mass_matrix2D module

Created on Sun Sep 3 13:00:52 2023

@author: Pavan Pranjivan Mehta

class mass_matrix2D.mass_matrix2D

Bases: object

Computes mass matrix in 2 spatial dimensions

legendre()

Computes Mass matrix Legendre Polynomials in [-1,1] x [-1,1] of dim = (k^2) x (k^2), where k-1 is highest degree

Parameters

degreeint

degree of the polynomial

Returns

2D Mass martix Legendre polynomials within the interval [-1,1] x [-1, 1]

M: numpy array

Matrix of dim (k)**2 X (k)**2, where k-1 is the highest degree of Legengre Polynomials

shift_legendre()

Computes 2D Mass matrix Shifted Legendre Polynomials in [0,1] x [0,1] of dim = (k^2) x (k^2), where k-1 is highest degree

Parameters

degreeint

degree of the polynomial

Returns

2D Mass martix Legendre polynomials within the interval [0,1] x[0,1]

M: 2D numpy array

Matrix of dim (k^2) X (k^2), where k-1 is the highest degree of Shifted Legengre Polynomials

homogenous_legendre()

Computes 2D Mass matrix Homogenous basis function using Legendre Polynomials in [-1,1] x [-1,1] of dim = (k^2) x (k^2), where k-1 is highest degree

Parameters

degreeint

max degree of the polynomial

Returns

Mass martix Legendre polynomials within the interval [-1,1] x [-1,1]

M: numpy array

Matrix of dim (k^2) X (k^2), where k-1 is the highest degree of Legengre Polynomials

homogenous_shift_legendre()

Computes 2D Mass matrix Homogenous basis function using Shifted Legendre Polynomials in [0,1] of dim = (k^2) x (k^2), where k-1 is highest degree

Parameters

degreeint

max degree of the polynomial

Returns

2D ass martix Shifted Legendre polynomials within the interval [0,1] x [0,1]

M: numpy array

2D Matrix of dim (k^2) X (k^2), where k-1 is the highest degree of Shifted Legengre Polynomials

class mass_matrix2D.test

Bases: object

legendre()

shift_legendre()

homogenous_legendre()

runge(y)

funx()

funy()

func(y)

legendre_proj()

legendre_proj_err()

shift_legendre_proj()

shift_legendre_proj_err()

homogenous_legendre_proj()

homogenous_legendre_proj_err()

homogenous_shift_legendre_proj()

homogenous_shift_legendre_proj_err()

proj_err()