Newton boundary condition term.
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\int_{\Gamma} \alpha q (p - p_{\rm outer})
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dw_bc_newton | (material_1, material_2, virtual, state) |
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Surface L^2(\Gamma) dot product for both scalar and vector fields.
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\int_\Gamma q p \mbox{ , } \int_\Gamma \ul{v} \cdot \ul{u} \mbox{ , } \int_\Gamma \ul{v} \cdot \ul{n} p \mbox{ , } \int_\Gamma q \ul{n} \cdot \ul{u} \mbox{ , } \int_\Gamma p r \mbox{ , } \int_\Gamma \ul{u} \cdot \ul{w} \mbox{ , } \int_\Gamma \ul{w} \cdot \ul{n} p \\ \int_\Gamma c q p \mbox{ , } \int_\Gamma c \ul{v} \cdot \ul{u} \mbox{ , } \int_\Gamma c p r \mbox{ , } \int_\Gamma c \ul{u} \cdot \ul{w} \\ \int_\Gamma \ul{v} \cdot \ull{M} \cdot \ul{u} \mbox{ , } \int_\Gamma \ul{u} \cdot \ull{M} \cdot \ul{w}
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dw_surface_dot | (opt_material, virtual, state) |
(opt_material, parameter_1, parameter_2) |
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Volume L^2(\Omega) weighted dot product for both scalar and vector fields. Can be evaluated. Can use derivatives.
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\int_\Omega q p \mbox{ , } \int_\Omega \ul{v} \cdot \ul{u} \mbox{ , } \int_\Omega p r \mbox{ , } \int_\Omega \ul{u} \cdot \ul{w} \\ \int_\Omega c q p \mbox{ , } \int_\Omega c \ul{v} \cdot \ul{u} \mbox{ , } \int_\Omega c p r \mbox{ , } \int_\Omega c \ul{u} \cdot \ul{w} \\ \int_\Omega \ul{v} \cdot \ull{M} \cdot \ul{u} \mbox{ , } \int_\Omega \ul{u} \cdot \ull{M} \cdot \ul{w}
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dw_volume_dot | (opt_material, virtual, state) |
(opt_material, parameter_1, parameter_2) |
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Fading memory volume L^2(\Omega) weighted dot product for scalar fields. This term has the same definition as dw_volume_dot_w_scalar_th, but assumes an exponential approximation of the convolution kernel resulting in much higher efficiency. Can use derivatives.
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\int_\Omega \left [\int_0^t \Gcal(t-\tau) p(\tau) \difd{\tau} \right] q
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dw_volume_dot_w_scalar_eth | (ts, material_0, material_1, virtual, state) |
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Fading memory volume L^2(\Omega) weighted dot product for scalar fields. Can use derivatives.
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\int_\Omega \left [\int_0^t \Gcal(t-\tau) p(\tau) \difd{\tau} \right] q
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dw_volume_dot_w_scalar_th | (ts, material, virtual, state) |
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Dot product of a scalar and the i-th component of gradient of a scalar. The index should be given as a ‘special_constant’ material parameter.
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Z^i = \int_{\Omega} q \nabla_i p
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dw_s_dot_grad_i_s | (material, virtual, state) |
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Volume dot product of a vector and a gradient of scalar. Can be evaluated.
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\int_{\Omega} \ul{v} \cdot \nabla p \mbox{ , } \int_{\Omega} \ul{u} \cdot \nabla q \\ \int_{\Omega} c \ul{v} \cdot \nabla p \mbox{ , } \int_{\Omega} c \ul{u} \cdot \nabla q \\ \int_{\Omega} \ul{v} \cdot \ull{M} \cdot \nabla p \mbox{ , } \int_{\Omega} \ul{u} \cdot \ull{M} \cdot \nabla q
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dw_v_dot_grad_s | (opt_material, virtual, state) |
(opt_material, state, virtual) | |
(opt_material, parameter_v, parameter_s) |
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Volume dot product of a vector and a scalar. Can be evaluated.
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\int_{\Omega} \ul{v} \cdot \ul{m} p \mbox{ , } \int_{\Omega} \ul{u} \cdot \ul{m} q\\
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dw_vm_dot_s | (material, virtual, state) |
(material, state, virtual) | |
(material, parameter_v, parameter_s) |
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