modify rhs of sheet1 exercise 1.3 (prev. exercise 2.2)

Author: jowezarek

exercises/poisson_2d_I.ipynb

@@ -21,7 +21,7 @@
     "\\end{align*}\n",
     "for the specific choice\n",
     "\\begin{align*}\n",
-    "    f(x, y) = 8\\pi^2\\sin(2\\pi x)\\sin(2\\pi y)\n",
+    "    f(x, y) = [ (-x^4 + x^3 + (-y^2 + \\pi^2)x^2 + (y^2 - 4y - \\pi^2)x + 2y - 2)  \\sin(\\pi y) + (2\\pi x^2(1-x))  \\cos(\\pi y)]  e^{xy}\n",
     "\\end{align*}\n",
     "\n",
     "## The Variational Formulation\n",
@@ -63,12 +63,12 @@
     "phi, psi    = elements_of(V, names='phi, psi')\n",
     "\n",
     "# bilinear form\n",
-    "a       = BilinearForm((phi, psi), integral(domain, dot(grad(phi), grad(psi))))\n",
+    "a       = BilinearForm((phi, psi), integral(domain, phi*psi))\n",
     "\n",
     "# linear form\n",
-    "from sympy import pi, sin\n",
+    "from sympy import pi, sin, cos, exp\n",
     "x,y     = domain.coordinates\n",
-    "f       = 8 * (pi**2) * sin(2 * pi * x) * sin(2 * pi * y)\n",
+    "f       = ( (-x**4 + x**3 + (-y**2 + pi**2)*x**2 + (y**2 - 4*y - pi**2)*x + 2*y - 2) * sin(pi*y) + (2*pi*x**2*(1-x)) * cos(pi*y) ) * exp(x*y)\n",
     "\n",
     "l       = LinearForm(psi, integral(domain, f*psi))"
    ]
@@ -167,12 +167,18 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "from psydac.linalg.solvers import inverse\n",
+    "import  time\n",
+    "\n",
+    "from    psydac.linalg.solvers import inverse\n",
     "\n",
     "tol     = 1e-12\n",
     "maxiter = 1000\n",
     "\n",
-    "phi_h   = inverse(A_bc, 'cg', tol=tol, maxiter=maxiter) @ f_bc"
+    "A_bc_inv = inverse(A_bc, 'cg', tol=tol, maxiter=maxiter)\n",
+    "\n",
+    "t0      = time.time()\n",
+    "phi_h   = A_bc_inv @ f_bc\n",
+    "t1      = time.time()"
    ]
   },
   {
@@ -186,7 +192,7 @@
     "In this example, the analytical solution is given by\n",
     "\n",
     "$$\n",
-    "phi_{ex}(x, y) = \\sin(2\\pi x)\\sin(2\\pi y)\n",
+    "phi_{ex}(x, y) = x(x-1)\\sin(\\pi y)e^{xy}\n",
     "$$"
    ]
   },
@@ -207,7 +213,7 @@
     "\n",
     "from sympde.expr        import Norm, SemiNorm\n",
     "\n",
-    "phi_ex  = sin(2*pi*x) * sin(2*pi*y)\n",
+    "phi_ex = x*(x-1)*sin(pi*y)*exp(x*y)\n",
     "phi_h_FemField = FemField(V_h, phi_h)\n",
     "\n",
     "error = phi_ex - phi\n",
@@ -219,10 +225,7 @@
     "l2norm_h = discretize(l2norm, domain_h, V_h, backend=backend)\n",
     "\n",
     "# assemble the norm\n",
-    "l2_error = l2norm_h.assemble(phi=phi_h_FemField)\n",
-    "\n",
-    "# print the result\n",
-    "print(l2_error)"
+    "l2_error = l2norm_h.assemble(phi=phi_h_FemField)"
    ]
   },
   {
@@ -245,10 +248,7 @@
     "h1norm_h = discretize(h1norm, domain_h, V_h)\n",
     "\n",
     "# assemble the norm\n",
-    "h1_error = h1norm_h.assemble(phi=phi_h_FemField)\n",
-    "\n",
-    "# print the result\n",
-    "print(h1_error)"
+    "h1semi_error = h1norm_h.assemble(phi=phi_h_FemField)"
    ]
   },
   {
@@ -274,7 +274,14 @@
     "h1_error = h1norm_h.assemble(phi=phi_h_FemField)\n",
     "\n",
     "# print the result\n",
-    "print(h1_error)"
+    "print( '> Grid          :: [{ne1},{ne2}]'.format( ne1=ncells[0], ne2=ncells[1]) )\n",
+    "print( '> Degree        :: [{p1},{p2}]'  .format( p1=degree[0], p2=degree[1] ) )\n",
+    "print( '> CG info       :: ',A_bc_inv.get_info() )\n",
+    "print( '> L2 error      :: {:.2e}'.format( l2_error ) )\n",
+    "print( '> H1-Semi error :: {:.2e}'.format( h1semi_error ) )\n",
+    "print( '> H1 error      :: {:.2e}'.format( h1_error ) )\n",
+    "print( '' )\n",
+    "print( '> Solution time :: {:.3g}'.format( t1-t0 ) )"
    ]
   },
   {