diff --git a/examples/modal_analysis_dynamics/cantilever_modal.py.rst b/examples/modal_analysis_dynamics/cantilever_modal.py.rst index c514ee453a51c995b322c4bcb272ecef6a88767d..54c45163a7f3c6c4547cba9a081886d342d40c66 100644 --- a/examples/modal_analysis_dynamics/cantilever_modal.py.rst +++ b/examples/modal_analysis_dynamics/cantilever_modal.py.rst @@ -106,15 +106,13 @@ can be solved using the SLEPcEigenSolver. :: eigensolver = SLEPcEigenSolver(K, M) eigensolver.parameters['problem_type'] = 'gen_hermitian' - eigensolver.parameters["spectrum"] = "smallest real" eigensolver.parameters['spectral_transform'] = 'shift-and-invert' eigensolver.parameters['spectral_shift'] = 0. The problem type is specified to be a generalized eigenvalue problem with -Hermitian matrices. By default, SLEPc computes the largest eigenvalues, here -we instead look for the smallest eigenvalues (they should all be real). To -improve convergence of the eigensolver for finding the smallest eigenvalues -(by default it computes the largest ones), a spectral transform is performed +Hermitian matrices. By default, SLEPc computes the largest eigenvalues. Here +we instead look for the smallest eigenvalues (they should all be real). A +spectral transform is therefore performed using the keyword shift-invert i.e. the original problem is transformed into an equivalent problem with eigenvalues given by :math:\dfrac{1}{\lambda - \sigma} instead of :math:\lambda where :math:\sigma is the value of the spectral shift. diff --git a/examples/periodic_homog_elas/.ipynb_checkpoints/periodic_homog_elas-checkpoint.ipynb b/examples/periodic_homog_elas/.ipynb_checkpoints/periodic_homog_elas-checkpoint.ipynb index 65e76eedb2f77b858e3ae83ca3b79f0f40dbacc6..ad785ba7c98f448cf1cb878dc8cc86dbd92e69cd 100644 --- a/examples/periodic_homog_elas/.ipynb_checkpoints/periodic_homog_elas-checkpoint.ipynb +++ b/examples/periodic_homog_elas/.ipynb_checkpoints/periodic_homog_elas-checkpoint.ipynb @@ -33,7 +33,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 1, "metadata": {}, "outputs": [ { @@ -819,7 +819,7 @@ { "data": { "text/html": [ - "" + "" ], "text/plain": [ "" @@ -837,7 +837,7 @@ "%matplotlib notebook\n", "\n", "a = 1. # unit cell width\n", - "b = sqrt(3)/2. # unit cell height\n", + "b = sqrt(3.)/2. # unit cell height\n", "c = 0.5 # horizontal offset of top boundary\n", "R = 0.2 # inclusion radius\n", "vol = a*b # unit cell volume\n", @@ -846,9 +846,10 @@ " [a, 0.],\n", " [a+c, b],\n", " [c, b]])\n", - "mesh = Mesh(\"hexag_incl.xml\")\n", - "subdomains = MeshFunction(\"size_t\", mesh, \"hexag_incl_physical_region.xml\")\n", - "facets = MeshFunction(\"size_t\", mesh, \"hexag_incl_facet_region.xml\")\n", + "fname = \"hexag_incl\"\n", + "mesh = Mesh(fname + \".xml\")\n", + "subdomains = MeshFunction(\"size_t\", mesh, fname + \"_physical_region.xml\")\n", + "facets = MeshFunction(\"size_t\", mesh, fname + \"_facet_region.xml\")\n", "plt.figure()\n", "plot(subdomains)\n", "plt.show()" @@ -897,42 +898,41 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "# class used to define the periodic boundary map\n", "class PeriodicBoundary(SubDomain):\n", - " def __init__(self, vertices):\n", + " def __init__(self, vertices, tolerance=DOLFIN_EPS):\n", " \"\"\" vertices stores the coordinates of the 4 unit cell corners\"\"\"\n", - " SubDomain.__init__(self)\n", + " SubDomain.__init__(self, tolerance)\n", + " self.tol = tolerance\n", " self.vv = vertices\n", " self.a1 = self.vv[1,:]-self.vv[0,:] # first vector generating periodicity\n", " self.a2 = self.vv[3,:]-self.vv[0,:] # second vector generating periodicity\n", " # check if UC vertices form indeed a parallelogram\n", - " assert np.linalg.norm(self.vv[2, :]-self.vv[3, :] - self.a1) <= 1e-8\n", - " assert np.linalg.norm(self.vv[2, :]-self.vv[1, :] - self.a2) <= 1e-8\n", + " assert np.linalg.norm(self.vv[2, :]-self.vv[3, :] - self.a1) <= self.tol\n", + " assert np.linalg.norm(self.vv[2, :]-self.vv[1, :] - self.a2) <= self.tol\n", " \n", " def inside(self, x, on_boundary):\n", " # return True if on left or bottom boundary AND NOT on one of the \n", " # bottom-right or top-left vertices\n", - " return bool((near(x[0], self.vv[0,0] + x[1]*self.a2[0]/self.vv[3,1]) or \n", - " near(x[1], self.vv[0,1] + x[0]*self.a1[1]/self.vv[1,0])) and \n", - " (not ((near(x[0], self.vv[1,0]) and near(x[1], self.vv[1,1])) or \n", - " (near(x[0], self.vv[3,0]) and near(x[1], self.vv[3,1])))) and on_boundary)\n", + " return bool((near(x[0], self.vv[0,0] + x[1]*self.a2[0]/self.vv[3,1], self.tol) or \n", + " near(x[1], self.vv[0,1] + x[0]*self.a1[1]/self.vv[1,0], self.tol)) and \n", + " (not ((near(x[0], self.vv[1,0], self.tol) and near(x[1], self.vv[1,1], self.tol)) or \n", + " (near(x[0], self.vv[3,0], self.tol) and near(x[1], self.vv[3,1], self.tol)))) and on_boundary)\n", "\n", " def map(self, x, y):\n", - " if near(x[0], self.vv[2,0]) and near(x[1], self.vv[2,1]): # if on top-right corner\n", + " if near(x[0], self.vv[2,0], self.tol) and near(x[1], self.vv[2,1], self.tol): # if on top-right corner\n", " y[0] = x[0] - (self.a1[0]+self.a2[0])\n", " y[1] = x[1] - (self.a1[1]+self.a2[1])\n", - " elif near(x[0], self.vv[1,0] + x[1]*self.a2[0]/self.vv[2,1]): # if on right boundary\n", + " elif near(x[0], self.vv[1,0] + x[1]*self.a2[0]/self.vv[2,1], self.tol): # if on right boundary\n", " y[0] = x[0] - self.a1[0]\n", " y[1] = x[1] - self.a1[1]\n", " else: # should be on top boundary\n", " y[0] = x[0] - self.a2[0]\n", - " y[1] = x[1] - self.a2[1]\n", - "\n", - "V = VectorFunctionSpace(mesh, \"CG\", 2, constrained_domain=PeriodicBoundary(vertices))" + " y[1] = x[1] - self.a2[1]" ] }, { @@ -944,7 +944,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -971,7 +971,17 @@ "\n", "The previous problem is very similar to a standard linear elasticity problem, except for the periodicity constraint which has now been included in the FunctionSpace definition and for the presence of an eigenstrain term $\\boldsymbol{E}$. It can easily be shown that the variational formulation of the previous problem reads as: Find $\\boldsymbol{v}\\in V$ such that:\n", "\$$\n", - "\\int_{\\mathcal{A}} (\\boldsymbol{E}+\\nabla^s\\boldsymbol{v}):\\mathbb{C}(\\boldsymbol{y}):\\nabla^s\\widehat{\\boldsymbol{v}}\\text{ d} \\Omega = 0 \\quad \\forall \\widehat{\\boldsymbol{v}}\\in V\n", + "F(\\boldsymbol{v},\\widehat{\\boldsymbol{v}}) = \\int_{\\mathcal{A}} (\\boldsymbol{E}+\\nabla^s\\boldsymbol{v}):\\mathbb{C}(\\boldsymbol{y}):\\nabla^s\\widehat{\\boldsymbol{v}}\\text{ d} \\Omega = 0 \\quad \\forall \\widehat{\\boldsymbol{v}}\\in V\n", + "\$$\n", + "\n", + "The above problem is not well-posed because of the existence of rigid body translations. One way to circumvent this issue would be to fix one point but instead we will add an additional constraint of zero-average of the fluctuation field $v$ as is classically done in homogenization theory. This is done by considering an additional vectorial Lagrange multiplier $\\lambda$ and considering the following variational problem: Find $(\\boldsymbol{v},\\boldsymbol{\\lambda})\\in V\\times \\mathbb{R}^2$ such that:\n", + "\$$\n", + "\\int_{\\mathcal{A}} (\\boldsymbol{E}+\\nabla^s\\boldsymbol{v}):\\mathbb{C}(\\boldsymbol{y}):\\nabla^s\\widehat{\\boldsymbol{v}}\\text{ d} \\Omega + \\int_{\\mathcal{A}} \\boldsymbol{\\lambda}\\cdot\\widehat{\\boldsymbol{v}} \\text{ d} \\Omega + \\int_{\\mathcal{A}} \\widehat{\\boldsymbol{\\lambda}}\\cdot\\boldsymbol{v} \\text{ d} \\Omega = 0 \\quad \\forall (\\widehat{\\boldsymbol{v}}, \\widehat{\\boldsymbol{\\lambda}})\\in V\\times\\mathbb{R}^2\n", + "\$$\n", + "\n", + "Which can be summarized as:\n", + "\$$\n", + "a(\\boldsymbol{v},\\widehat{\\boldsymbol{v}}) + b(\\boldsymbol{\\lambda},\\widehat{\\boldsymbol{v}}) + b(\\widehat{\\boldsymbol{\\lambda}}, \\boldsymbol{v}) = L(\\widehat{\\boldsymbol{v}}) \\quad \\forall (\\widehat{\\boldsymbol{v}}, \\widehat{\\boldsymbol{\\lambda}})\\in V\\times\\mathbb{R}^2\n", "\$$\n", "\n", "This readily translates into the following FEniCS code:" @@ -979,25 +989,31 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 15, "metadata": {}, "outputs": [], "source": [ - "v_ = TestFunction(V)\n", - "dv = TrialFunction(V)\n", - "v = Function(V)\n", + "Ve = VectorElement(\"CG\", mesh.ufl_cell(), 2)\n", + "Re = VectorElement(\"R\", mesh.ufl_cell(), 0)\n", + "W = FunctionSpace(mesh, MixedElement([Ve, Re]), constrained_domain=PeriodicBoundary(vertices, tolerance=1e-10))\n", + "V = FunctionSpace(mesh, Ve)\n", + "\n", + "v_,lamb_ = TestFunctions(W)\n", + "dv, dlamb = TrialFunctions(W)\n", + "w = Function(W)\n", "dx = Measure('dx')(subdomain_data=subdomains)\n", "\n", "Eps = Constant(((0, 0), (0, 0)))\n", "F = sum([inner(sigma(dv, i, Eps), eps(v_))*dx(i) for i in range(nphases)])\n", - "a, L = lhs(F), rhs(F)" + "a, L = lhs(F), rhs(F)\n", + "a += dot(lamb_,dv)*dx + dot(dlamb,v_)*dx" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "We have used a general implementation using a sum over the different phases for the functional F. We then used the lhs and rhs functions to respectively extract the corresponding bilinear and linear forms.\n", + "We have used a general implementation using a sum over the different phases for the functional F. We then used the lhs and rhs functions to respectively extract the corresponding bilinear $a$ and linear $L$ forms.\n", "\n", "## Resolution\n", "\n", @@ -1006,7 +1022,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 16, "metadata": {}, "outputs": [ { @@ -1016,9 +1032,9 @@ "Solving Exx case...\n", "Solving Eyy case...\n", "Solving Exy case...\n", - "[[35749.31 8205.86 5181.94]\n", - " [ 8205.78 28273.8 1331.63]\n", - " [ 5181.91 1331.65 14136.7 ]]\n" + "[[ 6.56e+04 1.74e+04 -2.10e-02]\n", + " [ 1.74e+04 6.56e+04 -4.07e-02]\n", + " [-2.45e-02 -4.21e-02 2.41e+04]]\n" ] } ], @@ -1036,7 +1052,8 @@ "for (j, case) in enumerate([\"Exx\", \"Eyy\", \"Exy\"]):\n", " print(\"Solving {} case...\".format(case))\n", " Eps.assign(Constant(macro_strain(j)))\n", - " solve(lhs(F) == rhs(F), v, [], solver_parameters={\"linear_solver\": \"cg\"})\n", + " solve(a == L, w, [], solver_parameters={\"linear_solver\": \"cg\"})\n", + " (v, lamb) = split(w)\n", " Sigma = np.zeros((3,))\n", " for k in range(3):\n", " Sigma[k] = assemble(sum([stress2Voigt(sigma(v, i, Eps))[k]*dx(i) for i in range(nphases)]))/vol\n", @@ -1056,14 +1073,14 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "35749.30527415909 36479.26730142249\n" + "65570.19577075752 65570.2553898389\n" ] } ], @@ -1082,15 +1099,15 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Apparent Young modulus: 33465.46042796117\n", - "Apparent Poisson ratio: 0.18363742779286404\n" + "Apparent Young modulus: 58239.72435202466\n", + "Apparent Poisson ratio: 0.21012531632724085\n" ] } ], @@ -1103,799 +1120,19 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 19, "metadata": {}, "outputs": [ { "data": { - "application/javascript": [ - "/* Put everything inside the global mpl namespace */\n", - "window.mpl = {};\n", - "\n", - "\n", - "mpl.get_websocket_type = function() {\n", - " if (typeof(WebSocket) !== 'undefined') {\n", - " return WebSocket;\n", - " } else if (typeof(MozWebSocket) !== 'undefined') {\n", - " return MozWebSocket;\n", - " } else {\n", - " alert('Your browser does not have WebSocket support.' +\n", - " 'Please try Chrome, Safari or Firefox ≥ 6. ' +\n", - " 'Firefox 4 and 5 are also supported but you ' +\n", - " 'have to enable WebSockets in about:config.');\n", - " };\n", - "}\n", - "\n", - "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n", - " this.id = figure_id;\n", - "\n", - " this.ws = websocket;\n", - "\n", - " this.supports_binary = (this.ws.binaryType != undefined);\n", - "\n", - " if (!this.supports_binary) {\n", - " var warnings = document.getElementById(\"mpl-warnings\");\n", - " if (warnings) {\n", - " warnings.style.display = 'block';\n", - " warnings.textContent = (\n", - " \"This browser does not support binary websocket messages. \" +\n", - " \"Performance may be slow.\");\n", - " }\n", - " }\n", - "\n", - " this.imageObj = new Image();\n", - "\n", - " this.context = undefined;\n", - " this.message = undefined;\n", - " this.canvas = undefined;\n", - " this.rubberband_canvas = undefined;\n", - " this.rubberband_context = undefined;\n", - " this.format_dropdown = undefined;\n", - "\n", - " this.image_mode = 'full';\n", - "\n", - " this.root = $(' ');\n", - " this._root_extra_style(this.root)\n", - " this.root.attr('style', 'display: inline-block');\n", - "\n", - "$(parent_element).append(this.root);\n", - "\n", - " this._init_header(this);\n", - " this._init_canvas(this);\n", - " this._init_toolbar(this);\n", - "\n", - " var fig = this;\n", - "\n", - " this.waiting = false;\n", - "\n", - " this.ws.onopen = function () {\n", - " fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n", - " fig.send_message(\"send_image_mode\", {});\n", - " if (mpl.ratio != 1) {\n", - " fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n", - " }\n", - " fig.send_message(\"refresh\", {});\n", - " }\n", - "\n", - " this.imageObj.onload = function() {\n", - " if (fig.image_mode == 'full') {\n", - " // Full images could contain transparency (where diff images\n", - " // almost always do), so we need to clear the canvas so that\n", - " // there is no ghosting.\n", - " fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n", - " }\n", - " fig.context.drawImage(fig.imageObj, 0, 0);\n", - " };\n", - "\n", - " this.imageObj.onunload = function() {\n", - " fig.ws.close();\n", - " }\n", - "\n", - " this.ws.onmessage = this._make_on_message_function(this);\n", - "\n", - " this.ondownload = ondownload;\n", - "}\n", - "\n", - "mpl.figure.prototype._init_header = function() {\n", - " var titlebar = $(\n", - " ' ');\n", - " var titletext =$(\n", - " '
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');\n", - " var button = $('');\n", - " button.click(function (evt) { fig.handle_close(fig, {}); } );\n", - " button.mouseover('Stop Interaction', toolbar_mouse_event);\n", - " buttongrp.append(button);\n", - " var titlebar = this.root.find($('.ui-dialog-titlebar'));\n", - " titlebar.prepend(buttongrp);\n", - "}\n", - "\n", - "mpl.figure.prototype._root_extra_style = function(el){\n", - " var fig = this\n", - " el.on(\"remove\", function(){\n", - "\tfig.close_ws(fig, {});\n", - " });\n", - "}\n", - "\n", - "mpl.figure.prototype._canvas_extra_style = function(el){\n", - " // this is important to make the div 'focusable\n", - " el.attr('tabindex', 0)\n", - " // reach out to IPython and tell the keyboard manager to turn it's self\n", - " // off when our div gets focus\n", - "\n", - " // location in version 3\n", - " if (IPython.notebook.keyboard_manager) {\n", - " IPython.notebook.keyboard_manager.register_events(el);\n", - " }\n", - " else {\n", - " // location in version 2\n", - " IPython.keyboard_manager.register_events(el);\n", - " }\n", - "\n", - "}\n", - "\n", - "mpl.figure.prototype._key_event_extra = function(event, name) {\n", - " var manager = IPython.notebook.keyboard_manager;\n", - " if (!manager)\n", - " manager = IPython.keyboard_manager;\n", - "\n", - " // Check for shift+enter\n", - " if (event.shiftKey && event.which == 13) {\n", - " this.canvas_div.blur();\n", - " event.shiftKey = false;\n", - " // Send a \"J\" for go to next cell\n", - " event.which = 74;\n", - " event.keyCode = 74;\n", - " manager.command_mode();\n", - " manager.handle_keydown(event);\n", - " }\n", - "}\n", - "\n", - "mpl.figure.prototype.handle_save = function(fig, msg) {\n", - " fig.ondownload(fig, null);\n", - "}\n", - "\n", - "\n", - "mpl.find_output_cell = function(html_output) {\n", - " // Return the cell and output element which can be found *uniquely* in the notebook.\n", - " // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n", - " // IPython event is triggered only after the cells have been serialised, which for\n", - " // our purposes (turning an active figure into a static one), is too late.\n", - " var cells = IPython.notebook.get_cells();\n", - " var ncells = cells.length;\n", - " for (var i=0; i= 3 moved mimebundle to data attribute of output\n", - " data = data.data;\n", - " }\n", - " if (data['text/html'] == html_output) {\n", - " return [cell, data, j];\n", - " }\n", - " }\n", - " }\n", - " }\n", - "}\n", - "\n", - "// Register the function which deals with the matplotlib target/channel.\n", - "// The kernel may be null if the page has been refreshed.\n", - "if (IPython.notebook.kernel != null) {\n", - " IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n", - "}\n" - ], + "image/png": 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\n", 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