Some Typical Cases
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· | Applied to the term , integration by parts yields
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Here is the x-direction cosine of the surface normal and is the differential path length. Since FlexPDE applies integration by parts only to second order terms, this rule is applied only if the function contains further derivatives of . Similar rules apply to derivatives with respect to other coordinates.
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· | Applied to the term , integration by parts yields
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Since this term is second order, it will always result in a contribution to the natural boundary condition.
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· | Applied to the term , integration by parts yields the Divergence Theorem
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Here is the outward surface normal unit vector.
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As with the x-derivative case, integration by parts will not be applied unless the vector itself contains further derivatives of u.
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· | Applied to the term , integration by parts yields the Curl Theorem
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Div(-k*grad(Temp)) + Source = 0
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dx(-k*dx(Temp)) + Source = 0
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curl(curl(A)/mu) = J
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dx(u)-dy(u)=0
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