SELECTED PUBLICATIONS


Article A125: Randolph E. Bank. A Two Level Solver for hp Adaptive Finite Element Equations Computing and Visualization in Science, submitted.

Article A124: Randolph E. Bank and Harry Yserentant. On the Convergence of Adaptive Feedback Loops Numerische Mathematik, submitted.

Article A123: Randolph E. Bank and Jeffrey S. Ovall. Some Remarks on Interpolation and Best Approximation Numerische Mathematik, to appear.

Article A122: Randolph E. Bank and Chris Deotte. Adventures in Adaptivity. Computing and Visualization in Science, 18, 79--92, 2017.

Article B20: Randolph E. Bank. PLTMG: A Software Package for Solving Elliptic Partial Differential Equations. Users' Guide 12.0. Department of Mathematics, University of California at San Diego, 2016.

Article A121: Randolph E. Bank, Panayot Vassilevski, and Ludmil Zikatanov. Arbitrary dimension convection-diffusion scheme for space-time discretizations. Journal of Computational and Applied Mathematics, 310, 19--31, 2017.

Article B19: Randolph E. Bank. Multigraph Users' Guide - Version 2.0. Department of Mathematics, University of California at San Diego, 2015.

Article A120: Randolph E. Bank and Chris Deotte. The influence of partitioning on domain decomposition convergence rates. Computing and Visualization in Science, 18, 53--64, 2017.

Article A119: Randolph E. Bank and Harry Yserentant. A note on interpolation, best approximation, and the saturation property. Numerische Mathematik, 131, 199--203, 2015.

Article A118: Randolph E. Bank, Aseih Parsania, and Stefan Sauter. Saturation estimates for $hp$-finite element mathods. Computing and Visualization in Science, 16, 195--218, 2013.

Article A116: Randolph E. Bank and Maximillian S. Metti. An error analysis of some higher order space-time moving finite elements. Computing and Visualization in Science, 16, 219--230, 2013.

Article A115: Randolph E. Bank, Rob Falgout, Toby Jones, Tom Manteuffel, Steve McCormick, and John Ruge. Algebraic Multigrid Domain and Range Decomposition (AMG-DD/AMG-RD). SIAM Journal on Scientific Computing, 37, s113--s136, 2015.

Article A114: Randolph E. Bank and Harry Yserentant. On the $H^1$ Stability of the $L_2$ Projection onto Finite Element Spaces. Numerische Mathematik, 126, 361-381, 2014.

Article A113: Randolph E. Bank and Hieu Nguyen. A Parallel hp-Adaptive Finite Element Method Scientific Computing and Applications VIII, Contemporary Mathematics 586, 23--33, 2013.

Article A112: Randolph E. Bank and Hieu Nguyen. Mesh Regularization in Bank-Holst Parallel hp-Adaptive Meshing Proceedings of the 20th International Symposium on Domain Decomposition Methods for Partial Differential Equations, Lecture Notes in Computational Science and Engineering 91. Springer-Verlag, 1-3-110, 2013.

Article A110: Randolph E. Bank and Hieu Nguyen. hp Adaptive Finite Elements Based on Derivative Recovery and Superconvergence Computing and Visualization in Science 14:287--299, 2012

Article A109: Randolph E. Bank, Luka Grubisic, and Jeffrey S. Ovall. A Framework for Robust Eigenvalue and Eigenvector Error Estimation and Ritz Value Convergence Enhancement Applied Numerical Mathematics, 66: 1--19, 2013.

Article A107: Randolph E. Bank and Hieu Nguyen. Domain Decomposition and hp-Adaptive Finite Elements Proceedings of the 19th International Symposium on Domain Decomposition Methods for Partial Differential Equations, Lecture Notes in Computational Science and Engineering. Springer-Verlag, pages 3--13, 2011.

Article A106: Randolph E. Bank and Harry Yserentant. Multigrid Convergence: A Brief Trip Down Memory Lane. Computing and Visualization in Science, 13:147--152, 2010.

Article A104: Randolph E. Bank, Jinchao Xu, and Bin Zheng. Superconvergent Derivative Recovery for Lagrange Triangular Elements of Degree p on Unstructured Grids SIAM J. on Numerical Analysis, 45:2032--2046 (electronic), 2007.

Article A103: Randolph E. Bank and Jeffrey S. Ovall. Dual Functions for A Parallel Adaptive Method SIAM J. on Scientific Computing, 29:1511--1524, 2007.

Article A102: Randolph E. Bank and Panayot S. Vassilevski. Convergence Analysis of a Domain Decomposition Paradigm. Computing and Visualization in Science, 11:333--350, 2008.

Article A100: Randolph E. Bank. Compatible Coarsening in the Multigraph Algorithm. Advances in Engineering Software, 38:287--294, 2007.

Article A99: Randolph E. Bank. A Domain Decomposition Solver for a Parallel Adaptive Meshing Paradigm. Proceedings of the Sixteenth International Symposium on Domain Decomposition Methods for Partial Differential Equations, Lecture Notes in Computational Science and Engineering. Springer-Verlag, pages 3--14, 2006.

Article A97: Randolph E. Bank. Some Variants of the Bank-Holst Parallel Adaptive Meshing Paradigm. Computing and Visualization in Science, 9:133--144, 2006.

Article A95: Randolph E. Bank and Shaoying Lu. A Domain Decomposition Solver for a Parallel Adaptive Meshing Paradigm SIAM J. on Scientific Computing, 26 (2004), 105-127.

Article A94: Randolph E. Bank and Michael J. Holst. A New Paradigm for Parallel Adaptive Meshing Algorithms. SIAM Review, 45 (2003) 292-323.

Article A93: Randolph E. Bank, Philip E. Gill, and Roummel F. Marcia. Interior Methods For a Class of Elliptic Variational Inequalities. Large-scale PDE-constrained Optimization, volume30 of Lecture Notes in Computational Science and Engineering, pages 218--235, Berlin, Heidelberg and New York, 2003. Springer-Verlag.

Article A92: Randolph E. Bank and Jinchao Xu. Asymptotically Exact A Posteriori Error Estimators, Part II: General Unstructured Grids. SIAM J. on Numerical Analysis, 41 (2003) 2313-2332.

Article A91: Randolph E. Bank and Jinchao Xu. Asymptotically Exact A Posteriori Error Estimators, Part I: Grids with Superconvergence. SIAM J. on Numerical Analysis, 41 (2003) 2294-2312.

Article A90: Randolph E. Bank, and R. Kent Smith. Multigraph Algorithms Based on Sparse Gaussian Elimination Gaussian Elimination. Thirteenth International Symposium on Domain Decomposition Methods for Partial Differential Equations, 2001, 15-26.

Article A89: Yingjie Liu, Randolph E. Bank, Todd F. Dupont, Sonia Garcia, and Rafael F. Santos. Symmetric Error Estimates for Moving Mesh Mixed Methods for Advection-Diffusion Equations. SIAM J. on Numerical Analysis, 40 (2003) 2270-2291.

Article A88: Randolph E. Bank and R. Kent Smith. An Algebraic Multilevel Multigraph Algorithm SIAM J. on Scientific Computing, 23 (2002) 1572-1592.

Article A87: Randolph E. Bank and Peter K. Jimack. A New Parallel Domain Decomposition Method for the Adaptive Finite Element Solution of Elliptic Partial Differential Equations. Concurrency, 13 (2001) 327-350.

Article A86: Randolph E. Bank, Peter K. Jimack, Sarfraz A. Nadeem, and Sergei V. Nepomnyaschikh. A Weakly Overlapping Domain Decomposition Preconditioner for the Finite Element Solution of Elliptic Partial Differential Equations SIAM J. on Scientific Computing, 23 (2002) 1817-1841.

Article A85: Randolph E. Bank and Michael J. Holst. A New Paradigm for Parallel Adaptive Meshing Algorithms. SIAM J. on Scientific Computing, 22 (2000), 1411-1443.

Article A83: Randolph E. Bank and Peter K. Jimack. A New Parallel Domain Decomposition Preconditioner II: Generalization to a Mesh-Free Parallel Solver. Parallel and Distributed Processing for Computational Mechanics II, (B. H. V. Topping ed.), Saxe-Coburg Publications, 1999.

Article A82: Randolph E. Bank and Peter K. Jimack. A New Parallel Domain Decomposition Preconditioner I: Application with an Adaptive Parallel Finite Element Solver. Parallel and Distributed Processing for Computational Mechanics II, (B. H. V. Topping ed.), Saxe-Coburg Publications, 1999.

Article A79: Randolph E. Bank, William M. Coughran and Lawrence C. Cowsar. Analysis of the Finite Volume Scharfetter-Gummel method for Steady Convection Diffusion Equations. Computing and Visualization in Science, 1 (1998), 123-136.

Article A78: Randolph E. Bank and Christian Wagner. Multilevel ILU Decomposition. Numerische Mathematik, 82 (1999), 543-576.

Article A77: Randolph E. Bank and R. Kent Smith. The Incomplete Factorization Multigraph Algorithm. SIAM J. on Scientific Computing, 20 (1999), 1349-1364.

Article A76: Randolph E. Bank and Sabine Gutsch. The Generalized Hierarchical Basis Two-Level Method for the Convection-Diffusion Equation on a Regular Grid. Proceedings of the Fifth European Multigrid Conference (G. Wittum, ed.). Springer-Verlag, Heidelberg, 1998,1-20.

Article A75: Randolph E. Bank and Jacques Periaux. Adaptive Algorithms and A Posteriori Error Estimates on Partitioned Meshes. In Computational Science in the 21st Century, J. Periaux, ed., J.Wiley, New York, 1997.

Article A74: Randolph E. Bank. A Simple Analysis of some A Posteriori Error Estimates. Applied Numerical Mathematics, 26 (1998), 153-164.

Article A73: Randolph E. Bank and Sabine Gutsch. Hierarchical Basis for the Convection-Diffusion Equation on Unstructured Meshes. In Ninth International Symposium on Domain Decomposition Methods for Partial Differential Equations (P. Bjorstad, M. Espedal and D. Keyes, eds.). Domain Decomposition Press, Bergen (1998), 251-265.

Article A72: Randolph E. Bank, Jun Cao, Bertrand Mantel, and Jacques Periaux. Mesh Quality Control for Industrial Navier-Stokes Problems via A Posteriori Error Estimates. Proceedings of ENUMATH-95 (A. Bespalov and Y. Kuznetsov, eds.), VSP, The Netherlands, to appear.

Article A70: Randolph E. Bank. Hierarchical Bases and the Finite Element Method. Acta Numerica 1996 (A. Iserles, ed.), Cambridge University Press (1996), 1-43.

Article A69: Randolph E. Bank and Jinchao Xu. An Algorithm for Coarsening Unstructured Meshes. Numerische Mathematik 73 (1996), 1-36.

Article A67: Randolph E. Bank and R. Kent Smith. Mesh Smoothing Using A Posteriori Error Estimates. SIAM J. Numerical Analysis, 34 (1997), 979-997.

Article A66: Randolph E. Bank and Jinchao Xu. The Hierarchical Basis Multigrid Method and Incomplete LU Decomposition. Seventh International Symposium on Domain Decomposition Methods for Partial Differential Equations (D. Keyes and J. Xu, eds.), AMS, Providence, Rhode Island (1994), 163-173.

Article A62: Randolph E. Bank and Tony F. Chan. An Analysis of the Composite Step Biconjugate Gradient Method. Numerische Mathematik, 66 (1993), 295-319.

Article A60: Randolph E. Bank and R. Kent Smith, A Posteriori Error Estimates Based On Hierarchical Bases. SIAM J. Numerical Analysis, 30 (1993), 921-935.

Article A59: Randolph E. Bank and Rafael F. Santos, Analysis of Some Moving Space-Time Finite Element Methods. SIAM J. Numerical Analysis, 31 (1993), 1-18.

Article A58: Randolph E. Bank and Mohamed Benbourenane, The Hierarchical Basis Multigrid Method for Convection Diffusion Equations. Numerische Mathematik, 61 (1992), 7-37.

Article A56: Randolph E. Bank and Bruno D. Welfert, A Posteriori Error Estimates for the Stokes Problem. SIAM J. Numerical Analysis, 28 (1991), 591-623.

Article A53: Randolph E. Bank, Josef Burgler, Wolfgang Fichtner and R. Kent Smith, Some Upwinding Techniques for Finite Element Approximations of Convection-Diffusion Equations. Numerische Mathematik, 58 (1990), 185-202.

Article A51: Randolph E. Bank, Bruno D. Welfert and Harry Yserentant. A Class of Iterative Methods for Solving Mixed Finite Element Equations. Numerische Mathematik, 56 (1990), 645-666.

Article A50: Randolph E. Bank and Donald J. Rose. On the Complexity of Sparse Gaussian Elimination. SIAM J. Scientific and Statistical Computing, 11 (1990), 145-160.

Article A46: Randolph E. Bank, and Hans D. Mittelmann. Stepsize Selection in Continuation Procedures and Damped Newton's Method. J. Comput. Appl. Math., 26 (1989), 67-78.

Article A45: Randolph E. Bank and L. Ridgway Scott. On the Conditioning of Finite Element Equations with Highly Refined Meshes. SIAM J. Numerical Analysis, 26 (1989), 1383-1394.

Article A42: Randolph E. Bank, Todd F. Dupont, and Harry Yserentant. The Hierarchical Basis Multigrid Method. Numerische Mathematik, 52 (1988), 427-458.

Article A41: Randolph E. Bank and Donald J. Rose. Some Error Estimates for the Box Method. SIAM J. Numerical Analysis, 24 (1987), 777-787.

Article A39: Randolph E. Bank and R. Kent Smith. General Sparse Elimination Requires no Permanent Integer Storage. SIAM J. Scientific and Statistical Computing, 8 (1987), 574-584.

Article A31: Randolph E. Bank and Craig C. Douglas. An Efficient Implementation for SSOR and Incomplete Factorization Preconditionings. Applied Numerical Mathematics, 1 (1985), 489-492.

Article A29: Randolph E. Bank and Craig C. Douglas. Sharp Estimates for Multigrid Rates of Convergence with General Smoothing and Acceleration. SIAM J. Numerical Analysis, 22 (1985), 617-633.

Article A28: Randolph E. Bank and Alan Weiser. Some A Posteriori Error Estimators for Elliptic Partial Differential Equations. Mathematics of Computation, 44 (1985), 283-301.

Article A23: Randolph E. Bank, Andrew H. Sherman, and Alan Weiser. Refinement Algorithms and Data Structures for Regular Local Mesh Refinement. Scientific Computing (Applications of Mathematics and Computing to the Physical Sciences) (R. S. Stepleman, ed.), North-Holland (1983), 3-17.

Article A20: Randolph E. Bank and Donald J. Rose, Analysis of a Multi-Level Iterative Method for Nonlinear Finite Element Equations. Mathematics of Computation, 39 (1982), 435-465.

Article A19: Randolph E. Bank. Analysis of a Multi-level Inverse Iteration Procedure for Eigenvalue Problems. SIAM J. Numerical Analysis, 19 (1982), 886-898.

Article A18: Randolph E. Bank and Donald J. Rose, Global Approximate Newton Methods. Numerische Mathematik, 37 (1981), 279-295.

Article A17: Randolph E. Bank. A Comparison of Two Multi-level Iterative Methods for Non-symmetric and Indefinite Elliptic Finite Element Equations. SIAM J. Numerical Analysis, 18 (1981), 724-743.

Article A15: Randolph E. Bank and Todd F. Dupont, An Optimal Order Process for Solving Finite Element Equations. Mathematics of Computation, 36 (1981), 35-51.

Article A13: Randolph E. Bank and Donal J. Rose. Parameter Selection for Newton-like Methods Applicable to Nonlinear Partial Differential Equations. SIAM J. Numerical Analysis, 17 (1980), 806-822.

Article B4: Randolph E. Bank, and Todd F. Dupont, Analysis of a Two-Level Scheme for Solving Finite Element Equations. Report CNA-159, Center for Numerical Analysis, University of Texas at Austin, May, 1980.