Publications

Journal Articles:

  1. P. M. Jordan and J. V. Lambers, "Revisiting Manne et al. (2000): A reformulation and alternative interpretation under the modified internal energy theory of second-sound", Wave Motion 105 (2021), 102756.
  2. P. M. Jordan and J. V. Lambers, "On the propagation and bifurcation of singular surface shocks under a class of wave equations based on second-sound flux models and logistic growth", International Journal of Non-Linear Mechanics 132 (2021), 103696.
  3. J. V. Lambers and P. M. Jordan, "On the application of a Krylov subspace spectral method to poroacoustic shocks in inhomogeneous gases", Numerical Methods for Partial Differential Equations 37(6) (2021), p. 2955-2972.
  4. S. Sheikholeslami, J. V. Lambers and C. Walker, "Convergence Analysis of Krylov Subspace Spectral Methods for Reaction-Diffusion Equations", Journal of Scientific Computing 78(3) (2019), p. 1768-1789. (PDF)
  5. S. D. Long, S. Sheikholeslami, J. V. Lambers and C. Walker, "Diagonalization of 1-D Differential Operators with Piecewise Constant Coefficients Using the Uncertainty Principle", Mathematics and Computers in Simulation 156 (2019), p. 194-226. (PDF)
  6. S. Sheikholeslami and J. V. Lambers, "Modeling of first-order photobleaching kinetics using Krylov subspace spectral methods", Computers and Mathematics with Applications 75(6) (2018), p. 2153-2172. (PDF)
  7. E. M. Garon and J. V. Lambers, "Modeling the Diffusion of Heat Energy within Composites of Homogeneous Materials using the Uncertainty Principle", Computational and Applied Mathematics 37(3) (2018), p. 2566-2587. (PDF)
  8. M. Richardson and J. V. Lambers, "Recurrence Relations for Orthogonal Polynomials for PDEs in Polar and Cylindrical Geometries", SpringerPLUS 5:1567 (2016) (PDF)
  9. A. Cibotarica, J. V. Lambers and E. M. Palchak, "Solution of Nonlinear Time-Dependent PDE Through Componentwise Approximation of Matrix Functions", Journal of Computational Physics 321 (2016), p. 1120-1143. (PDF)
  10. E. M. Palchak, A. Cibotarica and J. V. Lambers, "Solution of Time-Dependent PDE Through Rapid Estimation of Block Gaussian Quadrature Nodes", Linear Algebra and its Applications 468 (2015), p. 233-259. (PDF)
  11. P. Guidotti, Y. Kim and J. V. Lambers, "Image restoration with a new class of forward-backward-forward diffusion equations of Perona-Malik type with Applications to Satellite Image Enhancement", SIAM Journal on Imaging Sciences 6(3) (2013), p. 1416-1444. (PDF)
  12. J. V. Lambers, "Approximate Diagonalization of Variable-Coefficient Differential Operators Through Similarity Transformations", Computers and Mathematics with Applications 64(8) (2012), p. 2575-2593. (PDF)
  13. J. V. Lambers, "Explicit High-Order Time-Stepping Based on Componentwise Application of Asymptotic Block Lanczos Iteration", Numerical Linear Algebra with Applications 19(6) (2012), p. 970-991. (PDF)
  14. J. V. Lambers, "Solution of Time-Dependent PDE Through Component-wise Approximation of Matrix Functions", IAENG Journal of Applied Mathematics 41(1) (2011), p. 1-10. (PDF)
  15. T. Chen, M. G. Gerritsen, J. V. Lambers and L. J. Durlofsky, "Global variable compact multipoint methods for accurate upscaling with full-tensor effects", Computational Geosciences 14(1) (2010), p. 65-81. (PDF)
  16. J. V. Lambers, "A Multigrid Block Krylov Subspace Spectral Method for Variable-Coefficient Elliptic PDE", IAENG Journal of Applied Mathematics 39(4) (2009), p. 236-246. (PDF)
  17. J. V. Lambers, "A Spectral Time-Domain Method for Computational Electrodynamics", Advances in Applied Mathematics and Mechanics 1(6) (2009), p. 781-798. (PDF)
  18. J. V. Lambers, "Krylov Subspace Spectral Methods for the Time-Dependent Schrödinger Equation with Non-Smooth Potentials", Numerical Algorithms 51 (2009), p. 239-280. (PDF)
  19. J. V. Lambers, "An Explicit, Stable, High-Order Spectral Method for the Wave Equation Based on Block Gaussian Quadrature", IAENG Journal of Applied Mathematics 38 (2008), p. 233-248. (PDF)
  20. J. V. Lambers, "Enhancement of Krylov Subspace Spectral Methods by Block Lanczos Iteration", Electronic Transactions on Numerical Analysis 31 (2008), p. 86-109. (PDF)
  21. J. V. Lambers, "Implicitly Defined High-Order Operator Splittings for Parabolic and Hyperbolic Variable-Coefficient PDE Using Modified Moments", International Journal of Computational Science 2 (2008), p. 376-401. (PDF)
  22. P. Guidotti and J. V. Lambers, "Two New Nonlinear Nonlocal Diffusions for Noise Reduction", Journal of Mathematical Imaging and Vision 33 (2009), p. 27-35. (PDF)
  23. P. Guidotti and J. V. Lambers, "Eigenvalue Characterization and Computation for the Laplacian on General 2-D Domains", Numerical Functional Analysis and Optimization 29 (2008), p. 507-531. (PDF)
  24. J. V. Lambers, "Derivation of High-Order Spectral Methods for Time-Dependent PDE Using Modified Moments", Electronic Transactions on Numerical Analysis 28 (2008), p. 114-135. (PDF)
  25. J. V. Lambers, M. G. Gerritsen and B. T. Mallison, "Accurate Local Upscaling with Variable Compact Multi-point Transmissibility Calculations", Computational Geosciences 12, Special Issue on Multiscale Methods for Flow and Transport in Heterogeneous Porous Media (2008), p. 399-416. (PDF)
  26. J. V. Lambers, "Practical Implementation of Krylov Subspace Spectral Methods", Journal of Scientific Computing 32 (2007), p. 449-476. (PDF)
  27. M. G. Gerritsen and J. V. Lambers, "Integration of Local-Global Upscaling and Grid Adaptivity for Simulation of Subsurface Flow in Heterogeneous Formations", Computational Geosciences 12 (2008), p. 193-208. (PDF)
  28. P. Guidotti, J. V. Lambers and K. Sølna, "Analysis of the 1D Wave Equation in Inhomogeneous Media", Numerical Functional Analysis and Optimization 27 (2006), p. 25-55. (PDF)
  29. J. V. Lambers, "Krylov Subspace Spectral Methods for Variable-Coefficient Initial-Boundary Value Problems", Electronic Transactions on Numerical Analysis 20 (2005), p. 212-234. (PDF)

Refereed Conference Papers:

  1. H. Dozier and J. V. Lambers, "Krylov Subspace Spectral Methods with Coarse-Grid Residual Correction for Solving Time-Dependent, Variable Coefficient PDEs", Proceedings of the 2016 International Conference on Spectral and High-Order Methods, Rio de Janeiro, 2016. (PDF)
  2. J. V. Lambers, "High-order Time-stepping for Galerkin and Collocation Methods Based on Component-wise Approximation of Matrix Functions", Proceedings of the World Congress on Engineering, London, 2011. (PDF)
  3. J. V. Lambers, "Spectral Methods for Time-dependent Variable-coefficient PDE Based on Block Gaussian Quadrature", Proceedings of the World Congress on Engineering, London, 2010. (PDF)
  4. J. V. Lambers, "Krylov Subspace Spectral Methods for the Time-Dependent Schrödinger Equation with Non-Smooth Potentials", Proceedings of the 2010 International MultiConference of Engineers and Computer Scientists, Hong Kong, Winner, Best Paper Award, 2010 International Conference of Scientific Computing. (PDF)
  5. J. V. Lambers, "Spectral Methods for Time-dependent Variable-coefficient PDE Based on Block Gaussian Quadrature", Proceedings of the 2009 International Conference on Spectral and High-Order Methods, Trondheim, 2009. (PDF)
  6. J. V. Lambers, "A Spectral Time-Domain Method for Computational Electrodynamics", Proceedings of the 8th European Conference on Numerical Mathematics and Advanced Applications, Uppsala, 2009. (PDF)
  7. K. T. Chu and J. V. Lambers, "Using Optimal Time Step Selection to Boost the Accuracy of FD Schemes for Variable Coefficient PDEs", Proceedings of the World Congress on Engineering, London, 2009. (PDF)
  8. J. V. Lambers, "Block Krylov Subspace Spectral Methods for Variable-Coefficient Elliptic PDE", Proceedings of the World Congress on Engineering, London, 2009. (PDF)
  9. J. V. Lambers, "A Spectral Time-Domain Method for Computational Electrodynamics", Proceedings of the 2009 International MultiConference of Engineers and Computer Scientists, Hong Kong (PDF)
  10. J. V. Lambers, "Enhancement of Krylov Subspace Spectral Methods by Block Lanczos Iteration", Proceedings of the 6th International Conference on Numerical Analysis and Applied Mathematics, Kos, Greece, 2008 (PDF)
  11. J. V. Lambers, "Implicitly Defined High-Order Operator Splittings for Parabolic and Hyperbolic Variable-Coefficient PDE Using Modified Moments", Proceedings of the 2008 World Congress of Engineering, London, Winner, Best Paper Award, 2008 International Conference of Applied and Engineering Mathematics (PDF)
  12. J. V. Lambers, "Krylov Subspace Spectral Methods for Systems of Variable-Coefficient PDE", Proceedings of the 5th International Conference on Numerical Analysis and Applied Mathematics, Corfu, Greece, 2007, American Institute of Physics Conference Proceedings 936 (2007), p. 332-335 (PDF)

Non-refereed Conference Papers:

  1. J. V. Lambers, "High-Order Time-Stepping for Nonlinear PDE through Rapid Estimation of Block Gaussian Quadrature Nodes", Proceedings of the 13th International Conference on Numerical Analysis and Applied Mathematics, Rhodes, Greece, 2015. (PDF)
  2. J. V. Lambers, "High-Order Time-Stepping for Nonlinear PDE through Rapid Estimation of Block Gaussian Quadrature Nodes", Proceedings of the 12th International Conference on Numerical Analysis and Applied Mathematics, Rhodes, Greece, 2014. (PDF)
  3. J. V. Lambers, "A Spectral Time-Domain Method for Computational Electrodynamics", Proceedings of the 7th International Conference on Numerical Analysis and Applied Mathematics, Crete, Greece, 2009, American Institute of Physics Conference Proceedings 1168 (2009), p. 1192-1195. (PDF)
  4. J. V. Lambers, M. G. Gerritsen, and D. Fragola, "Multiphase, 3-D Flow Simulation with Integrated Upscaling, MPFA Discretization, and Adaptivity", Proceedings of the SPE Reservoir Simulation Symposium, The Woodlands, Texas, 2009, SPE 118983.
  5. T. Chen, M. G. Gerritsen, L. J. Durlofsky, and J. V. Lambers, "Adaptive local-global VCMP methods for coarse-scale reservoir modeling", Proceedings of the SPE Reservoir Simulation Symposium, The Woodlands, Texas, 2009, SPE 118994.
  6. J. V. Lambers, "Implicitly Defined High-Order Operator Splittings for Parabolic and Hyperbolic Variable-Coefficient PDE Using Modified Moments", International Journal on Pure and Applied Mathematics 50(2), Proceedings of the Fifth International Conference on Applied Mathematics and Computing, Plovdiv, Bulgaria (2009), p. 239-244. (PDF)
  7. J. V. Lambers and M. G. Gerritsen, "Spatially-varying Compact Multi-point Flux Approximations for 3-D Adapted Grids with Guaranteed Monotonicity", Proceedings of the 2008 ASME International Mechanical Engineering Congress and Exposition, Boston (PDF)
  8. J. V. Lambers and M. G. Gerritsen, "Spatially-varying Compact Multi-point Flux Approximations for 3-D Adapted Grids with Guaranteed Monotonicity", Proceedings of the 11th European Conference on the Mathematics of Oil Recovery, Bergen, Norway, 2008 (PDF)
  9. J. V. Lambers, "Recent Advances in Krylov Subspace Spectral Methods", Proceedings of the 4th International Conference on Applied Mathematics and Computing, Plovdiv, Bulgaria, 2007, International Journal of Pure and Applied Mathematics 42 (2008), p. 495-500 (PDF)
  10. J. V. Lambers, "Recent Advances in Krylov Subspace Spectral Methods", Proceedings in Applied Mathematics and Mechanics 7(1), Proceedings of the Sixth International Congress on Industrial and Applied Mathematics, Zurich (2007), p. 2020143-2020144. (PDF)
  11. M. G. Gerritsen, J. V. Lambers and B. T. Mallison, "A Variable and Compact MPFA for Transmissibility Upscaling with Guaranteed Monotonicity", Proceedings of the 10th European Conference on the Mathematics of Oil Recovery, Amsterdam, 2006 (PDF)
  12. M. G. Gerritsen, K. Jessen, B. T. Mallison, and J. V. Lambers, "A Fully Adaptive Streamline Framework for the Challenging Simulation of Gas-Injection Processes", Proceedings of the SPE Annual Technical Conference and Exhibition, Dallas, 2005, SPE 97270.
  13. J. V. Lambers and M. G. Gerritsen, "An Integration of Multilevel Local-Global Upscaling with Grid Adaptivity", Proceedings of the SPE Annual Technical Conference and Exhibition, Dallas, 2005, SPE 97250.

Book Chapters:

  1. J. V. Lambers, A. Cibotarica and E. M. Palchak, "Matrices, Moments and Quadrature: Applications to Time-Dependent PDE", Applied Linear Algebra in Action (2016) (PDF)
  2. J. V. Lambers, "Block Krylov Subspace Spectral Methods for Variable-Coefficient Elliptic PDE", Current Themes in Engineering Science (2010) (PDF)
  3. J. V. Lambers, "Application of Block Krylov Subspace Spectral Methods to Maxwell's Equations", IAENG Transactions on Engineering Technologies 3 (2010)
  4. J. V. Lambers, "Coarse-scale Modeling of Flow in Gas-injection Processes for Enhanced Oil Recovery", Multiscale Modeling and Simulation in Science, Lecture Notes in Computational Science and Engineering 66 (2009), p. 303-306. (PDF)

Thesis:

J. V. Lambers, "Krylov Subspace Methods for Variable-Coefficient Initial-Boundary Value Problems", Ph.D. thesis, SC/CM Program, Stanford University, 2003 (PDF)