mass_matrix module

Created on Thu Aug 31 16:29:13 2023

@author: Pavan Pranjivan Mehta

class mass_matrix.mass_matrix

Bases: object

Computes mass matrix

legendre()

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

Parameters

degreeint

degree of the polynomial

Returns

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

M: numpy array

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

shift_legendre()

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

Parameters

degreeint

degree of the polynomial

Returns

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

M: numpy array

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

jacobi(beta, degree)

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

Parameters

alphafloat

paramter assocated with Jacobi Polynomials, alpha > -1

betafloat

paramter assocated with Jacobi Polynomials, beta > -1

degreeint

degree of the polynomial

Returns

Mass martix Jacobi polynomials within the interval [-1,1]

M: numpy array

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

shift_jacobi(beta, degree)

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

Parameters

alphafloat

paramter assocated with Jacobi Polynomials, alpha > -1

betafloat

paramter assocated with Jacobi Polynomials, beta > -1

degreeint

degree of the polynomial

Returns

Mass martix Jacobi polynomials within the interval [0,1]

M: numpy array

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

Q_poly(beta, degree)

Computes Mass matrix Q Polynomials in [0,1] of dim = (k) x (k), where k-1 is highest degree

Parameters

alphafloat

paramter assocated with Q Polynomials, alpha > -1

betafloat

paramter assocated with Q Polynomials, beta > -1

degreeint

degree of the polynomial

Returns

Mass martix Q polynomials within the interval [0,1]

M: numpy array

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

Notes

Q (x) := P_n (1-2x), where P_n is a Jacobi polynomial with paramter, alpha and beta.

shift_arbitary_jacobi(b, alpha, beta, degree)

Computes Mass matrix Shifted (arbitary) Jacobi Polynomials in [a,b] of dim = (k) x (k), where k-1 is highest degree

Parameters

afloat

min of interval [a, b]

bfloat

max of interval [a, b]

alphafloat

paramter assocated with Jacobi Polynomials, alpha > -1

betafloat

paramter assocated with Jacobi Polynomials, beta > -1

degreeint

degree of the polynomial

Returns

Mass martix Jacobi polynomials within the interval [0,1]

M: numpy array

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

homogenous_legendre()

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

Parameters

degreeint

max degree of the polynomial

Returns

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

M: numpy array

Matrix of dim (k) X (k), where k-1 is the highest degree of homogeous legendre Polynomials

homogenous_shift_legendre()

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

Parameters

degreeint

max degree of the polynomial

Returns

Mass martix Shifted Legendre polynomials within the interval [0,1]

M: numpy array

Matrix of dim (k) X (k), where k-1 is the highest degree of homogeous shifted legendre Polynomials

class mass_matrix.test

Bases: object

legendre()

shift_legendre()

homogenous_legendre()

runge()

runge_arb(b, x)

func()

legendre_proj()

legendre_proj_err()

shift_legendre_proj()

Q_proj(beta, degree)

shift_jacob_arb_proj(b, alpha, beta, degree)

shift_legendre_proj_err()

shift_jacobi_project_coeff(beta, degree)

Comuptes the coeffients for L2 projection over shifted Jacobi basis

homogenous_legendre_proj()

homogenous_legendre_proj_err()

homogenous_shift_legendre_proj()

homogenous_shift_legendre_proj_err()

proj_err()