A rule of thumb for choosing points-per-wavelength for finite difference approximations of Helmholtz problems.

Jeffrey W. Banks http://www.overtureframework.org/banks/banks.html https://scholar.google.com/citations?user=R236ICAAAAAJ https://orcid.org/0000-0001-6413-5113

Daniel Appelö Jeffrey W. Banks William D. Henshaw Donald W. Schwendeman A rule of thumb for choosing points-per-wavelength for finite difference approximations of Helmholtz problems. 2026 114703 553 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2026.114703 db/journals/jcphy/jcphy553.html#AppeloBHS26 streams/journals/jcphy

Daniel Appelö Jeffrey W. Banks William D. Henshaw Ngan Le Donald W. Schwendeman EigenWave: An optimal O(N) method for computing eigenvalues and eigenvectors by time-filtering the wave equation. 2026 114758 555 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2026.114758 db/journals/jcphy/jcphy555.html#AppeloBHLS26 streams/journals/jcphy

Jeffrey W. Banks Jalal Shatah A new approach to direct discretization of wave kinetic equations with application to a nonlinear Schrödinger system in 2D. 2026 114770 555 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2026.114770 db/journals/jcphy/jcphy555.html#BanksS26 streams/journals/jcphy

Daniel Appelö Jeffrey W. Banks William D. Henshaw Donald W. Schwendeman An \({O(N)}\) Helmholtz Solver Using WaveHoltz and Overset Grids. 2026 1367- 48 SIAM J. Sci. Comput. 3 https://doi.org/10.1137/25m1749347 db/journals/siamsc/siamsc48.html#AppeloBHS26 streams/journals/siamsc

Peter Lindstrom 0001 Jeffrey Hittinger James Diffenderfer Alyson Fox Daniel Osei-Kuffuor Jeffrey W. Banks ZFP: A compressed array representation for numerical computations. 104-122 2025 39 Int. J. High Perform. Comput. Appl. 1 https://doi.org/10.1177/10943420241284023 db/journals/ijhpca/ijhpca39.html#LindstromHDFOB25 streams/journals/ijhpca

Allison M. Carson Jeffrey W. Banks William D. Henshaw Donald W. Schwendeman High-order accurate implicit-explicit time-stepping schemes for wave equations on overset grids. 113513 2025 520 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2024.113513 db/journals/jcphy/jcphy520.html#CarsonBHS25 streams/journals/jcphy

Jeffrey W. Banks William D. Henshaw On the Coefficients in Finite Difference Series Expansions of Derivatives. 2009-2025 2025 63 SIAM J. Numer. Anal. 5 https://doi.org/10.1137/25m1731782 db/journals/siamnum/siamnum63.html#BanksH25 streams/journals/siamnum

Daniel Appelö Jeffrey W. Banks William D. Henshaw Donald W. Schwendeman An Optimal O(N) Helmholtz Solver for Complex Geometry using WaveHoltz and Overset Grids. 2025 April abs/2504.03074 CoRR https://doi.org/10.48550/arXiv.2504.03074 db/journals/corr/corr2504.html#abs-2504-03074 streams/journals/corr

Daniel Appelö Jeffrey W. Banks William D. Henshaw Ngan Le Donald W. Schwendeman EigenWave: An Optimal O(N) Method for Computing Eigenvalues and Eigenvectors by Time-Filtering the Wave Equation. 2025 July abs/2507.18282 CoRR https://doi.org/10.48550/arXiv.2507.18282 db/journals/corr/corr2507.html#abs-2507-18282 streams/journals/corr

Daniel Appelö Francis Appiah Jeffrey W. Banks Cassandra Carrick William D. Henshaw Donald W. Schwendeman A Multi-Frequency Helmholtz Solver Based on the WaveHoltz Algorithm. 2025 July abs/2507.23613 CoRR https://doi.org/10.48550/arXiv.2507.23613 db/journals/corr/corr2507.html#abs-2507-23613 streams/journals/corr

Jeffrey W. Banks Jalal Shatah A New Approach to Direct Discretization of Wave Kinetic Equations with Application to a Nonlinear Schrodinger System in 2D. 2025 September abs/2509.03432 CoRR https://doi.org/10.48550/arXiv.2509.03432 db/journals/corr/corr2509.html#abs-2509-03432 streams/journals/corr

William J. Arrighi Jeffrey W. Banks Richard Berger Thomas Chapman Andre Gianesini Odu J. Gorman A new approach to the evaluation and solution of the relativistic kinetic dispersion relation and verification with continuum kinetic simulation. 113001 2024 508 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2024.113001 db/journals/jcphy/jcphy508.html#ArrighiBBCOG24

Allison M. Carson Jeffrey W. Banks William D. Henshaw Donald W. Schwendeman High-order Accurate Implicit-Explicit Time-Stepping Schemes for Wave Equations on Overset Grids. 2024 abs/2404.14592 CoRR https://doi.org/10.48550/arXiv.2404.14592 db/journals/corr/corr2404.html#abs-2404-14592

Ge Yan 0004 Sharanjeet Kaur Jeffrey W. Banks Jason E. Hicken Entropy-stable discontinuous Galerkin difference methods for hyperbolic conservation laws. 114885 2023 422 J. Comput. Appl. Math. https://doi.org/10.1016/j.cam.2022.114885 https://www.wikidata.org/entity/Q115580968 db/journals/jcam/jcam422.html#YanKBH23

Jeffrey W. Banks William D. Henshaw A. Newell Donald W. Schwendeman Fractional-step finite difference schemes for incompressible elasticity on overset grids. 112221 2023 September 488 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2023.112221 db/journals/jcphy/jcphy488.html#BanksHNS23

Jordan B. Angel Jeffrey W. Banks Allison M. Carson William D. Henshaw Efficient Upwind Finite-Difference Schemes for Wave Equations on Overset Grids. 2703- 2023 October 45 SIAM J. Sci. Comput. 5 https://doi.org/10.1137/22m1516178 db/journals/siamsc/siamsc45.html#AngelBCH23

Qing Xia 0006 Jeffrey W. Banks William D. Henshaw Alexander V. Kildishev Gregor Kovacic Ludmila J. Prokopeva Donald W. Schwendeman High-order accurate schemes for Maxwell's equations with nonlinear active media and material interfaces. 111051 2022 456 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2022.111051 db/journals/jcphy/jcphy456.html#XiaBHKKPS22

Jeffrey W. Banks Benjamin Brett Buckner Thomas M. Hagstrom Continuous/Discontinuous Galerkin Difference Discretizations of High-Order Differential Operators. 45 2022 92 J. Sci. Comput. 2 https://doi.org/10.1007/s10915-022-01891-y https://www.wikidata.org/entity/Q114225554 db/journals/jscic/jscic92.html#BanksBH22

Nour G. Al Hassanieh Jeffrey W. Banks William D. Henshaw Donald W. Schwendeman Local Compatibility Boundary Conditions for High-Order Accurate Finite-Difference Approximations of PDEs. 3645- 2022 44 SIAM J. Sci. Comput. 6 https://doi.org/10.1137/21m1458454 db/journals/siamsc/siamsc44.html#HassaniehBHS22

Jeffrey W. Banks Benjamin Brett Buckner Thomas M. Hagstrom Karl Juhnke Discontinuous Galerkin Galerkin Differences for the Wave Equation in Second-Order Form. A1497-A1526 2021 43 SIAM J. Sci. Comput. 2 https://doi.org/10.1137/20M1328671 db/journals/siamsc/siamsc43.html#BanksBHJ21

Ge Yan 0004 Sharanjeet Kaur Jeffrey W. Banks Jason E. Hicken Entropy-stable discontinuous Galerkin difference methods for hyperbolic conservation laws. 2021 abs/2103.03826 CoRR https://arxiv.org/abs/2103.03826 db/journals/corr/corr2103.html#abs-2103-03826

Qing Xia 0006 Jeffrey W. Banks William D. Henshaw Alexander V. Kildishev Gregor Kovacic Ludmila J. Prokopeva Donald W. Schwendeman High-order accurate schemes for Maxwell's equations with nonlinear active media and material interfaces. 2021 abs/2108.09519 CoRR https://arxiv.org/abs/2108.09519 db/journals/corr/corr2108.html#abs-2108-09519

Nour G. Al Hassanieh Jeffrey W. Banks William D. Henshaw Donald W. Schwendeman Local Compatibility Boundary Conditions for High-Order Accurate Finite-Difference Approximations of PDEs. 2021 abs/2111.02915 CoRR https://arxiv.org/abs/2111.02915 db/journals/corr/corr2111.html#abs-2111-02915

Jeffrey W. Banks Benjamin Brett Buckner William D. Henshaw Michael J. Jenkinson Alexander V. Kildishev Gregor Kovacic Ludmila J. Prokopeva Donald W. Schwendeman A high-order accurate scheme for Maxwell's equations with a Generalized Dispersive Material (GDM) model and material interfaces. 109424 2020 412 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2020.109424 db/journals/jcphy/jcphy412.html#BanksBHJKKPS20

J. Jacangelo Jeffrey W. Banks Thomas M. Hagstrom Galerkin Differences for High-Order Partial Differential Equations. B447-B471 2020 42 SIAM J. Sci. Comput. 2 https://doi.org/10.1137/19M1259456 db/journals/siamsc/siamsc42.html#JacangeloBH20

Jordan B. Angel Jeffrey W. Banks William D. Henshaw Michael J. Jenkinson Alexander V. Kildishev Gregor Kovacic Ludmila J. Prokopeva Donald W. Schwendeman A high-order accurate scheme for Maxwell's equations with a generalized dispersive material model. 411-444 2019 378 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2018.11.021 https://www.wikidata.org/entity/Q128878891 db/journals/jcphy/jcphy378.html#AngelBHJKKPS19

Jeremy E. Kozdon Lucas C. Wilcox Thomas M. Hagstrom Jeffrey W. Banks Robust approaches to handling complex geometries with Galerkin difference methods. 483-510 2019 392 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2019.04.031 https://www.wikidata.org/entity/Q127926592 db/journals/jcphy/jcphy392.html#KozdonWHB19

Daniel A. Serino Jeffrey W. Banks William D. Henshaw Donald W. Schwendeman A stable added-mass partitioned (AMP) algorithm for elastic solids and incompressible flow. 2019 399 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2019.108923 db/journals/jcphy/jcphy399.html#SerinoBHS19

Thomas M. Hagstrom Jeffrey W. Banks Benjamin Brett Buckner Karl Juhnke Discontinuous Galerkin Difference Methods for Symmetric Hyperbolic Systems. 1509-1526 2019 81 J. Sci. Comput. 3 https://doi.org/10.1007/s10915-019-01070-6 https://www.wikidata.org/entity/Q126992449 db/journals/jscic/jscic81.html#HagstromBBJ19

Daniel A. Serino Jeffrey W. Banks William D. Henshaw Donald W. Schwendeman A Stable Added-Mass Partitioned (AMP) Algorithm for Elastic Solids and Incompressible Flow: Model Problem Analysis. A2464-A2484 2019 41 SIAM J. Sci. Comput. 4 https://doi.org/10.1137/18M1232358 db/journals/siamsc/siamsc41.html#SerinoBHS19

Jeffrey W. Banks Andre Gianesini Odu Richard Berger Thomas Chapman William J. Arrighi Stephan Brunner High-Order Accurate Conservative Finite Difference Methods for Vlasov Equations in 2D+2V. B953-B982 2019 41 SIAM J. Sci. Comput. 5 https://doi.org/10.1137/19M1238551 db/journals/siamsc/siamsc41.html#BanksOBCAB19

Michael J. Jenkinson Jeffrey W. Banks High-order accurate FDTD schemes for dispersive Maxwell's equations in second-order form using recursive convolutions. 192-218 2018 336 J. Comput. Appl. Math. https://doi.org/10.1016/j.cam.2017.12.016 db/journals/jcam/jcam336.html#JenkinsonB18

Jordan B. Angel Jeffrey W. Banks William D. Henshaw High-order upwind schemes for the wave equation on overlapping grids: Maxwell's equations in second-order form. 534-567 2018 352 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2017.09.037 db/journals/jcphy/jcphy352.html#AngelBH18

Jeffrey W. Banks Thomas M. Hagstrom J. Jacangelo Galerkin Differences for acoustic and elastic wave equations in two space dimensions. 864-892 2018 372 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2018.06.029 db/journals/jcphy/jcphy372.html#BanksHJ18

Jeffrey W. Banks William D. Henshaw Donald W. Schwendeman Qi Tang 0001 A stable partitioned FSI algorithm for rigid bodies and incompressible flow in three dimensions. 455-492 2018 373 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2018.06.072 db/journals/jcphy/jcphy373.html#BanksHST18

Jeffrey W. Banks William D. Henshaw Donald W. Schwendeman Qi Tang 0001 A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part I: Model problem analysis. 432-468 2017 343 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2017.01.015 db/journals/jcphy/jcphy343.html#BanksHST17

Jeffrey W. Banks William D. Henshaw Donald W. Schwendeman Qi Tang 0001 A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part II: General formulation. 469-500 2017 343 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2017.04.064 db/journals/jcphy/jcphy343.html#BanksHST17a

Fanlong Meng Jeffrey W. Banks William D. Henshaw Donald W. Schwendeman A stable and accurate partitioned algorithm for conjugate heat transfer. 51-85 2017 344 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2017.04.052 db/journals/jcphy/jcphy344.html#MengBHS17

Jeffrey W. Banks William D. Henshaw Ashwana K. Kapila Donald W. Schwendeman An added-mass partition algorithm for fluid-structure interactions of compressible fluids and nonlinear solids. 1037-1064 2016 305 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2015.10.043 db/journals/jcphy/jcphy305.html#BanksHKS16

Longfei Li William D. Henshaw Jeffrey W. Banks Donald W. Schwendeman Alex Main A stable partitioned FSI algorithm for incompressible flow and deforming beams. 272-306 2016 312 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2016.02.002 db/journals/jcphy/jcphy312.html#LiHBSM16

Jeffrey W. Banks Thomas M. Hagstrom On Galerkin difference methods. 310-327 2016 313 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2016.02.042 db/journals/jcphy/jcphy313.html#BanksH16

Jeffrey W. Banks William D. Henshaw Donald W. Schwendeman An analysis of a new stable partitioned algorithm for FSI problems. Part II: Incompressible flow and structural shells. 399-416 2014 268 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2014.03.004 db/journals/jcphy/jcphy268.html#BanksHS14

Jeffrey W. Banks William D. Henshaw Donald W. Schwendeman An analysis of a new stable partitioned algorithm for FSI problems. Part I: Incompressible flow and elastic solids. 108-137 2014 269 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2014.03.006 db/journals/jcphy/jcphy269.html#BanksHS14a

Jeffrey W. Banks A note on the convergence of Godunov type methods for shock reflection problems. 19-23 2013 66 Comput. Math. Appl. 1 https://doi.org/10.1016/j.camwa.2013.04.024 db/journals/cma/cma66.html#Banks13

Jeffrey A. F. Hittinger Jeffrey W. Banks Block-structured adaptive mesh refinement algorithms for Vlasov simulation. 118-140 2013 241 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2013.01.030 db/journals/jcphy/jcphy241.html#HittingerB13

Jeffrey W. Banks William D. Henshaw Björn Sjögreen A stable FSI algorithm for light rigid bodies in compressible flow. 399-430 2013 245 J. Comput. Phys. https://doi.org/10.1016/j.jcp.2013.02.050 db/journals/jcphy/jcphy245.html#BanksHS13

Jeffrey W. Banks Tariq D. Aslam Richardson Extrapolation for Linearly Degenerate Discontinuities. 1-18 2013 57 J. Sci. Comput. 1 https://doi.org/10.1007/s10915-013-9693-0 db/journals/jscic/jscic57.html#BanksA13

Jeffrey M. Connors Jeffrey W. Banks Jeffrey A. F. Hittinger Carol S. Woodward A Method to Calculate Numerical Errors Using Adjoint Error Estimation for Linear Advection. 894-926 2013 51 SIAM J. Numer. Anal. 2 https://doi.org/10.1137/110845100 db/journals/siamnum/siamnum51.html#ConnorsBHW13

Jeffrey W. Banks William D. Henshaw Donald W. Schwendeman Deforming composite grids for solving fluid structure problems. 3518-3547 2012 231 J. Comput. Phys. 9 https://doi.org/10.1016/j.jcp.2011.12.034 db/journals/jcphy/jcphy231.html#BanksHS12

Jeffrey W. Banks William D. Henshaw Upwind schemes for the wave equation in second-order form. 5854-5889 2012 231 J. Comput. Phys. 17 https://doi.org/10.1016/j.jcp.2012.05.012 db/journals/jcphy/jcphy231.html#BanksH12

Daniel Appelö Jeffrey W. Banks William D. Henshaw Donald W. Schwendeman Numerical methods for solid mechanics on overlapping grids: Linear elasticity. 6012-6050 2012 231 J. Comput. Phys. 18 https://doi.org/10.1016/j.jcp.2012.04.008 db/journals/jcphy/jcphy231.html#AppeloBHS12

Jeffrey A. F. Hittinger Jeffrey W. Banks Block-Structured Adaptive Mesh Refinement Algorithms for Vlasov Simulation http://arxiv.org/abs/1204.3853 2012 CoRR abs/1204.3853 db/journals/corr/corr1204.html#abs-1204-3853

John N. Shadid Roger P. Pawlowski Jeffrey W. Banks Luis Chacón Paul T. Lin Raymond S. Tuminaro Towards a scalable fully-implicit fully-coupled resistive MHD formulation with stabilized FE methods. 7649-7671 2010 229 J. Comput. Phys. 20 https://doi.org/10.1016/j.jcp.2010.06.018 db/journals/jcphy/jcphy229.html#ShadidPBCLT10

Jeffrey W. Banks William D. Henshaw John N. Shadid An evaluation of the FCT method for high-speed flows on structured overlapping grids. 5349-5369 2009 228 J. Comput. Phys. 15 https://doi.org/10.1016/j.jcp.2009.04.033 db/journals/jcphy/jcphy228.html#BanksHS09

Jeffrey W. Banks Tariq D. Aslam William J. Rider On sub-linear convergence for linearly degenerate waves in capturing schemes. 6985-7002 2008 227 J. Comput. Phys. 14 https://doi.org/10.1016/j.jcp.2008.04.002 db/journals/jcphy/jcphy227.html#BanksAR08

Jeffrey W. Banks Donald W. Schwendeman Ashwana K. Kapila William D. Henshaw A high-resolution Godunov method for compressible multi-material flow on overlapping grids. 262-297 2007 223 J. Comput. Phys. 1 https://doi.org/10.1016/j.jcp.2006.09.014 db/journals/jcphy/jcphy223.html#BanksSKH07

Jordan B. Angel Daniel Appelö Francis Appiah William J. Arrighi Tariq D. Aslam Richard Berger Stephan Brunner Benjamin Brett Buckner Cassandra Carrick Allison M. Carson Luis Chacón Thomas Chapman Jeffrey M. Connors James Diffenderfer Alyson Fox J. Gorman Thomas M. Hagstrom Nour G. Al Hassanieh William D. Henshaw Jason E. Hicken Jeffrey A. F. HittingerJeffrey Hittinger J. Jacangelo Michael J. Jenkinson Karl Juhnke Ashwana K. Kapila Sharanjeet Kaur Alexander V. Kildishev Gregor Kovacic Jeremy E. Kozdon T. Hoang Ngan LeNgan Le Longfei Li Paul T. Lin Peter Lindstrom 0001 Alex Main Fanlong Meng A. Newell Andre Gianesini Odu Daniel Osei-Kuffuor Roger P. Pawlowski Ludmila J. Prokopeva William J. Rider Donald W. Schwendeman Daniel A. Serino John N. Shadid Jalal Shatah Björn Sjögreen Qi Tang 0001 Ray S. TuminaroRaymond S. Tuminaro Lucas C. Wilcox Carol S. Woodward Qing Xia 0006 Ge Yan 0004