Self consistent method for eigenvalues

Click For Summary
SUMMARY

The discussion focuses on improving the convergence of Self Consistent Field (SCF) calculations for finding eigenvalues of nonlinear Schrödinger equations, akin to methods used in Hartree-Fock problems. The primary technique recommended for enhancing SCF convergence is the Direct Inversion in the Iterative Subspace (DIIS) method, which is widely recognized for its effectiveness. Participants are encouraged to explore various DIIS variants to optimize their calculations further.

PREREQUISITES
  • Understanding of Self Consistent Field (SCF) methods
  • Familiarity with nonlinear Schrödinger equations
  • Knowledge of Hartree-Fock theory
  • Basic principles of numerical methods for eigenvalue problems
NEXT STEPS
  • Research the Direct Inversion in the Iterative Subspace (DIIS) method
  • Explore variants of DIIS for SCF calculations
  • Study numerical techniques for solving nonlinear Schrödinger equations
  • Investigate convergence acceleration methods in computational physics
USEFUL FOR

Researchers and practitioners in computational physics, quantum chemistry, and applied mathematics who are focused on eigenvalue problems and SCF methods.

babylonia
Messages
9
Reaction score
0
Hi all,

I am trying to find numerically the eigenvalues of a nonlinear schroedinger equation in a similar way as the Self Consistent Field method for Hatree-Fock problems. Does anybody know in the SCF calculation how to improve the convergency? Is there any trick other than simply inserting the solution back for the next iteration?

Any clues would be appreciated. Thank you.
 
Last edited:
Physics news on Phys.org
There are a number of techniques to stabilize and improve SCF convergence. The one that's most used by far is http://en.wikipedia.org/wiki/DIIS" (and variants of it) though. So that's probably a good place to start.
 
Last edited by a moderator:

Similar threads

Graduate The eigenvalue power method for quantum problems
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Eigenvalues for a non self adjoint operator
  • · Replies 4 ·
Replies
4
Views
3K
Graduate Numerical Hartree Fock with Finite Difference Matrices for Helium
  • · Replies 4 ·
Replies
4
Views
3K
Mathematica What could be causing spurious eigenvalues in my Eigensystem command?
  • · Replies 1 ·
Replies
1
Views
3K
I need help please for Simulation of Xenon Oscillations in a Nuclear Reactor
  • · Replies 4 ·
Replies
4
Views
2K
Graduate Eigenvalues of nonlinearly coupled equations
  • · Replies 5 ·
Replies
5
Views
2K
Graduate Solving an ODE Eigenvalue Problem via the Ritz method
  • · Replies 1 ·
Replies
1
Views
2K
Intro Math Comprehensive math-physics books for self-study
  • · Replies 7 ·
Replies
7
Views
4K
Graduate Some questions regarding the ADI Method
  • · Replies 1 ·
Replies
1
Views
2K
Studying What Are the Best Steps for Self-Teaching Theoretical Physics?
  • · Replies 14 ·
Replies
14
Views
5K