mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-08-29 23:52:49 +00:00
added description how to formulate new problems
This commit is contained in:
Jukka Aho
@@ -64,18 +64,7 @@
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Creating element Point1: 1 node point element\n",
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"Creating element Seg2: 2 node linear line element\n",
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"Creating Lagrange basis for element Seg2. Number of basis functions: 2. Element dimension: 1\n",
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"Calculating inverse of A\n"
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]
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}
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],
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"outputs": [],
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"source": [
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"using JuliaFEM: Element"
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]
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@@ -93,27 +82,7 @@
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"Element JuliaFEM.Seg2 created.\n",
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"Creating element Seg3: 3 node quadratic line element\n",
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"Creating Lagrange basis for element Seg3. Number of basis functions: 3. Element dimension: 1\n",
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"Calculating inverse of A\n",
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"Element JuliaFEM.Seg3 created.\n",
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"Creating element Quad4: 4 node bilinear quadrangle element\n",
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"Creating Lagrange basis for element Quad4. Number of basis functions: 4. Element dimension: 2\n",
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"Calculating inverse of A\n",
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"Element JuliaFEM.Quad4 created.\n",
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"Creating element Tet10: 10 node quadratic tetrahedron\n",
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"Creating Lagrange basis for element Tet10. Number of basis functions: 10. Element dimension: 3\n",
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"Calculating inverse of A\n",
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"Element JuliaFEM.Tet10 created.\n"
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]
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}
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],
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"outputs": [],
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"source": [
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"type MyQuad4 <: Element\n",
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" connectivity :: Array{Int, 1}\n",
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@@ -167,7 +136,7 @@
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{
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"data": {
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"text/plain": [
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"get_element_dimension (generic function with 6 methods)"
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"get_element_dimension (generic function with 7 methods)"
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]
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},
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"execution_count": 5,
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@@ -197,7 +166,7 @@
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{
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"data": {
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"text/plain": [
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"get_dbasisdxi (generic function with 6 methods)"
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"get_dbasisdxi (generic function with 7 methods)"
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]
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},
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"execution_count": 6,
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@@ -239,12 +208,12 @@
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"10-Sep 20:16:49:INFO:root:Testing element MyQuad4\n",
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"10-Sep 20:16:49:INFO:root:number of basis functions in this element: 4\n",
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"10-Sep 20:16:49:INFO:root:Initializing element\n",
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"10-Sep 20:16:49:INFO:root:Element dimension: 2\n",
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"10-Sep 20:16:49:INFO:root:Setting scalar field [1 2 3 4] to element.\n",
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"10-Sep 20:16:50:INFO:root:Interpolating scalar field at [0.0,0.0]\n"
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"24-Sep 21:04:04:INFO:root:Testing element MyQuad4\n",
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"24-Sep 21:04:04:INFO:root:number of basis functions in this element: 4\n",
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"24-Sep 21:04:04:INFO:root:Initializing element\n",
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"24-Sep 21:04:04:INFO:root:Element dimension: 2\n",
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"24-Sep 21:04:04:INFO:root:Setting scalar field [1 2 3 4] to element.\n",
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"24-Sep 21:04:04:INFO:root:Interpolating scalar field at [0.0,0.0]\n"
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]
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},
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{
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@@ -256,14 +225,6 @@
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"execution_count": 7,
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"metadata": {},
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"output_type": "execute_result"
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},
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"10-Sep 20:16:50:INFO:root:Value: [2.5]\n",
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"10-Sep 20:16:50:INFO:root:Element MyQuad4 passed tests.\n"
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]
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}
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],
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"source": [
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@@ -284,12 +245,21 @@
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"metadata": {
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"collapsed": false
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},
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"outputs": [],
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"24-Sep 21:04:04:INFO:root:Value: [2.5]\n",
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"24-Sep 21:04:04:INFO:root:Element MyQuad4 passed tests.\n"
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]
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}
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],
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"source": [
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"using JuliaFEM: set_field, interpolate\n",
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"el1 = MyQuad4([1, 2, 3, 4])\n",
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"set_field(el1, :temperature, [1 2 3 4])\n",
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"set_field(el1, :geometry, [0.0 0.0 0.0; 10.0 0.0 0.0; 10.0 1.0 0.0; 0.0 1.0 0.0]');\n",
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"set_field(el1, :temperature, [1, 2, 3, 4])\n",
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"set_field(el1, :Geometry, Vector[[0.0,0.0,0.0], [10.0,0.0,0.0], [10.0,1.0,0.0], [0.0,1.0,0.0]]);\n",
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"set_field(el1, :\"heat coefficient\", 1);"
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]
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},
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@@ -339,12 +309,12 @@
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],
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"source": [
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"# geometry midpoint of element\n",
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"interpolate(el1, :geometry, [0.0, 0.0])"
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"interpolate(el1, :Geometry, [0.0, 0.0])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 12,
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"execution_count": 11,
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"metadata": {
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"collapsed": false
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},
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@@ -355,7 +325,7 @@
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"1"
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]
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},
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"execution_count": 12,
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"execution_count": 11,
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"metadata": {},
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"output_type": "execute_result"
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}
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@@ -365,6 +335,15 @@
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"interpolate(el1, :\"heat coefficient\", [0.0, 0.0])"
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"### Summary of developing own elements\n",
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"\n",
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"Element itself if not calculating anything but only stores fields and basis functions so that the fields can be interpolated. We will provide command `test_element` which will ensure that everything necessary is defined. While lot of things needs to be defined, by subclassing from `Element` most of these are already defined, thanks to multiple dispatch."
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]
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},
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{
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"cell_type": "markdown",
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"metadata": {},
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@@ -398,7 +377,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"execution_count": 12,
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"metadata": {
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"collapsed": false
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},
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@@ -418,7 +397,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"execution_count": 13,
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"metadata": {
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"collapsed": false
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},
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@@ -443,7 +422,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"execution_count": 14,
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"metadata": {
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"collapsed": false
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},
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@@ -454,7 +433,7 @@
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"DC2D4"
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]
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},
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"execution_count": 17,
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"execution_count": 14,
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"metadata": {},
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"output_type": "execute_result"
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}
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@@ -466,7 +445,7 @@
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" IntegrationPoint(1.0/sqrt(3.0)*[ 1, -1], 1.0),\n",
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" IntegrationPoint(1.0/sqrt(3.0)*[ 1, 1], 1.0),\n",
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" IntegrationPoint(1.0/sqrt(3.0)*[-1, 1], 1.0)]\n",
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" set_field(el, :temperature, zeros(2, 4))\n",
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" set_field(el, :temperature, zeros(2, 4)) # assign new field \"temperature\" to element\n",
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" DC2D4(el, integration_points, [])\n",
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"end"
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]
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@@ -480,7 +459,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"execution_count": 15,
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"metadata": {
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"collapsed": false
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},
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@@ -491,13 +470,13 @@
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"has_lhs (generic function with 2 methods)"
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]
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},
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"execution_count": 18,
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"execution_count": 15,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"using JuliaFEM: get_element, get_dbasisdX\n",
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"using JuliaFEM: get_element, get_dbasisdX, has_lhs, has_rhs\n",
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"\n",
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"\"\"\"\n",
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"Left hand side defined in integration point\n",
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@@ -520,7 +499,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 19,
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"execution_count": 16,
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"metadata": {
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"collapsed": false
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},
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@@ -535,7 +514,7 @@
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" -1.0 -2.0 -1.0 4.0"
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]
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},
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"execution_count": 19,
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"execution_count": 16,
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"metadata": {},
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"output_type": "execute_result"
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}
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@@ -543,7 +522,7 @@
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"source": [
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"using JuliaFEM: integrate, integrate_lhs, integrate_rhs\n",
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"el = Quad4([1, 2, 3, 4])\n",
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"set_field(el, :geometry, [0 0; 1 0; 1 1; 0 1]')\n",
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"set_field(el, :Geometry, Vector[[0,0], [1,0], [1,1], [0,1]])\n",
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"set_field(el, :\"temperature thermal conductivity\", 6)\n",
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"eq = DC2D4(el)\n",
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"integrate_lhs(eq)"
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@@ -558,7 +537,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 20,
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"execution_count": 17,
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"metadata": {
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"collapsed": false
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},
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@@ -569,7 +548,7 @@
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"true"
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]
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},
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"execution_count": 20,
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"execution_count": 17,
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"metadata": {},
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"output_type": "execute_result"
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}
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@@ -587,7 +566,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"execution_count": 18,
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"metadata": {
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"collapsed": false
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},
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@@ -598,7 +577,7 @@
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"has_rhs (generic function with 2 methods)"
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]
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},
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"execution_count": 21,
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"execution_count": 18,
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"metadata": {},
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"output_type": "execute_result"
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}
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@@ -636,7 +615,7 @@
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},
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{
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"cell_type": "code",
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"execution_count": 22,
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"execution_count": 19,
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"metadata": {
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"collapsed": false
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},
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@@ -649,14 +628,14 @@
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" 50.0"
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]
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},
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"execution_count": 22,
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"execution_count": 19,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"el = Seg2([1, 2])\n",
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"set_field(el, :geometry, [0.0 0.0; 0.0 1.0]')\n",
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"set_field(el, :Geometry, Vector[[0.0,0.0], [0.0,1.0]])\n",
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"set_field(el, :\"temperature flux\", 100.0)\n",
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"eq = DC2D2(el)\n",
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"integrate_rhs(eq)"
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@@ -669,94 +648,132 @@
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"## Defining own problem\n",
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"\n",
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"- takes a set of elements and maps corresponding equations for them\n",
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"- boundary conditions\n",
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"- solve!(problem) updates fields"
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"- problem should have all required information in order to be solvable"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 20,
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"metadata": {
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"collapsed": true
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"collapsed": false
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},
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"outputs": [],
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"outputs": [
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{
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"data": {
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"text/plain": [
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"PlaneHeatProblem"
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]
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},
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"execution_count": 20,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"abstract Problem\n",
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"using JuliaFEM: Problem, get_equation, get_dimension\n",
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"\n",
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"type HeatProblem <: Problem\n",
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" elements: Array{Any, 1}\n",
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" equations: Array{Any, 1}\n",
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" boundary_conditions: Array{Any, 1}\n",
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"end"
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"type PlaneHeatProblem <: Problem\n",
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" equations :: Array{Any, 1}\n",
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"end\n",
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"PlaneHeatProblem() = PlaneHeatProblem([])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 21,
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"metadata": {
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"collapsed": false
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},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"get_equation (generic function with 3 methods)"
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]
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},
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"execution_count": 21,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"JuliaFEM.get_dimension(pr::Type{PlaneHeatProblem}) = 1\n",
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"JuliaFEM.get_equation(pr::Type{PlaneHeatProblem}, el::Type{Quad4}) = DC2D4\n",
|
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"JuliaFEM.get_equation(pr::Type{PlaneHeatProblem}, el::Type{Seg2}) = DC2D2"
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]
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},
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{
|
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"cell_type": "markdown",
|
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"metadata": {},
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"source": [
|
||||
"Developing boundary conditions"
|
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"Our solution procedure so far is therefore"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"execution_count": 23,
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"metadata": {
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"collapsed": true
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"collapsed": false
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},
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"outputs": [],
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"outputs": [
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{
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"name": "stderr",
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"output_type": "stream",
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"text": [
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"24-Sep 21:04:17:DEBUG:root:Problem (matrix) dimension: 4\n"
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]
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},
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{
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"data": {
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"text/plain": [
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"(\n",
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"4x4 Array{Float64,2}:\n",
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" 4.0 -1.0 -2.0 -1.0\n",
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" -1.0 4.0 -1.0 -2.0\n",
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" -2.0 -1.0 4.0 -1.0\n",
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" -1.0 -2.0 -1.0 4.0,\n",
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"\n",
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"[50.0,50.0,0.0,0.0])"
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]
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},
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"execution_count": 23,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"abstract BC\n",
|
||||
"using JuliaFEM: set_global_dofs!, get_global_dofs, add_element!, get_equations, get_matrix_dimension\n",
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"\n",
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"type DefaultBC <: BC\n",
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" \n",
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"end"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"bc = NodalBC()\n",
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"bc[:displacement, [1, 2, 3], 1:2] = 3.0"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"bc = WeakBC()\n",
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"bc[:displacement, [el1, el2, el3]] = (X) -> X[0] + X[1] - 2"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
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"outputs": [],
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"source": [
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"bc = MPCBC()\n",
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"bc[:displacement, "
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"metadata": {
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"collapsed": true
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},
|
||||
"outputs": [],
|
||||
"source": [
|
||||
"bc = MortarBC()\n"
|
||||
"# create elements and add necessary properties like connectivity and geometry\n",
|
||||
"el1 = Quad4([1, 2, 3, 4])\n",
|
||||
"set_field(el1, :Geometry, Vector[[0,0], [1,0], [1,1], [0,1]])\n",
|
||||
"set_field(el1, :\"temperature thermal conductivity\", 6)\n",
|
||||
"el2 = Seg2([1, 2])\n",
|
||||
"set_field(el2, :Geometry, Vector[[0.0,0.0], [0.0,1.0]])\n",
|
||||
"set_field(el2, :\"temperature flux\", 100.0)\n",
|
||||
"\n",
|
||||
"problem = PlaneHeatProblem()\n",
|
||||
"add_element!(problem, el1)\n",
|
||||
"add_element!(problem, el2)\n",
|
||||
"\n",
|
||||
"# set global dofs for equations\n",
|
||||
"set_global_dofs!(problem)\n",
|
||||
"\n",
|
||||
"n = get_matrix_dimension(problem)\n",
|
||||
"\n",
|
||||
"# integrate and assembly\n",
|
||||
"A = zeros(n, n)\n",
|
||||
"b = zeros(n)\n",
|
||||
"for eq in get_equations(problem)\n",
|
||||
" dofs = get_global_dofs(eq)\n",
|
||||
" if has_lhs(eq)\n",
|
||||
" A[dofs, dofs] += integrate_lhs(eq)\n",
|
||||
" end\n",
|
||||
" if has_rhs(eq)\n",
|
||||
" b[dofs] += integrate_rhs(eq)\n",
|
||||
" end\n",
|
||||
"end\n",
|
||||
"A, b"
|
||||
]
|
||||
}
|
||||
],
|
||||
|
||||
+3
-1
@@ -10,7 +10,9 @@ using Logging
|
||||
include("types.jl") # type definitions
|
||||
include("elements.jl") # elements
|
||||
include("equations.jl") # formulations
|
||||
include("math.jl") # basic mathematical operations
|
||||
include("problems.jl") # problems
|
||||
|
||||
include("math.jl") # basic mathematical operations -- obsolete ..?
|
||||
|
||||
include("elasticity_solver.jl")
|
||||
include("xdmf.jl")
|
||||
|
||||
+4
-1
@@ -27,13 +27,16 @@ has_rhs(eq::Equation) = false
|
||||
get_rhs(eq::Equation, xi) = nothing
|
||||
get_element(eq::Equation) = eq.element
|
||||
get_integration_points(eq::Equation) = eq.integration_points
|
||||
|
||||
# couple convenient functions -- could make weak form definition easier
|
||||
get_connectivity(eq::Equation) = get_connectivity(get_element(eq))
|
||||
get_basis(eq::Equation, ip::IntegrationPoint) = get_basis(get_element(eq), ip.xi)
|
||||
get_dbasisdx(eq::Equation, ip::IntegrationPoint) = get_dbasisdx(get_element(eq), ip.xi)
|
||||
interpolate(eq::Equation, field::Union(ASCIIString, Symbol), ip::IntegrationPoint) = interpolate(get_element(el), field, ip.xi)
|
||||
integrate_lhs(eq::Equation) = has_lhs(eq) ? integrate(eq, get_lhs) : nothing
|
||||
integrate_rhs(eq::Equation) = has_rhs(eq) ? integrate(eq, get_rhs) : nothing
|
||||
|
||||
|
||||
"""
|
||||
Return determinant of Jacobian for numerical integration.
|
||||
"""
|
||||
@@ -72,7 +75,7 @@ function get_global_dofs(eq::Equation)
|
||||
eq.global_dofs
|
||||
end
|
||||
|
||||
function set_global_dofs(eq::Equation, dofs)
|
||||
function set_global_dofs!(eq::Equation, dofs)
|
||||
eq.global_dofs = dofs
|
||||
end
|
||||
|
||||
|
||||
@@ -0,0 +1,52 @@
|
||||
# This file is a part of JuliaFEM.
|
||||
# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
|
||||
|
||||
abstract Problem
|
||||
|
||||
get_equations(pr::Problem) = pr.equations
|
||||
get_dimension(pr::Type{Problem}) = nothing
|
||||
get_equation(pr::Type{Problem}, el::Type{Element}) = nothing
|
||||
|
||||
"""
|
||||
Add new element to problem
|
||||
"""
|
||||
function add_element!(pr::Problem, el::Element)
|
||||
eq = get_equation(typeof(pr), typeof(el))
|
||||
push!(pr.equations, eq(el))
|
||||
end
|
||||
|
||||
"""
|
||||
Return total number of basis functions in problem
|
||||
"""
|
||||
function get_number_of_basis_functions(pr::Problem)
|
||||
conn = Int[]
|
||||
for eq in get_equations(pr)
|
||||
append!(conn, get_connectivity(eq))
|
||||
end
|
||||
length(unique(conn))
|
||||
end
|
||||
|
||||
"""
|
||||
Problem matrix size dimension
|
||||
"""
|
||||
function get_matrix_dimension(pr::Problem)
|
||||
get_dimension(typeof(pr))*get_number_of_basis_functions(pr)
|
||||
end
|
||||
|
||||
"""
|
||||
Assign global dofs for element. This doesn't do any reordering.
|
||||
"""
|
||||
function set_global_dofs!(pr::Problem)
|
||||
#ndim = get_dimension(pr)*get_number_of_basis_functions(pr)
|
||||
#ndim = get_matrix_dimension(pr)
|
||||
dim = get_dimension(typeof(pr))
|
||||
nconn = get_number_of_basis_functions(pr)
|
||||
ndim = dim*nconn
|
||||
Logging.debug("Problem (matrix) dimension: $ndim")
|
||||
gdofs = reshape(collect(1:ndim), dim, nconn)
|
||||
for eq in get_equations(pr)
|
||||
lconn = get_connectivity(eq)
|
||||
gconn = gdofs[:, lconn][:]
|
||||
set_global_dofs!(eq, gconn)
|
||||
end
|
||||
end
|
||||
Reference in New Issue
Block a user