UFL Specification and User Manual 0.3 - FEniCS Project
UFL Specification and User Manual 0.3 - FEniCS Project
UFL Specification and User Manual 0.3 - FEniCS Project
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<strong>UFL</strong> <strong>Specification</strong> <strong>and</strong> <strong>User</strong> <strong>Manual</strong> <strong>0.3</strong>Martin S. Alnæs, Anders Logg2.5.4 Implicit summationImplicit summation can occur in only a few situations. A product of twoterms that shares the same free index is implicitly treated as a sum over thatfree index:• v[i]*v[i]: ∑ i v iv i• A[i,j]*v[i]*v[j]: ∑ j (∑ i A ijv i )v jA tensor valued expression indexed twice with the same free index is treatedas a sum over that free index:• A[i,i]: ∑ i A ii• C[i,j,j,i]: ∑ i∑j C ijjiThe spatial derivative, in the direction of a free index, of an expression withthe same free index, is treated as a sum over that free index:• v[i].dx(i): ∑ i v i• A[i,j].dx(i): ∑ id(A ij )dx iNote that these examples are some times written v i,i <strong>and</strong> A ij,i in pen-<strong>and</strong>paperindex notation.2.6 Basic algebraic operatorsThebasicalgebraicoperators+,-,*,/canbeusedfreelyon<strong>UFL</strong>expressions.They do have some requirements on their oper<strong>and</strong>s, summarized here:Addition or subtraction, a + b or a - b:34
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