Generalizations of Davidson's method for computing eigenvalues of sparse symmetric matrices
SIAM Journal on Scientific and Statistical Computing
A Jacobi--Davidson Iteration Method for Linear EigenvalueProblems
SIAM Journal on Matrix Analysis and Applications
Immersed Interface Methods for Stokes Flow with Elastic Boundaries or Surface Tension
SIAM Journal on Scientific Computing
Using Generalized Cayley Transformations within an Inexact Rational Krylov Sequence Method
SIAM Journal on Matrix Analysis and Applications
Rational Krylov: A Practical Algorithm for Large Sparse Nonsymmetric Matrix Pencils
SIAM Journal on Scientific Computing
The immersed finite volume element methods for the elliptic interface problems
Mathematics and Computers in Simulation - Special issue from IMACS sponsored conference: “Modelling '98”
Templates for the solution of algebraic eigenvalue problems: a practical guide
Templates for the solution of algebraic eigenvalue problems: a practical guide
Locking and Restarting Quadratic Eigenvalue Solvers
SIAM Journal on Scientific Computing
Numerical methods for semiconductor heterostructures with band nonparabolicity
Journal of Computational Physics
Iterative projection methods for computing relevant energy states of a quantum dot
Journal of Computational Physics
An efficient algorithm for the Schrödinger-Poisson eigenvalue problem
Journal of Computational and Applied Mathematics
Journal of Computational Physics
A discrete geometric approach to solving time independent Schrödinger equation
Journal of Computational Physics
NEHIPISIC'11 Proceeding of 10th WSEAS international conference on electronics, hardware, wireless and optical communications, and 10th WSEAS international conference on signal processing, robotics and automation, and 3rd WSEAS international conference on nanotechnology, and 2nd WSEAS international conference on Plasma-fusion-nuclear physics
Solving Rational Eigenvalue Problems via Linearization
SIAM Journal on Matrix Analysis and Applications
Electronic states in three dimensional quantum dot/wetting layer structures
ICCSA'06 Proceedings of the 6th international conference on Computational Science and Its Applications - Volume Part I
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We present a simple and efficient numerical method for the simulation of the three-dimensional pyramid quantum dot heterostructure. The pyramid-shaped quantum dot is placed in a computational box with uniform mesh in Cartesian coordinates. The corresponding Schrödinger equation is discretized using the finite volume method and the interface conditions are incorporated into the discretization scheme without explicitly enforcing them. The resulting matrix eigenvalue problem is then solved using a Jacobi-Davidson based method. Both linear and non-linear eigenvalue problems are simulated. The scheme is 2nd order accurate and converges extremely fast. The superior performance is a combined effect of the uniform spacing of the grids and the nice structure of the resulting matrices. We have successfully simulated a variety of test problems, including a quintic polynomial eigenvalue problem with more than 32 million variables.