Jan S Hesthaven (Brown - Applied Mathematics)

Summary | Recent Manuscripts | All Publications

Summary

Research interests

Development and numerical analysis of high-order accurate and spectral methods for partial differential equations. Discontinuous Galerkin methods, nodal elements, complex geometries, and time-advancement methods. Absorbing layers. Reduced basis methods. High-performance and parallel computing. Applications to CFD, electromagnetics, plasma physics, general relativity.

Recently completed manuscripts

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These manuscripts are currenty in review and available on request.

J. S. Hesthaven and S. M. Kaber, Pade-Jacobi Approximants, J. Comp. Appl. Math. - submitted (2005).
S. Chun and J. S. Hesthaven, High-order accurate thin layer approximations for time-domain electromagnetics. Part I: General metal backed coatings, J. Comp. Appl. Math. - submitted (2008).
G. J. Gassner, F. Lorcher, C.-D. Munz, and J. S. Hesthaven, Polymorphic Nodal Elements and their Application in Discontinuous Galerkin Methods, J. Comput. Phys. - submitted (2008).
A.P. Engsig-Karup, J.S. Hesthaven, H.B. Bingham, and T Warburton, DG-FEM Solution for Nonlinear Wave-Structure Interaction using Boussinesq-type Equations, Costal Engineering (2006) - to appear.
Eivind Brodal, Jan S. Hesthaven, and Frank Melandsoe, Numerical Modeling of Double-Layered Piezoelectric Transducer Systems Using a High-Order Discontinuous Galerkin Method, Computers and Structures (2007) - to appear.

All publications

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Books

J. S. Hesthaven, S. Gottlieb, and D. Gottlieb, 2007, Spectral Methods for Time-Dependent Problems. Cambridge Monographs on Applied and Computational Mathematics 21, Cambridge University Press, Cambrigde, UK, 275 pages.

List of corrections

J.S. Hesthaven and T. Warburton, 2008, Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications. Springer Texts in Applied Mathematics 54, Springer Verlag, New York. XIV+500 pages.

Book webpage with software

Editorial

J. S. Hesthaven, D. Gottlieb, and E. Turkel (Eds.), Proceedings of the 4th International Conference on Spectral and High-Order Methods (ICOSAHOM'98). Applied Numerical Mathematics, 33(1-4), Elsevier Publishing, Holland. May 2000.
M.H. Carpenter, D. Gottlieb, J. S. Hesthaven, and C.-W. Shu (Eds.), Proceedings of AFOSR Workshop on Advances and Challenges in Time-Integration of PDE's, J. Sci. Comput. 25(1-2), Kluver Publishing, Holland. October 2005.
D. Gottlieb, J.S.Hesthaven, G.E. Karniadakis, and C.-W. Shu. (Eds.), Proceedings of the 6th International Conference on Spectral and High-Order Methods (ICOSAHOM'04), J. Sci. Comput 27(1-3), Kluver Publishing, Holland. June 2006.
G.E. Karniadakis and J.S. Hesthaven(Eds.), Special Issue on "Spectral Interpolation in Non-Orthogonal Domains: Algorithms and Applications", J. Engin. Math. 56(3), November 2006.
H. Haddar and J.S. Hesthaven (Eds.), Proceedings of the 7th International Conference on Mathematical and Numerical Aspects of Waves (WAVES'05), J. Comp. Appl. Math. 204(2), July 2007.

Book chapters

J. S. Hesthaven, 2003, High-Order Accurate Methods in Time-Domain Computational Electromagnetics. A Review. Advances in Imaging and Electron Physics 127, 59-123.

Journal articles

J. S. Hesthaven and R. M. Kirby, 2008, Filtering in Legendre Spectral Methods, Math. Comp. 77(263), 1425-1452.
S. Chun and J.S. Hesthaven, 2008, PDE Constrained Optimization and Design of Frozen Mode Crystals, Comm. Comput. Phys. 3(4), 878-898.
S. Chun and J.S. Hesthaven, 2007, Modeling of the Frozen Mode Phenomenon and its Sensitivity using Discontinuous Galerkin Methods, Commu. Comput. Phys. 2(4), 611-639.
L.N. Olson, J.S. Hesthaven, and L.C. Wilcox, 2007, Developments in Overlapping High-Order Nodal Discontinuous Galerkin Methods, Lect. Notes Comput. Sci. Eng. 55, 325-332.
A. Kanevsky, M.H. Carpenter, D. Gottlieb, and J.S. Hesthaven, 2007, Application of implicit-explicit high-order Runge-Kutta Methods to Discontinuous Galerkin Schemes, J. Comput. Phys. 225(2), 1753-1781.
C. Chauviere, J.S. Hesthaven, and L. Wilcox, 2007, Efficient Computation of RCS from Scatterers of Uncertain Shapes, IEEE Trans. Antennas Propagat. 55(5), 1437-1448.
H. Salman, J.S. Hesthaven, T. Warburton, and G. Haller, 2007, Predicting Transport by Lagrangian Coherent Structures with a High Order Method, J. Theo. Comput. Fluid Dyn. 21(1), 39-58.
A.P. Engsig-Karup, J. S. Hesthaven, H. Bingham, and P. Madsen, 2006, Nodal DG-FEM Solution of High Order Boussinesq-Type Equations, J. Engin. Math. 56(3), 351-370.
A. Kanevsky, M. Carpenter, and J. S. Hesthaven, 2006, Idempotent Filtering in Spectral and Spectral Element Methods, J. Comput. Phys. 220(1), 41-58.
J. S. Hesthaven, S.M. Kaber, and L. Lurati, 2006, Pade-Legendre Interpolants for Gibbs Reconstruction, J. Sci. Comput. 28(2-3), 337-359.
S. Abarbanel, D. Gottlieb, and J. S. Hesthaven, 2006, Nonlinear PML for Electromagnetics, J. Sci. Comput. 28(2-3), 125-137.
M.S. Kilic, G.B. Jacobs, J.S. Hesthaven, and G. Haller, 2006, Reduced Navier-Stokes Equations Near a Flow Boundary, Physics D 217, 161-185.
C. Chauviere, J.S. Hesthaven, and L. Lurati, 2006, Computational Modeling of Uncertainty in Time-Domain Electromagnetics, SIAM J. Sci. Comp. 28, 751-775.
J. Grooss and J.S. Hesthaven, 2006, A Levelset Discontinuous Galerkin Method for Free Surface Flows, Comput. Methods Appl. Mech Engrg. 195, 3406-3429.
G. Jacobs and J.S. Hesthaven, 2006, High-Order Nodal Discontinuous Galerkin Particle-in-Cell Methods on Unstructured Grids, J. Comput. Phys. 214, 96-121.
D. Xiu and J.S. Hesthaven, 2005, High-Order Collocation Methods for Differential Equations with Random Inputs, SIAM J. Sci. Comput. 27, 1118-1139.
Q. Y. Chen, D. Gottlieb, and J. S. Hesthaven, 2005, Pseudospectral Methods using Prolate Spheroidal Wavefunctions, SIAM J. Numer. Anal. 43, 1912-1933.
R. Horvath, L.C. Wilcox, H.C. Pedersen, N. Skiversen, J.S. Hesthaven and P.M. Johansen, 2005, Analytical Theory of Grating Couplers for Waveguide Sensing: A Perturbational Approach and its Limitations, Appl. Phys. B: Lasers and Optics 81, 65-73.
Q. Y. Chen, D. Gottlieb, and J. S. Hesthaven, 2005, Uncertainty Analysis for Steady-State Inviscid Burgers Equation. J. Comput. Phys. 204, 378-398.
L. Wilcox, P. G. Dinesen, and J. S. Hesthaven, 2004, Fast and Accurate Boundary Variation Method for Multilayered Diffraction Optics, J. Opt. Soc. Ame. A 21(5), 757-769.
J. S. Hesthaven and T. Warburton, 2004, High-Order Accurate Methods for Time-domain Electromagnetics, Comp. Mod. Engin. Sci. 5(5), 395-408.
J.S. Hesthaven and T. Warburton, 2004, High Order Nodal Discontinuous Galerkin Methodsfor the Maxwell Eigenvalue Problem, Royal Soc. London Ser A 362, 493-524.
P.J. Diamessis, J.A. Domaradzki, and J.S. Hesthaven, 2004, A Spectral Multidomain Penalty Method Model for the Simulation of High Reynolds Number Localized Incompressible Stratified Turbulence, J. Comput. Phys 202, 298-322.
J. S. Hesthaven and T. Warburton, 2004, Discontinuous Galerkin Methods for the Time-Domain Maxwell's Equations: An Introduction, ACES Newsletter 19(1), 10-29.
T. Warburton and J. S. Hesthaven, 2003, On the Constants in hp-Finite Element Trace Inequalities, Comput. Methods Appl. Mech. Engin. 192, 2765-2773.
G. X. Fan, Q. H. Liu, and J. S. Hesthaven, 2002, Multi-Domain Pseudospectral Time-Domain Simulations of Scattering by Objects Buried in Lossy Media, IEEE Trans. Geosci. Remote Sens. 40(6), 1366-1373.
J. S. Hesthaven and T. Warburton, 2002, High-Order Nodal Methods on Unstructured Grids. I. Time-Domain Solution of Maxwell's Equations, J. Comput. Phys. 181(1), 186-221.
F. X. Giraldo, J. S. Hesthaven, and T. Warburton, 2002, Nodal High-Order Discontinuous Galerkin Method for the Spherical Shallow Water Equations, J. Comput. Phys. 181(2), 499-525.
S. A. Nielsen, J. S. Hesthaven, 2002, A Multi-Domain Chebyshev Collocation Method for Predicting Ultrasonic Field Parameters in Complex Material Geometries, Ultrasonics 40(1-8), 177-180.
S. Abarbanel, D. Gottlieb, and J. S. Hesthaven, 2002, Long Time Behavior of the Perfectly Matched Layer Equations in Computational Electromagnetics, J. Sci. Comput. 17(1-4), 405-422.
P. Dinesen and J. S. Hesthaven, 2001, Fast And Accurate Modeling of Waveguide Grating Couplers. II. The Three-Dimensional Vectorial Case, J. Opt. Soc. Am. A 18(11), 2876-2885.
A. Ditkowski, K. H. Dridi, and J. S. Hesthaven, 2001, Convergent Cartesian Grid Methods for Maxwells Equations in Complex Geometries. , J. Comput. Phys. 170, 39-80.
I. Fatkullin and J. S. Hesthaven, 2001, Adaptive High-Order Finite-Difference Method for Nonlinear Wave Problems, J. Sci. Comput.16(1), 47-67.
K. H. Dridi, J. S. Hesthaven, and A. Ditkowski, 2001, Staircase Free Finite-Difference Time-Domain Formulation for General Materials in Complex Geometries, IEEE Trans. Antennas Propaga. 49(5), 749-756.
D. Gottlieb and J. S. Hesthaven, 2001, Spectral Methods for Hyperbolic Problems, J. Comput. Appl. Math. 128(1-2), 83-131.
V. Zharnitsky, E. Grenier, S. K. Turitsyn, C. K. R. T. Jones, and J. S. Hesthaven, 2000, Ground States of Dispersion Managed NLS, Phys. Rev. E. 62(5), 7358-7364.
T. Warburton, L. Pavarino, and J. S. Hesthaven, 2000, A Pseudospectral Scheme for Incompressible Navier-Stokes using Unstructured Nodal Elements, J. Comput. Phys. 164(1), 1-21.
J. S. Hesthaven and C. H. Teng, 2000, Stable Spectral Methods on Tetrahedral Elements, SIAM J. Sci. Comput. 21(6), 2352-2380.
P. G. Dinesen and J. S. Hesthaven, 2000, Fast and Accurate Modeling of Waveguide Grating Couplers , J. Opt. Soc. Ame. A 17(9), 1565-1572.
J. S. Hesthaven, 2000, Spectral Penalty Methods, Appl. Numer. Math. 33(1-4), 23-41.
B. Yang and J. S. Hesthaven, 2000, Multidomain Pseudospectral Computation of Maxwell's Equations in 3-D General Curvilinear Coordinates, Appl. Numer. Math. 33(1-4), 281-289.
P. G. Dinesen, J. S. Hesthaven and J. P. Lynov, 2000, A Pseudospectral Collocation Time-Domain Method for Diffractive Optics, Appl. Numer. Math. 33(1-4), 199-206.
J. S. Hesthaven, P. G. Dinesen and J. P. Lynov, 1999, Spectral Collocation Time-Domain Modeling of Diffractive Optical Elements, J. Comput. Phys. 155(1), 287-306.
S. Abarbanel, D. Gottlieb and J. S. Hesthaven, 1999, Wellposed Perfectly Matched Layers for Advective Acoustics, J. Comput. Phys 154(2), 266-283.
J. S. Hesthaven and D. Gottlieb, 1999, Stable Spectral Methods for Conservation Laws on Triangles with Unstructured Grids, Comput. Methods Appl. Mech. Engin. 175, 361-381.
P. G. Dinesen, J. S. Hesthaven, J. P. Lynov and L. Lading, 1999, Pseudospectral Method for the Analysis of Diffractive Optical Elements, J. Opt. Soc. Am. A 16(5), 1124-1130.
B. Yang and J. S. Hesthaven, 1999, A Pseudospectral Method for Time-Domain Computation of Electromagnetic Scattering by Bodies of Revolution, IEEE Trans. Antennas Propaga. 47(1), 132-141.
J. S. Hesthaven, 1999, A Stable Penalty Method for the Compressible Navier-Stokes Equations. III. Multi Dimensional Domain Decomposition Schemes, SIAM J. Sci. Comp. 20(1), 62-93.
J. S. Hesthaven and L. Jameson, 1998, A Wavelet Optimized Adaptive Multi-Domain Method, J. Comput. Phys. 145, 280-296.
J. S. Hesthaven, 1998, On the Analysis and Construction of Perfectly Matched Layers for the Linearized Euler Equations, J. Comput. Phys. 142, 129-147.
J. S. Hesthaven, 1998, Integration Preconditioning of Pseudospectral Operators. I. Basic Linear Operators, SIAM J. Numer. Anal. 35(2), 1571-1593.
J. S. Hesthaven, 1998, From Electrostatics to Almost Optimal Nodal Sets for Polynomial Interpolation in a Simplex, SIAM J. Numer. Anal. 35(2), 655-676.
J. S. Hesthaven, J. Juul Rasmussen, L. Berge and J. Wyller, 1997, Numerical studies of localized wave fields govenered by the Raman-extended derivative nonlinear Schrodinger equation, J. Phys. A: Math. Gen. 30, 8207-8224.
B. Yang, D. Gottlieb and J. S. Hesthaven, 1997, Spectral Simulation of Electromagnetic Wave Scattering, J. Comput. Phys. 134(2), 216-230.
J. S. Hesthaven, 1997, A Stable Penalty Method for the Compressible Navier-Stokes Equations. II. One-Dimensional Domain Decomposition Schemes, SIAM J. Sci. Comp. 18(3), 658-685.
J. S. Hesthaven and D. Gottlieb, 1996, A Stable Penalty Method for the Compressible Navier-Stokes Equations. I. Open Boundary Conditions, SIAM J. Sci. Comp. 17(3), 579-612.
J. Juul Rasmussen, J. S. Hesthaven, J. P. Lynov, A. H. Nielsen and M. R. Schmidt, 1996, Dipolar Vortices in Two-Dimensional Flows, Math. Comp. Simu., 40, 207-221.
J. S. Hesthaven, J. P. Lynov, A. H. Nielsen, J. Juul Rasmussen, M.R. Schmidt, E.G. Shapiro and S.K. Turitsyn, 1995, Dynamics of a Non-Linear Dipole Vortex, Phys. Fluids A 7(9), 2220-2229.
J. S. Hesthaven, A. H. Nielsen, H. L. Pecseli and J. Juul Rasmussen, 1995, The Eulerian-Lagrangian Transformation in Two-Dimensional Random Flows, J. Atmos. Terres. Phys. 57(3), 215-223.
J. Juul Rasmussen, J. P. Lynov, J. S. Hesthaven and G. G. Sutyrin, 1994, Vortex Dynamics in Plasmas and Fluids, Plasma Phys. Control. Fusion 36, B193-B202.
G. G. Sutyrin, J. S. Hesthaven, J. P. Lynov and J. Juul Rasmussen, 1994, Dynamical Properties of Vortical Structures on the Beta-Plane, J. Fluid Mech. 268, 303-331.
J. S. Hesthaven, J. P. Lynov, J. Juul Rasmussen and G. G. Sutyrin, 1993, Generation of Tri-Polar Vortices on the Beta-Plane , Phys. Fluids A 5(7), 1674-1678.
J. S. Hesthaven, J. Nycander and J. P. Lynov, 1993, Dynamics of Non-Stationary Dipole Vortices, Phys. Fluids A 5(3), 622-629.
J. Du Croz, J. S. Hesthaven and J. Wasniewski, 1992, Comparison of Two FFT Libraries on the Amdahl/Fujitsu VP Computer - NAG and Siemens Libraries, Supercomputer 51, 4-10.

Jan S Hesthaven [Research]