Evaluate material parameter m in a volume/surface region.
Depending on evaluation mode, integrate a material parameter over a volume/surface region (‘eval’), average it in elements/faces (‘el_avg’) or interpolate it into volume/surface quadrature points (‘qp’).
Uses reference mapping of y variable.
Supports ‘eval’, ‘el_avg’ and ‘qp’ evaluation modes.
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\int_\Omega m
\mbox{vector for } K \from \Ical_h: \int_{T_K} m / \int_{T_K} 1
m|_{qp}
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ev_integrate_mat | (material, parameter) |
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Surface integral of a test function weighted by a scalar function c.
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\int_{\Gamma} q \mbox{ or } \int_\Gamma c q
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dw_surface_integrate | (opt_material, virtual) |
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Evaluate (weighted) variable in a surface region.
Depending on evaluation mode, integrate a variable over a surface region (‘eval’), average it in element faces (‘el_avg’) or interpolate it into surface quadrature points (‘qp’). For vector variables, setting term_mode to ‘flux’ leads to computing corresponding fluxes for the three modes instead.
Supports ‘eval’, ‘el_avg’ and ‘qp’ evaluation modes.
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\int_\Gamma y \mbox{ , } \int_\Gamma \ul{y} \mbox{ , } \int_\Gamma \ul{y} \cdot \ul{n} \\ \int_\Gamma c y \mbox{ , } \int_\Gamma c \ul{y} \mbox{ , } \int_\Gamma c \ul{y} \cdot \ul{n} \mbox{ flux }
\mbox{vector for } K \from \Ical_h: \int_{T_K} y / \int_{T_K} 1 \mbox{ , } \int_{T_K} \ul{y} / \int_{T_K} 1 \mbox{ , } \int_{T_K} (\ul{y} \cdot \ul{n}) / \int_{T_K} 1 \\ \mbox{vector for } K \from \Ical_h: \int_{T_K} c y / \int_{T_K} 1 \mbox{ , } \int_{T_K} c \ul{y} / \int_{T_K} 1 \mbox{ , } \int_{T_K} (c \ul{y} \cdot \ul{n}) / \int_{T_K} 1
y|_{qp} \mbox{ , } \ul{y}|_{qp} \mbox{ , } (\ul{y} \cdot \ul{n})|_{qp} \mbox{ flux } \\ c y|_{qp} \mbox{ , } c \ul{y}|_{qp} \mbox{ , } (c \ul{y} \cdot \ul{n})|_{qp} \mbox{ flux }
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ev_surface_integrate | (opt_material, parameter) |
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Volume integral of a test function weighted by a scalar function c.
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\int_\Omega q \mbox{ or } \int_\Omega c q
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dw_volume_integrate | (opt_material, virtual) |
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Evaluate (weighted) variable in a volume region.
Depending on evaluation mode, integrate a variable over a volume region (‘eval’), average it in elements (‘el_avg’) or interpolate it into volume quadrature points (‘qp’).
Supports ‘eval’, ‘el_avg’ and ‘qp’ evaluation modes.
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\int_\Omega y \mbox{ , } \int_\Omega \ul{y} \\ \int_\Omega c y \mbox{ , } \int_\Omega c \ul{y}
\mbox{vector for } K \from \Ical_h: \int_{T_K} y / \int_{T_K} 1 \mbox{ , } \int_{T_K} \ul{y} / \int_{T_K} 1 \\ \mbox{vector for } K \from \Ical_h: \int_{T_K} c y / \int_{T_K} 1 \mbox{ , } \int_{T_K} c \ul{y} / \int_{T_K} 1
y|_{qp} \mbox{ , } \ul{y}|_{qp} \\ c y|_{qp} \mbox{ , } c \ul{y}|_{qp}
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ev_volume_integrate | (opt_material, parameter) |
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Sum nodal values.
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d_sum_vals | (parameter) |
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Surface integral of the outer product of the unit outward normal \ul{n} and the coordinate \ul{x} shifted by \ul{x}_0
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\int_{\Gamma} \ul{n} (\ul{x} - \ul{x}_0)
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d_surface_moment | (parameter, shift) |
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Surface of a domain. Uses approximation of the parameter variable.
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\int_\Gamma 1
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d_surface | (parameter) |
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Volume of a D-dimensional domain, using a surface integral. Uses approximation of the parameter variable.
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1 / D \int_\Gamma \ul{x} \cdot \ul{n}
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d_volume_surface | (parameter) |
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Volume of a domain. Uses approximation of the parameter variable.
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\int_\Omega 1
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d_volume | (parameter) |
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