mass_matrix via convolution module#
Created on Wed Aug 28 10:36:58 2024
@author: Pavan Pranjivan Mehta
- class conv_mass_matrix.conv_mass_matrix#
Bases:
objectComputes convolution mass matrix
- 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
- 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.
Untested
- 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