{ How do line_integrals work in 1D geometries?} {The LINE_INTEGRAL (alias INTEGRAL) operator in SPHERE1 geometry is weighted by R*R, representing the fact that the equations are solved in a whole region} TITLE '1D integral test' COORDINATES sphere1 VARIABLES q DEFINITIONS test1 = 10 test2 = r*r int_test1 = integral(test1,"path1") int_test2 = integral(test2,"path1") int_test3 = integral(q,"path1") int_test4 = integral(test1,"path2") int_test5 = integral(test2,"path2") int_test6 = integral(q,"path2") int_test7 = integral(test1,"path1") + integral(test1,"path2") int_test8 = integral(test2,"path1") + integral(test2,"path2") int_test9 = integral(q,"path1") + integral(q,"path2") EQUATIONS div(grad(q))=0 BOUNDARIES REGION "path1" START (0) point value(q)=0 LINE TO (1) REGION "path2" START (1) LINE TO (3) point value(q)=1 PLOTS elevation(test1) elevation(test2) elevation(q) SUMMARY report int_test1 as "integral test1 on path1 " report int_test2 as "integral test2 on path1 " report int_test3 as "integral u on path1 " report "" report int_test4 as "integral test1 on path2 " report int_test5 as "integral test2 on path2 " report int_test6 as "integral u on path2 " report "" report int_test7 as "integral test1 on path1 + path2 " report int_test8 as "integral test2 on path1 + path2 " report int_test9 as "integral u on path1 + path2 " END