Weighted_Spiral_Spectra

Matlab code to compute the spectra of spiral waves using and exponentially weighted preconditioner.

Matlab Scripts

The main components of the code are:

compute_spectra_weighted.m: Computes the eigenvalues of a spiral wave using the exponentially weighted operator.

solve_spiral_wave.m: Uses Newton's method to solve for a spiral wave solution in a polar co-rotating frame.

spiral_pseudospec_conditionNum.m: Computes the condition number and minimum svd values of the linearized spiral wave operator across a grid of defined points in the complex plane.

Auxiliary Functions

The following are helper functions that are called by the main scripts.

Barkley_2D_rotating.m: Defines the right-hand side of the Barkley model equation. Used to solve for spiral solutions in the co-rotating polar frame.

Barkley_jacobian_weighted_operator: Defines the weighted Jacobian matrix of the Barkley model.

ComputeLinearOperator_shortGrid.m: Defines the relevant 2D polar differentiation operators used for computing eigenvalues.

ComputeLinearOperator.m: Defines the relevant 2D polar differentiation operators used for solving for spiral wave solutions.

fourdif.m: Defines 1D Fourier differentiation matrices

plot_spiral.m: Function to plot spiral wave solutions.

Matlab Files

Barkley_spiral_r25_h0p05_delta0p2_b0p001_a0p7_ep0p02.mat: Spiral wave solution to the Barkley model with radius 25. Other parameters are define in the par structure and in the file name. Specifically, $\delta = 0.2$, $b = 0.001$, $a = 0.7$, and $\epsilon = 0.02$.

Barkley_spiral_r50_h0p05_delta0p2_b0p001_a0p7_ep0p02_positiveOmega.mat: Spiral wave solution to the Barkley model with radius 50. Other parameters are define in the par structure and are equivalent to the radius 25 case.