texas at Austin, August 16–18, 2006.
134. D. Pardo, C. Torres-Verdin, and L. Demkowicz. Feasibility Study for Two-Dimensional Frequency Dependent Electromagnetic Sensing Through Casing. Geophysics. Accepted. Preprint available at: www.ices.utexas.edu/%7Epardo, 2006.
135. D. Pardo, C. Torres-Verdin, and L. Demkowicz. Simulation of multi-frequency borehole resistivity measurements through metal casing using a goal-oriented hp-finite element method. IEEE T. Geosci. Remote. 44:2125–2135, 2006.
136. M. Paszyński, L. Demkowicz, and D. Pardo. Verification of goal-oriented hp-adaptivity. Comput. Math. Appl. 50:1395–1404, 2005.
137. M. Paszyński and K. Milfeld. h-relation personalized communication strategy for hp-adaptive computations. Technical Report 04-40, ICES Report, 2004.
138. M. Paszyński, J. Kurtz, and L. Demkowicz. Parallel, fully automatic hp-adaptive 2D finite element package. Comput. Methods Appl. Mech. Engrg. 195(7-8):711–741, 2005.
139. M. Paszyński and P. Maciol. Application of fully automatic 3D hp adaptive code to orthotropic heat transfer in structurally graded materials. J. Mater. Process. Technol. 177(1–3):68–71, 2006.
140. P.H. Pathak and R.J. Burkholder. Modal, ray and beam techniques for analyzing the EM scattering by open-ended waveguide cavities. IEEE Trans. Antennas Propagat. 37(5):635–647, May 1989.
141. A. Patra. Parallel hp Adaptive Finite Element Analysis for Viscous Incompressible Fluid. Dissertation, University of Texas at Austin, 1995.
142. A. Patra and D. Kim. Efficient mesh partitioning for adaptive hp finite element meshes. Proc. Ninth Int. Conf. on Domain Decomposition Methods, The University of Greenwich, 1998.
143. L.F. Pavarino and O.B. Widlund. A polylogarithmic bound for iterative subtruc-turing method for spectral elements in three dimensions. SIAM J. Numer. Anal. 33(4):1303–1335, 1996.
144. P.G. Petropoulos. An analytical study of the discrete perfectly matched layer for the time-domain Maxwell equations in cylindrical coordinates. IEEE Trans. Antennas Propagat. 51(7):1671–1675, 2003.
145. G. Pike, L. Semenzato, P. Colella, and P.N. Hilfinger. Parallel 3D Adaptive Mesh Refinement in Titanium. Proc. Ninth SIAM Conf. on Parallel Processing for Scientific Computing, San Antonio, Texas, 1999.
146. W. Rachowicz, D. Pardo, and L. Demkowicz. Fully automatic hp-adaptivity in three dimensions. Comput. Methods Appl. Mech. Engrg., 195:4816–4842, 2006.
147. W. Rachowicz and L. Demkowicz. An hp-adaptive finite element method for electromagnetics. Part 1: Data structure and constrained approximation. Comput. Methods Appl. Mech. Engrg. 187:625–643, 2000. see also TICAM Report 98–15.
148. W. Rachowicz and L. Demkowicz. An hp-adaptive finite element method for electromagnetics. Part 2: A 3D implementation. Internat. J. Numer. Methods Engrg. 53(1):147–180, 2002. p and hp finite element methods: mathematics and engineering practice (St. Louis, MO, 2000).
149. W. Rachowicz and A. Zdunek. An hp-adaptive finite element method for scattering problems in electromagnetics. Int. J. Numer. Meth. Engrg., 62(9):1226–1249, March 2005.
150. E. Rank, A. Duester, and Z. Alam. Adaptive computation of thin-walled structures based on high order solid finite elements. In Proceedings of WCCM VI with APCOM’04, Sept. 5–10, 2004, Beijing, China. Tsinghua University Press and Springer-Verlag, 2004.
151. C.J. Reddy and M.D. Deshpande. User’s Manual for FEMOM3DS. National Aeronautics and Space Administration, NASA, Langley Research Center, Hampton, Virginia, 23681-0001, version 1.0 edition, 1997. Contractor Report 201730.
152. J.F. Remacle, X. Li, M.S. Shephard, and J.E. Flaherty. Anisotropic adaptive simulations of transient flows using discontinuous Galerkin methods. Int. J. Num. Meth. Eng. 99(1–6), 2000.
153. W.C. Rheinboldt and C.K. Mesztenyi. On a data structure for adaptive finite element mesh refinements. ACM Transactions on Mathematical Software, 6(2):166– 187, 1980.
154. 1, H(curl) and H(div) extension operators on a tetrahedron. in preparation, 2007.
155. Ch. Schwab. A posteriori modeling error estimation for hierarchic plate models. Numer. Math. 74:221–259, 1996.
156. N. Sehlstedt, A. Zdunek, W. Rachowicz, L. Demkowicz, and J.T. Oden. EMCC— open pipe code assessment FOI, PK and ICES cooperative results. Technical Report FOI-R-1662-SE, Swedish Defence Research Agency, Systems Technology, SE-164 90 Stockholm, Sweden, June 2004.
157. J.R. Shewchuk. An introduction to the conjugate gradient algorithm without the agonizing pain. Technical Report 0, School of Computer Science, Carnegie Mellon University, 1994.
158. B.F. Smith, P.E. Bjorstad, and W.D. Gropp. Domain Decomposition. Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University Press, New York, 1996.
159. E. Stein, W. Rust, and S. Ohnimus. h-and d-adaptive FE methods for two-dimensional structural problems including post-buckling of shells. Comput. Methods Appl. Mech. Engrg. 101:315–354, 1992.
160. J.R. Stewart and H.C. Edwards. SIERRA framework version 3: h-adaptivity design and use. Technical report, SAND2002-4016, Albuquerque, NM: Sandia National Laboratories, 2002.
161. B. Szabo, A. Duester, and E. Rank. The p-version of the Finite Element Method. In Encyclopedia of Computational Mechanics. John Wiley & Sons, 2004.
162. B.A. Szabo and G.J. Sharmann. Hierarchic plate and shell models based on p-extensions. Int. J. Num. Meth. Eng. 26:1855–1881, 1988.
163. C.-T. Tai. Dyadic Green Functions in Electromagnetic Theory. IEEE Press, New York, second edition, 1994.
164. A. Tosseli and O.B. Widlund. Domain Decomposition Methods-Algorithms and Theory. Comput. Math. Springer, 2005.
165. L. Vardapetyan and L. Demkowicz. hp-Adaptive finite elements in electromagnetics. Comput. Methods Appl. Mech. Engrg. 169:331–344, 1999.
166. M. Vogelius and I. Babuška. On a dimensional reduction method I. The optimal selection of basis functions. Math. Comp. 37:31–46, 1981.
167. M. Vogelius and I. Babuška. On a dimensional reduction method II. Some approximation-theoretical results. Math. Comp. 37:47–68, 1981.
168. M. Vogelius and I. Babuška. On a dimensional reduction method III. A posteriori error estimation and an adaptive approach. Math. Comp. 37:361–384, 1981.
169. T. Walsh and L. Demkowicz. A parallel multifrontal solver for hp-adaptive finite elements. Technical Report 99/1, TICAM, The University of Texas at Austin, Austin, TX 78712, 1999.
170. J.P. Webb. Hierarchical vector based funtions of arbitrary order for triangular and tetrahedral finite elements. IEEE Antennas Propagat. Mag. 47(8):1244–1253, 1999.
171. www.netlib.org/lapack. Linear Algebra Package., 2006.
172. Z. Xiang and T.-T. Chia. A hybrid BEM/WTM approach for analysis of the EM scattering from large open-ended cavities. IEEE Trans. Antennas Propagat. 49(2):165–173, February 2001.
173. J. Xu. Iterative methods by space decomposition and subspace correction. SIAM Rev. 34(4):581–613, 1992.
174. K. Yelick et al. Titanium: A High-Performance Java Dialect. ACM 1998 Workshop on Java for High-Performance Network Computing, Stanford, California, 1998.
175. S. Zaglmayr. Higher-order exact sequence for pyramid. in preparation.
176. S. Zaglmayr. High Order Finite Element Methods for Electromagnetic Field Computation. Ph.D. thesis, Johannes Kepler University, Linz, July 2006.
177. G. Zboiński. Application of the three-dimensional triangular-prism hpq adaptive finite element method to plate and shell analysis. Comput. Struct. 65:497–514, 1997.
178. G. Zboiński and L. Demkowicz. Application of the 3D hpq adaptive finite element for plate and shell analysis. Technical Report 94-13, The University of Texas at Austin, ICAM, Austin, TX 78712, 1994.
179. G. Zboiński and W. Ostachowicz. An algorithm of a family of 3D-based solid-to-shell transition, hpq / hp-adaptive finite elements. J. Theoret. Appl. Mech. 38:791– 806, 2000.
180. A. Zdunek and W. Rachowicz. A goal-oriented hp-adaptive finite element approach to radar scattering problems. Comput. Methods Appl. Mech. Engrg. 194: 657–674, 2005.
181. A. Zdunek, W. Rachowicz, and N. Sehlstedt. Toward hp-adaptive solution of 3D electromagnetic scattering from cavities. Comput. Math. Appl. 49:23–38, 2005.
182. G. Zumbusch. Simultaneous hp Adaption in Multilevel Finite Elements. Shaker Verlag, Aachen, 1996.
183. H. T. Anastassiu. NATO-SET85, (RTG-049) Radar Signature Prediction of Cavities on Aircrafts, Vehicles and Ships, Private communication.