Jay Gopalakrishnan

Publications

• Generalizing Riemann curvature to Regge metrics
  (with M. Neunteufel, J. Schöberl, and M. Wardetzky) Submitted.
  
  
  
• The Johnson-Mercier elasticity element in any dimension
  (with J. Guzmán and J. Lee) Submitted.
  
  
  
• Adaptive resolution of fine scales in modes of microstructured optical fibers
  (with J. Grosek, G. Pinochet-Soto, and P. Vandenberge) To appear in SIAM Journal on Scientific Computing.
  
  
  
• On the improved convergence of lifted distributional Gauss curvature from Regge elements
  (with M. Neunteufel, J. Schöberl, and M. Wardetzky) Submitted.
  
  
  

• Stability analysis for acoustic waveguides: impedance boundary conditions
  (with L. Demkowicz and N. Heuer) Appl. Math., pp. 1-19, dedicated to the memory of Ivo Babuška, 2024. [Preprint]
  
  
  
• PT-symmetry-enabled stable modes in multi-core fiber
  (with T. Gratcheva and Y. N. Joglekar) Physical Review Research, Volume 6, pp. 033025, 2024. [Open Access]
  
  
  
• Discrete elasticity exact sequences on Worsey-Farin splits
  (with S. Gong, J. Guzmán, and M. Neilan) ESIAM: M2AN, Volume 57, pp. 3373-3402, 2023. [Open Access]
  
  
  
• Analysis of curvature approximations via covariant curl and incompatibility for Regge metrics
  (with M. Neunteufel, J. Schöberl, and M. Wardetzky) The SMAI Journal of Computational Mathematics, Volume 9, pp. 151-195, 2023. [Open Access]
  
  
  
• A discrete elasticity complex on three-dimensional Alfeld splits
  (with S. H. Christiansen, J. Guzmán, and K. Hu) Numerische Mathematik, Volume 156, pp. 159-204, 2024. [Preprint]
  
  
  
• Sensitivity of confinement losses in optical fibers to modeling approach
  (with J. Grosek and P. Vandenberge) Optics Express, Volume 31, Issue 16, pp. 26735-26756, 2023. [Open Access]
  
  
  
• Divergence-conforming velocity and vorticity approximations for incompressible fluids obtained with minimal inter-element coupling
  (with L. Kogler, P. L. Lederer, and J. Schöberl) Journal of Scientific Computing, Volume 95, Article 91, 2023. [Preprint]
  
  
  
• Stability of Structure-Aware Taylor methods for tents
  (with Z. Sun) Mathematics of Computation, Volume 92, Number 341, pp. 1061-1086, 2023. [Preprint]
  
  
  
• A one-dimensional field dislocation mechanics model using discontinuous Galerkin method
  (with J. Breeden, D. Drake, and S. Puri) Computational Material Science, Volume 216, Issue 5, p.111870, 2023. [Preprint]
  
  
  
• A computational framework for time dependent deformation in viscoelastic magmatic systems
  (with C. Rucker, B. A. Erickson, L. Karlstrom, and B. Lee) Journal of Geophysical Research--Solid Earth, Volume 127, Issue 9, e2022JB024506, 2022. [Preprint]
  
  
  
• Convergence analysis of some tent-based schemes for linear hyperbolic systems
  (with D. Drake, J. Schöberl and C. Wintersteiger) Math. Comp., Volume 91, pp. 699-733, 2022. [Preprint]
  
  
  
• Computing leaky modes of optical fibers using a FEAST algorithm for polynomial eigenproblems
  (with B. Q. Parker and P. Vandenberge) Wave Motion, Volume 108, pp. 102826, 2022. [Preprint]
  
  
  
• Simulations of single- and two-tone Tm-doped optical fiber laser amplifiers
  (with T. Goswami and J. Grosek) Optics Express, Volume 29, Issue 8, pp. 12599-12615, 2021. [Open Access]
  
  
  
• Structure-aware Runge-Kutta time stepping for spacetime tents
  (with J. Schöberl and C. Wintersteiger) SN Partial Differential Equations and Applications, Volume 1, Article 19, 2020. [Open Access]
  
  
  
• An explicit mapped tent pitching scheme for Maxwell equations
  (with M. Hochsteger, J. Schöberl and C. Wintersteiger) In: Spectral and High Order Methods for Partial Differential Equations, Lecture Notes in Computational Science and Engineering 134, pp. 359-369, 2020. [Open Access]
  
  
  
• Lectures on Mathematical Computing with Python
  PDXOpen: Open Educational Resource 29 (for undergraduate education), Portland State University Library, DOI: 10.15760/pdxopen-28, 2020. [Open Access]
  
  
  
• A mass conserving mixed stress formulation for Stokes flow with weakly imposed stress symmetry
  (with P. Lederer and J. Schöberl) SIAM Journal on Numerical Analysis, Volume 58, Number 1, pp. 706-732, 2020 [Preprint]
  
  
  
• Spectral discretization errors in filtered subspace iteration
  (with L. Grubišić and J. Ovall). Mathematics of Computation, Volume 89, Number 321, pp. 203-228, 2020 [Preprint]
  
  
  
• The DPG-star method
  (with L. Demkowicz and B. Keith) Computers and Mathematics with Applications, Volume 79, Number 11, pp. 3092-3116, 2020. [Preprint]
  
  
  
• Simulation of optical fiber amplifier gain using equivalent short fibers
  (with D. Drake, T. Goswami and J. Grosek) Computer Methods in Applied Mechanics and Engineering, Volume 360, 112698, October 2019. [Preprint]
  
  
  
• A spacetime DPG method for the wave equation in multiple dimensions
  (with P. Sepúlveda). In collection "Space-Time Methods: Applications to Partial Differential Equations" (ISBN: 9783110548488) pp. 117-140, 2019. [Preprint]
  
  
  
• A mass conserving mixed stress formulation for the Stokes equations
  (with P. Lederer and J. Schöberl) IMA Journal of Numerical Analysis, Volume 40, Number 3, pp. 1838-1874, 2020. [Preprint]
  
  
  
• Analysis of FEAST spectral approximations using the DPG discretization
  (with L. Grubišić, J. Ovall and B. Q. Parker). Computational Methods in Applied Mathematics, Volume 19, pp. 251-266, DOI: 10.1515/cmam-2019-0030, 2019 [Preprint]
  
  
  
• The auxiliary space preconditioner for the de Rham complex
  (with M. Neumüller and P. Vassilevski). SIAM Journal on Numerical Analysis, Volume 56, pp. 3196-3218, 2018 [Preprint]
  
  
  
• Dispersion analysis of HDG methods
  (with M. Solano and F. Vargas). Journal of Scientific Computation, Volume 77, pp. 1703-1735, 2018 [Preprint]
  
  
  
• A scalable preconditioner for the DPG method
  (with A. T. Barker, V. Dobrev, and T. Kolev). SIAM Journal on Scientific Computing, Volume 40, Issue 2, pp. A1187-A1203, 2018 [Preprint]
  
  
  
• Mapped tent pitching schemes for hyperbolic systems
  (with J. Schöberl and C. Wintersteiger). SIAM Journal on Scientific Computing, Vol. 39, No. 6, pp. B1043-B1063, 2017 [Preprint]
  
  
  
• Discontinuous Petrov Galerkin (DPG) Method
  (with L. Demkowicz). Invited review. In collection: Encyclopedia of Computational Mechanics, Part 2: Fundamentals, pp. 1-15, 2017 [Preprint]
  
  
  
• A spacetime DPG method for the Schrödinger equation
  (with L. Demkowicz, S. Nagaraj, and P. Sepúlveda). SIAM Journal on Numerical Analysis, Vol. 55, No. 4, pp. 1740-1759, 2017 [Preprint]
  
  
  
• Reduced test spaces for DPG methods using rectangular elements
  (with D. Drake and A. Harb). Computers and Mathematics with Applications, DOI:10.1016/j.camwa.2017.06.046, 2017 [Preprint]
  
  
  
• Scattering of electromagnetic waves by thin high contrast dielectrics II
  (with D. M. Ambrose, S. Moskow and S. Rome). Communications in Mathematical Sciences, Vol. 15, No. 4, pp. 1041-1053, 2017. [Preprint]
  
  
  
• Breaking spaces and forms for the DPG method and applications including Maxwell equations
  (with C. Carstensen and L. Demkowicz). Computers and Mathematics with Applications, Volume 72, Issue 3, pp. 494-522, 2016. [Preprint]
  
  
  
• Degree and wavenumber [in]dependence of a Schwarz preconditioner for the DPG method
  (with J. Schöberl). Spectral and High Order Methods for Partial Differential Equations, Springer, pp. 257-265. 2015. Proceedings of the 2014 ICOSAHOM, Salt Lake City, Utah. [Preprint]
  
  
  
• A tent pitching scheme motivated by Friedrichs theory
  (with P. Monk and P. Sepúlveda). Computers and Mathematics with Applications, Volume 70, Issue 5, pp. 1114-1135, 2015. [Preprint]
  
  
  
• Mathematical model for bone mineralization
  (with S. V. Komarova, M. D. McKee, M. Murshed, M.-Y Ou, F. Rauch, L. Safranek, and E. Zuhr). Frontiers in Cell and Developmental Biology, Volume 3, Article Number 51 (11 pages), 2015. [Open Access]
  
  
  
• Stabilization in relation to wavenumber in HDG methods
  (with S. Lanteri, N. Olivares and R. Perrussel). Advanced Modeling and Simulation in Engineering Sciences, Volume 2, Issue 1, Article 13 (24 pages), 2015. [Open Access]
  
  
  
• Spectral approximations by the HDG method
  (with F. Li, N.-C. Nguyen, and J. Peraire). Mathematics of Computation, Volume 84, Number 293, pp. 1037-1059, 2015. [Preprint]
  
  
  
• Convergence rates of the DPG method with reduced test space degree
  (with T. Bouma and A. Harb). Computers and Mathematics with Applications, Volume 68, Issue 11, pp. 1550-1561, 2014. [Preprint]
  
  
  
• A posteriori error control for DPG methods
  (with C. Carstensen and L. Demkowicz). SIAM Journal on Numerical Analysis, Volume 52, Number 3, pp. 1335-1353, 2014. [Preprint]
  
  
  
• Dispersive and dissipative errors in the DPG method with scaled norms for Helmholtz equation
  (with I. Muga and N. Olivares). SIAM Journal on Scientific Computing, Volume 36, Number 1, pp. A20-A39, 2014. [Preprint]
  
  
  
• Multigrid for an HDG method
  (with B. Cockburn, O. Dubois, and S. Tan). IMA Journal of Numerical Analysis, Volume 34, Issue 4, pp. 1386-1425, 2014. [Preprint]
  
  
  
• A primal DPG method without a first order reformulation
  (with L. Demkowicz). Computers and Mathematics with Applications, Volume 66, Issue 6, pp. 1058-1064, 2013. [Preprint]
  
  
  
• An analysis of the practical DPG method
  (with W. Qiu). Mathematics of Computation, Volume 83, No. 286, pp. 537-552, 2014. [Preprint]
  
  
  
• Nonnegativity of exact and numerical solutions of some chemotactic models
  (with P. De Leenheer and E. Zuhr). Computers and Mathematics with Applications, Volume 66, pp. 356-375, 2013. [Preprint]
  
  
  
• Instability in a generalized Keller-Segel model
  (with P. De Leenheer and E. Zuhr). Journal of Biological Dynamics Volume 6, pp. 974-991, 2012. [Open Access]
  
  
  
• Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions
  (with D. N. Arnold and R. S. Falk). Mathematical Models and Methods in Applied Sciences (M3AS), Volume 22, No. 9, Article 1250024 (26 pages), 2012. [Preprint]
  
  
  
• A locking-free hp DPG method for linear elasticity with symmetric stresses
  (with J. Bramwell, L. Demkowicz, and W. Qiu). Numerische Mathematik, Volume 122, Issue 4, pp. 671-707, 2012. [Preprint]
  
  
  
• Wavenumber explicit analysis for a DPG method for the multidimensional Helmholtz equation
  (with L. Demkowicz, I. Muga, and J. Zitelli). Computer Methods in Applied Mechanics and Engineering, Volume 213/216, pp. 126-138, 2012. [Preprint]
  
  
  
• Partial expansion of a Lipschitz domain and some applications
  (with W. Qiu). Frontiers of Mathematics in China, Volume 7, Issue 2, pp. 249-272, 2012. [Preprint]
  
  
  
• Convergence analysis of a multigrid algorithm for the acoustic single layer equation
  (with S. Gemmrich and N. Nigam). Applied Numerical Mathematics, Volume 62, pp. 767-786, 2012. [Preprint]
  
  
  
• Analysis of the DPG method for the Poisson equation
  (with L. Demkowicz). SIAM Journal on Numerical Analysis, Volume 49, pp. 1788-1809, 2011. [Preprint]
  
  
  
• Determination of the electric field intensity and space charge density with height prior to triggered lightning
  (with C. Biagi, M. Uman, et al). Journal of Geophysical Research, Volume 116, Article D15201 (15 pages), 2011. [Preprint]
  
  
  
• Polynomial extension operators. Part III
  (with L. Demkowicz and J. Schöberl). Mathematics of Computation, Volume 81, pp. 1289-1326, 2012. [Preprint]
  
  
  
• A class of discontinuous Petrov-Galerkin methods. Part III: Adaptivity
  (with L. Demkowicz and A. Niemi) Applied Numerical Mathematics, Volume 62, pp. 396-427, 2012. [Preprint]
  
  
  
• A second elasticity element using the matrix bubble
  (with J. Guzmán). IMA Journal of Numerical Analysis, Volume 32, pp. 352-372, 2012. [Preprint]
  
  
  
• Commuting smoothed projectors in weighted norms with an application to axisymmetric Maxwell equations
  (with M. Oh). Journal of Scientific Computation, Volume 51, pp. 394-420, 2012. [Preprint]
  
  
  
• Symmetric non-conforming mixed finite elements for linear elasticity
  (with J. Guzmán). SIAM Journal on Numerical Analysis, Volume 49, pp. 1504-1520, 2011. [Preprint]
  
  
  
• Analysis of HDG methods for Stokes flow
  (with B. Cockburn, N.-C Nguyen, J. Peraire, and F.-J. Sayas). Mathematics of Computation, Volume 80, pp. 723-760, 2011. [Preprint]
  
  
  
• A class of discontinuous Petrov-Galerkin methods. Part IV: The optimal test norm and time-harmonic wave propagation in 1D
  (with V. Calo, L. Demkowicz, I. Muga, D. Pardo, and J. Zitelli) Journal of Computational Physics, Volume 230, pp. 2406-2432, 2011. [Preprint]
  
  
  
• A class of discontinuous Petrov-Galerkin methods. Part II: Optimal test functions
  (with L. Demkowicz). Numerical Methods for Partial Differential Equations, Volume 27, Issue 1, pp. 70-105, January 2011. [Preprint]
  
  
  
• Hybridization and postprocessing techniques for mixed eigenfunctions
  (with B. Cockburn, F. Li, N.-C. Nguyen and J. Peraire). SIAM Journal on Numerical Analysis, Volume 48, pp. 857-881, 2010. [Preprint]
  
  
  
• Multigrid in a weighted space arising from axisymmetric electromagnetics
  (with D. Copeland and M. Oh). Mathematics of Computation, Volume 79, pp. 2033-2058, 2010. [Preprint]
  
  
  
• A projection-based error analysis of HDG methods
  (with B. Cockburn and F.-J. Sayas). Mathematics of Computation, Volume 79, pp.1351-1367, 2010. [Preprint]
  
  
  
• A class of discontinuous Petrov-Galerkin methods. Part I: The transport equation
  (with L. Demkowicz). Computer Methods in Applied Mechanics and Engineering, Volume 199, pp. 1558-1572, 2010. [Preprint]
  
  
  
• A new elasticity element made for enforcing weak stress symmetry
  (with B. Cockburn and J. Guzmán). Mathematics of Computation, Volume 79, pp.1331-1349, 2010. [Preprint]
  
  
  
• Polynomial extension operators. Part II
  (with L. Demkowicz and J. Schöberl). SIAM Journal on Numerical Analysis, Volume 47, No. 5, pp. 3293-3324, 2009 [Preprint]
  
  
  
• The derivation of hybridizable discontinuous Galerkin methods for Stokes flow
  (with B. Cockburn). SIAM Journal on Numerical Analysis, Volume 47, pp. 1092-1125, 2009. [Preprint]
  
  
  
• A convergent multigrid cycle for the hybridized mixed method
  (with S. Tan). Numerical Linear Algebra with Applications, Volume 16, Issue 9, pp. 689-714, 2009. [Preprint]
  
  
  
• Unified hybridization of discontinuous Galerkin, mixed, and continuous Galerkin methods for second order elliptic problems
  (with B. Cockburn and R. Lazarov). SIAM Journal on Numerical Analysis, Volume 47, pp. 1319-1365, 2009. [Preprint]
  
  
  
• Multigrid convergence for second order elliptic problems with smooth complex coefficients
  (with J. E. Pasciak). Computer Methods in Applied Mechanics and Engineering, Volume 127, pp. 4411-4418, 2008. [Preprint]
  
  
  
• Polynomial extension operators. Part I
  (with L. Demkowicz and J. Schöberl). SIAM Journal on Numerical Analysis, Volume 46, Issue 6, pp. 3006-3031, 2008. [Preprint]
  
  
  
• Asymptotic and numerical techniques for resonances of thin photonic structures
  (with S. Moskow and F. Santosa). SIAM Journal on Applied Mathematics, Volume 69, Issue 1, pp. 37-63, 2008. [Preprint]
  
  
  
• A mixed method for axisymmetric div-curl systems
  (with D. Copeland and J. E. Pasciak). Mathematics of Computation, Volume 77, pp. 1941-1965, 2008. [Preprint]
  
  
  
• Locally conservative fluxes for the continuous Galerkin method
  (with B. Cockburn and H. Wang). SIAM Journal on Numerical Analysis, Volume 45, Issue 4, pp. 1742-1776, 2007. [Preprint]
  
  
  
• The convergence of V-cycle multigrid algorithms for axisymmetric Laplace and Maxwell equations
  (with J. E. Pasciak). Mathematics of Computation, Volume 75, pp. 1697-1719, 2006. [Preprint]
  
  
  
• New hybridization techniques
  (with B. Cockburn). A review of old and new hybridization techniques. GAMM-Mitteilungen, Volume 28, Number 2, pp. 154-182, 2005. [Preprint]
  
  
  
• Integration of hp-adaptivity and a two grid solver for electromagnetic problems
  (with L. Demkowicz and D. Pardo). Computer Methods in Applied Mechanics and Engineering, Volume 195, pp 2533-2573, 2006. [Preprint]
  
  
  
• Incompressible finite elements via hybridization: Part II
  (with B. Cockburn). SIAM Journal on Numerical Analysis, Volume 43, Number 4, pp. 1651-1672, 2005. [Preprint]
  
  
  
• Incompressible finite elements via hybridization: Part I
  (with B. Cockburn). SIAM Journal on Numerical Analysis, Volume 43, Number 4, pp. 1627-1650, 2005. [Preprint]
  
  
  
• Nédélec spaces in affine coordinates
  (with L. F. Demkowicz and L. E. García-Castillo). Computers and Mathematics with Applications, Volume 49, Issue 7-8, pp. 1285-1294, 2005. [Preprint]
  
  
  
• Error analysis of variable degree mixed methods for elliptic problems via hybridization
  
  (with B. Cockburn). Mathematics of Computation, Volume 74, pp. 1653-1677, 2005. [Preprint]
  
  
  
• Quasioptimality of some spectral mixed methods
  
  (with L. F. Demkowicz). Journal of Computational and Applied Mathematics, Volume 167, Issue 1, pp. 163-182, 2004. [Preprint]
  
  
  
• A characterization of hybridized mixed methods for second order elliptic problems
  
  (with B. Cockburn). SIAM Journal on Numerical Analysis, Volume 42, No. 1, pp. 283-301, 2004. [Preprint]
  
  
  
• Analysis of a multigrid algorithm for time harmonic Maxwell equations
  
  (with L. F. Demkowicz and J. E. Pasciak). SIAM Journal on Numerical Analysis, Volume 42, No. 1, pp. 90-108, 2004. [Preprint]
  
  
  
• A Schwarz preconditioner for a hybridized mixed method
  
  Computational Methods in Applied Mathematics, Volume 3, No. 1, pp. 116-134, 2003. [Preprint]
  
  
  
• Application of unified DG analysis to preconditioning DG methods
  
  (with G. Kanschat). Proc. 2nd MIT Conference on Computational Fluid and Solid Mechanics, pp.1943-1945, 2003. [Preprint]
  
  
  
• A multilevel discontinuous Galerkin method
  
  (with G. Kanschat). Numerische Mathematik, Volume 95, No. 3, pp. 527-550, 2003. [Preprint]
  
  
  
• A mathematical model for irrigated epicardial radiofrequency ablation
  
  Annals of Biomedical Engineering, Volume 30, Issue 7, pp. 884-893, 2002. [Preprint]
  
  
  
• Overlapping Schwarz preconditioners for indefinite time harmonic Maxwell equations
  
  (with J. E. Pasciak). Mathematics of Computation, Volume 72, No. 241, pp. 1-15, 2003. [Preprint]
  
  
  
• An efficient method for band structure calculations in 3D photonic crystals
  
  (with D. C. Dobson and J. E. Pasciak). Journal of Computational Physics, Volume 161, No. 2, pp. 668-679, Jul 2000. [Preprint]
  
  
  
• Mortar estimates independent of number of subdomains.
  
  East-West Journal of Numerical Mathematics, Volume 8, No. 2, pp. 83-152, 2000. [Preprint]
  
  
  
• Multigrid for the mortar finite element method
  (with J. E. Pasciak). SIAM Journal on Numerical Analysis, Volume 37, No. 3, pp. 1029-1052, March 2000. [Preprint]