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9 …ithub.com/CEED/libCEED/), the low-level API library for efficient high-order discretization method…
11 …"While libCEED's focus is on high-order finite/spectral element method implementations, the approa…
21     "uses high-order finite elements/spectral elements, namely, the high-order Lagrange\n",
22     "polynomials defined over $P$ non-uniformly spaced nodes, the\n",
23     "Gauss-Legendre-Lobatto (GLL) points, and quadrature points $\\{q_i\\}_{i=1}^Q$, with\n",
25     "or Gauss-Lobatto quadratures, that are built in the library).\n",
34     "$\\boldsymbol{X}=(X,Y,Z) \\equiv (X_1,X_2,X_3) \\in I=[-1,1]^3$\n",
37     "### Ex1-Volume\n",
42     "simple usage of libCEED to compute the volume of a given body using a matrix-free\n",
167     "Now run `ex1-volume` by running"
180       "  Ceed specification [-c] : /cpu/self\n",
181       "  Mesh dimension     [-d] : 3\n",
182       "  Mesh order         [-m] : 4\n",
183       "  Solution order     [-o] : 4\n",
184       "  Num. 1D quadr. pts [-q] : 6\n",
185       "  Approx. # unknowns [-s] : 262144\n",
186       "  QFunction source   [-g] : gallery\n",
195       "Volume error         : -2.7444713168734e-13\n"
200     "! ./ex1-volume -d 3 -g"
207 …-d` specifies the dimensionality of the domain Ω. The option `-g` specifies that the mass operator…
214     "### Ex2-Surface\n",
219     "surface area of a given body using matrix-free application of a diffusion operator.\n",
222     "Similarly to the Ex1-Volume example, it computes:\n",
224     "\\begin{equation}\\label{eq-ex2-surface}\\tag{eq. 1}\n",
240 …"   \\int_\\Omega \\nabla v \\cdot \\nabla u \\, dV - \\int_{\\partial \\Omega} v \\nabla u \\cdot…
258     "Now run `ex2-surface` by running "
271       "  Ceed specification [-c] : /cpu/self\n",
272       "  Mesh dimension     [-d] : 3\n",
273       "  Mesh order         [-m] : 4\n",
274       "  Solution order     [-o] : 4\n",
275       "  Num. 1D quadr. pts [-q] : 6\n",
276       "  Approx. # unknowns [-s] : 262144\n",
277       "  QFunction source   [-g] : gallery\n",
286       "Surface area error         : -0.022629650914673\n"
291     "! ./ex2-surface -d 3 -g"
298 …-free application of a Laplace's (diffusion) operator. The command line option `-d` specifies the …
304    "display_name": "Python 3",
305    "language": "python",
311     "version": 3
314    "mimetype": "text/x-python",
315    "name": "python",
316    "nbconvert_exporter": "python",
318    "version": "3.8.5"