By P. W. Partridge, C. A. Brebbia, L. C. Wrobel (auth.)
The boundary point technique (BEM) is now a well-established numerical process which gives a good replacement to the existing finite distinction and finite point tools for the answer of a variety of engineering difficulties. the most benefit of the BEM is its specific skill to supply an entire challenge resolution by way of boundary values simply, with enormous reductions in computing device time and knowledge coaching attempt. An preliminary restrict of the BEM was once that the basic strategy to the unique partial differential equation was once required on the way to receive an identical boundary in tegral equation. one other used to be that non-homogeneous phrases accounting for results equivalent to disbursed so much have been integrated within the formula through area integrals, therefore making the approach lose the allure of its "boundary-only" personality. many various ways were built to beat those difficulties. it's our opinion that the main profitable up to now is the twin reciprocity procedure (DRM), that is the subject material of this publication. the fundamental thought in the back of this strategy is to hire a primary answer such as a less complicated equation and to regard the remainder phrases, in addition to different non-homogeneous phrases within the unique equation, via a technique which includes a chain growth utilizing international approximating capabilities and the applying of reciprocity principles.
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Following KODE is the parameter VAL, which is the known value of u or q respectively. At internal nodes, u is unknown and q not defined. There is no need to read KODE for internal nodes, the routine will automatically assign these to zero. All input data is then printed. SUBROUTINE INPUTl COMMON/ONE/NN,NE,L,X(200) ,Y(200) ,U(200),D(200) ,LE(200) , 1 CON(200,2) ,KODE(200) ,Q(200) ,POEI(4) ,FDEP(4),ALPHA(200) ,N I COMMON/FlVE/XY(200),A(200,200) COMMON/CELL/NCI,MKJ(200,3) ,WW(7) ,CP(7,3) ,DA(200) ,COIST, IPI C C COORDINATES OF NUMERICAL IITEGRATIOI POIITS FOR BOUIDARY ELEMEITS II POEI.
55) where x is a vector of unknowns and A is a square matrix, the columns of which contain either columns of the matrix H, columns of the matrix G after a change of sign or the sum of two consecutive columns of G with a change of sign when the unknown is the unique value of the flux at the corresponding node. The known vector y is computed from the product of the known boundary conditions and the corresponding coefficients of the matrices G or H. When the number of unknowns at a corner node is two (case 4), one extra equation is needed for the node.
In this case there are four possibilities depending on the boundary conditions: 1. Known values: fluxes "before" and "after" the corner. Unknown value: potential. 2. Known values: potential, and flux "before" the corner. Unknown value: flux "after" the corner. 3. Known values: potential, and flux "after" the corner. Unknown value: flux "before" the corner. 4. Known value: potential. Unknown values: flux "before" and "after" the corner. e. 55) where x is a vector of unknowns and A is a square matrix, the columns of which contain either columns of the matrix H, columns of the matrix G after a change of sign or the sum of two consecutive columns of G with a change of sign when the unknown is the unique value of the flux at the corresponding node.