My research is in numerical analysis, which is the study of the design, analysis and implementation of numerical methods that would be used by computers to solve a variety of mathematical problems such as those arising in calculus, linear algebra, and differential equations. Such problems are of fundamental importance in application areas throughout the sciences and engineering, as they occur in models for myriad processes such as the diffusion of heat energy, the propagation of sound waves, or the evolution of the prices of financial derivatives, but they generally cannot be solved by analytical methods due to their complexity or the amount of data required.
I am particularly interested in working with undergraduate students who have background in calculus and/or linear algebra and familiarity with a programming language in order to aid in the development of new methods for solving various problems in numerical analysis that stem from application areas such as image processing, simulation of oil recovery, or the evolution of quantum states.
1. 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.
2. J. V. Lambers, "Approximate Diagonalization of Variable-Coefficient Differential Operators Through Similarity Transformations", Computers and Mathematics with Applications 64(8) (2012), p. 2575-2593.
3. 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.
4. 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.
5. 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.
6. 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.
7. J. V. Lambers, "A Spectral Time-Domain Method for Computational Electrodynamics", Advances in Applied Mathematics and Mechanics 1(6) (2009), p. 781-798.
8. J. V. Lambers, "Krylov Subspace Spectral Methods for the Time-Dependent Schrödinger Equation with Non-Smooth Potentials", Numerical Algorithms 51 (2009), p. 239-280.
9. 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.
10. J. V. Lambers, "Enhancement of Krylov Subspace Spectral Methods by Block Lanczos Iteration", Electronic Transactions on Numerical Analysis 31 (2008), p. 86-109.
11. 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.
12. 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.
13. 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.
14. 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.
15. 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.
16. J. V. Lambers, "Practical Implementation of Krylov Subspace Spectral Methods", Journal of Scientific Computing 32 (2007), p. 449-476.
17. 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.
18. 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.
19. J. V. Lambers, "Krylov Subspace Spectral Methods for Variable-Coefficient Initial-Boundary Value Problems", Electronic Transactions on Numerical Analysis 20 (2005), p. 212-234.