{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"ChEn-5310: Computational Continuum Transport Phenomena Fall 2021 UMass Lowell; Prof. V. F. de Almeida **29Sep21**\n",
"\n",
"# 05c. Rayleigh-Ritz Method w/ Finite Element Lagrange Basis Functions\n",
"$ \n",
" \\newcommand{\\Amtrx}{\\boldsymbol{\\mathsf{A}}}\n",
" \\newcommand{\\Bmtrx}{\\boldsymbol{\\mathsf{B}}}\n",
" \\newcommand{\\Mmtrx}{\\boldsymbol{\\mathsf{M}}}\n",
" \\newcommand{\\Imtrx}{\\boldsymbol{\\mathsf{I}}}\n",
" \\newcommand{\\Pmtrx}{\\boldsymbol{\\mathsf{P}}}\n",
" \\newcommand{\\Lmtrx}{\\boldsymbol{\\mathsf{L}}}\n",
" \\newcommand{\\Umtrx}{\\boldsymbol{\\mathsf{U}}}\n",
" \\newcommand{\\Smtrx}{\\boldsymbol{\\mathsf{S}}}\n",
" \\newcommand{\\xvec}{\\boldsymbol{\\mathsf{x}}}\n",
" \\newcommand{\\avec}{\\boldsymbol{\\mathsf{a}}}\n",
" \\newcommand{\\bvec}{\\boldsymbol{\\mathsf{b}}}\n",
" \\newcommand{\\cvec}{\\boldsymbol{\\mathsf{c}}}\n",
" \\newcommand{\\rvec}{\\boldsymbol{\\mathsf{r}}}\n",
" \\newcommand{\\fvec}{\\boldsymbol{\\mathsf{f}}}\n",
" \\newcommand{\\mvec}{\\boldsymbol{\\mathsf{m}}}\n",
" \\newcommand{\\gvec}{\\boldsymbol{\\mathsf{g}}}\n",
" \\newcommand{\\zerovec}{\\boldsymbol{\\mathsf{0}}}\n",
" \\newcommand{\\norm}[1]{\\bigl\\lVert{#1}\\bigr\\rVert}\n",
" \\newcommand{\\transpose}[1]{{#1}^\\top}\n",
" \\DeclareMathOperator{\\rank}{rank}\n",
" \\newcommand{\\Reals}{\\mathbb{R}}\n",
" \\newcommand{\\thetavec}{\\boldsymbol{\\theta}}\n",
" \\newcommand{\\Ecal}{\\mathcal{E}}\n",
"$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"\n",
"## Table of Contents\n",
"* [Objectives](#obj)\n",
"1. [Poisson Problem with Dirichlet/Robin Boundary Conditions](#problem)\n",
"1. [Rayleigh-Ritz Method with Dirichlet/Robin Boundary Conditions](#rayleigh-ritz)\n",
" + [Data](#data)\n",
" + [Lift function](#lift-function)\n",
" + [Finite Element Lagrange Basis Functions](#fem-lagrange-basis)\n",
" + [Results](#results)\n",
"1. [Poisson Problem with Dirichlet/Robin Boundary Conditions](#problem-left)\n",
"1. [Rayleigh-Ritz Method with Dirichlet/Robin Boundary Conditions](#rayleigh-ritz-left)\n",
" + [Data](#data-left)\n",
" + [Lift function](#lift-function-left)\n",
" + [Finite Element Lagrange Basis Functions](#fem-lagrange-basis-left)\n",
" + [Results](#results-left)\n",
"---"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## [Objectives](#toc)\n",
"\n",
" + Describe the Rayleigh-Ritz method for solving linear differential equations with symmetric positive definite operators (OneNote [Engy-5310-rayleigh-ritz-method](https://studentuml-my.sharepoint.com/:o:/g/personal/valmor_dealmeida_uml_edu/EsTzIb2Mcv5OkcSk0kSXXF8BXM4OnlzGfAd7sdcWLky-Gw?e=FQvvy1)).\n",
" + Use the function approximation theory described in the course (see previous notebooks and notes).\n",
" + Apply the finite element Lagrange basis functions."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## [Poisson Problem with Dirichlet/Robin Boundary Conditions](#toc)\n",
"\n",
"The following sections describe what is referred to in the literature as the one-dimensional Poisson problem with Dirichlet boundary conditions. This is a classical boundary-value problem of mathematics."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Solve the Poisson model problem. Find $u:[a,b]\\subset\\Reals\\rightarrow\\Reals$ such that:\n",
"\n",
"\\begin{align*}\n",
" -\\bigl(-D(x)\\, u'\\bigr)'(x) + S(x)\\,u(x) + f(x) &= 0 \\quad\\quad \\forall \\quad\\quad x\\in\\ ]a,b[, \\\\\n",
" u(a) &= u_a, \\\\\n",
" q_n(b) &= h\\,\\bigl(u(b)-u_\\text{ref}\\bigr).\n",
"\\end{align*}\n",
" \n",
"This problem is linear and has an analytical solution for given data: diffusion coefficient, $D(x)$, source, $S(x)$ slope, source bias, $f(x)$. The *diffusion flux* associated to the quantity $u$, is denoted $q := -D(x)\\,u'$, and it is often of interest as a derived quantity.\n",
"\n",
"The normal diffusive flux at $x=b$ is $q_n(b) = -D\\,u'(b) = h\\bigl(u(b)-u_\\text{ref}\\bigr)$\n",
"\n",
"The values of the dependent variable are given on the two end points of the domain. This is called *essential* boundary conditions or *Dirichlet boundary conditions*. If the values are equal to zero, the boundary condition is referred to as homogeneous."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## [Rayleigh-Ritz Method w/ Dirichlet/Robin Boundary Conditions](#toc)\n",
"\n",
"Find $u^*_N \\in V_N(a,b)\\subset V(a,b) = \\bigl\\{ u:[a,b]\\subset\\Reals\\rightarrow\\Reals \\bigr\\}$ such that it minimizes the constrained Poisson energy norm:\n",
"\n",
"\\begin{equation*}\n",
" \\min\\limits_{u_0\\, \\in\\, V} \\norm{u_0+w-u_N}^2_{\\Ecal},\n",
"\\end{equation*}\n",
"\n",
"where \n",
"$V_N(a,b) := \\bigl\\{ u_N = \\sum\\limits_{i=1}^N\\,c_i\\,\\phi_i \\mid u_N(a) = 0, (u'_N,u'_N) < \\infty \\bigr\\}$, $\\{\\phi_i\\mid i=1\\ldots,N\\}$ is a basis of $V_N(a,b)$, and any $w \\in V$ with $w(a) = u_a$ is called the *lift* function.\n",
"\n",
"The optimum coefficients $\\cvec^* := \\{c_i\\mid i=1,\\ldots,N\\}$ solve\n",
"\n",
"\\begin{equation*}\n",
" \\overset{(N\\times N)}{\\Amtrx}\\,\\overset{(N\\times 1)}{\\cvec^*} = \\overset{(N\\times 1)}\\bvec ,\n",
"\\end{equation*}\n",
"\n",
"where:\n",
" + $A_{i,j} = (D\\,\\phi'_i,\\phi'_j) - (S\\,\\phi_i,\\phi_j) + h\\phi_j(b)\\,\\phi_i(b) $\n",
" + $b_i = (f,\\phi_i) - (D\\,w',\\phi'_i) + (S\\,w,\\phi_i) - h\\,\\bigl(w(b)-u_\\text{ref}\\bigr) \\,\\phi_i(b)$\n",
" \n",
"This formulation uses basis functions that satisfy the left homogeneous boundary condition, however the linear algebraic problem for the optimum coefficients accounts for the inhomogeneous boundary condition data through the lift function $w$."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### [Data](#toc)\n",
"\n",
"Solve problem with parameter values:\n",
"\n",
"> + a = 0 cm\n",
"> + b = 25 cm\n",
"> + $u_a$ = 2 g/cc\n",
"> + $h$ = see next cm/s\n",
"> + $u_\\text{ref}$ = 0 g/cc\n",
"> + D = 0.1 cm^2/s\n",
"> + S = 2e-3 $s^{-1}$\n",
"> + f = 1e-3 g/cc-s"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"ExecuteTime": {
"end_time": "2022-04-23T05:49:41.439616Z",
"start_time": "2022-04-23T05:49:41.436885Z"
}
},
"outputs": [],
"source": [
"'''Domain'''\n",
"\n",
"x_a = 0\n",
"x_b = 25"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"ExecuteTime": {
"end_time": "2022-04-23T05:49:56.192494Z",
"start_time": "2022-04-23T05:49:56.189458Z"
}
},
"outputs": [],
"source": [
"'''Parameters and data'''\n",
"\n",
"diff_coeff = 0.1\n",
"source_bias_value = 1e-2\n",
"source_slope_value = 1.87e-2\n",
"\n",
"u_a = 2\n",
"h = 1\n",
"u_ref = 4.8125"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"ExecuteTime": {
"end_time": "2022-04-23T05:49:58.305362Z",
"start_time": "2022-04-23T05:49:56.947277Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"# shape pts = 3\n"
]
},
{
"data": {
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