gusto.rexi package

Submodules

gusto.rexi.rexi module

class gusto.rexi.rexi.Rexi(equation, rexi_parameters, *, solver_parameters=None, manager=None, cpx_type='mixed')[source]

Bases: object

Class defining the solver for the system

(A_n + tau L)V_n = U

required for computing the matrix exponential.

Parameters:

  • equation (PrognosticEquation) – the model’s equation

  • rexi_parameters (RexiParameters) – Rexi configuration parameters

  • solver_parameters (dict, optional) – dictionary of parameters to pass to the solver. Defaults to None.

  • manager (Ensemble) – the space and ensemble sub- communicators. Defaults to None.

  • cpx_type (str, optional) – implementation of complex-valued space, can be ‘mixed’ or ‘vector’.

solve(x_out, x_in, dt)[source]

Solve method for approximating the matrix exponential by a rational sum. Solves

(A_n + tau L)V_n = U

multiplies by the corresponding B_n and sums over n.

Parameters:

  • x_in – the mixed function on the rhs.

  • dt – the value of tau

gusto.rexi.rexi_coefficients module

gusto.rexi.rexi_coefficients.RexiCoefficients(rexi_parameters)[source]

Compute the A_n and B_n coefficients in the REXI sum

exp(ix) pprox sum_{n=0}^{P} B_n (ix + A_n)

where P = 4N+1 if rexi_parameters.reduce_to_half is False else 2N+1 if True.

Returns 3 numpy arrays: alpha contains the A_n coefficients beta contains the B_n coefficients beta2 contains zeros if rexi_parameters.reduce_to_half is False else it contains the coefficients that multiply the conjugate terms

Parameters:

rexi_parameters – class containing the parameters (h, M and

reduce_to_half) necessary to compute the coefficients

class gusto.rexi.rexi_coefficients.RexiParameters(**kwargs)[source]

Bases: Configuration

mu and a coefficients from “A high-order time-parallel scheme for solving wave propagation problems via the direct construction of an approximate time-evolution operator”, Haut et.al.

Parameters:

**kwargs – attributes and their values to be stored in the object.

L = 11
M = 64
a = [(-1.0845749544592896e-07+2.77075431662228e-08j), (1.858753344202957e-08-9.105375434750162e-07j), (3.6743713227243024e-06+7.073284346322969e-07j), (-2.7990058083347696e-06+1.12564827639346e-05j), (1.4918577548849352e-05-3.16278486761932e-05j), (-0.0010751767283285608-0.00047282220513073084j), (0.003816465653840016+0.017839810396560574j), (0.12124105653274578-0.12327042473830248j), (-0.9774980792734348-0.1877130220537587j), (1.3432866123333178+3.2034715228495942j), (4.072408546157305-6.123755543580666j), (-9.442699917778205+0j), (4.072408620272648+6.123755841848161j), (1.3432860877712938-3.2034712658530275j), (-0.9774985292598916+0.18771238018072134j), (0.1212417070363373+0.12326987628935386j), (0.0038169724770333343-0.017839242222443888j), (-0.0010756025812659208+0.0004731874917343858j), (1.4713754789095218e-05+3.1358475831136815e-05j), (-2.659323898804944e-06-1.1341571201752273e-05j), (3.6970377676364553e-06-6.517457477594937e-07j), (3.883933649142257e-09+9.128496023863376e-07j), (-1.0816457995911385e-07-2.954309729192276e-08j)]
h = 0.2
mu = (-4.315321510875024+0j)
reduce_to_half = False
gusto.rexi.rexi_coefficients.b_coefficients(h, M)[source]

Compute the b coefficients where b_m = h^2 exp(imh)

Module contents