shared elements

One issue that does not exist in parallel atomistic simulations but requires special attention in par- allel finite element implementations is that in the latter some elements may be shared between neighboring processors. In CAC, this issue originates from the difference in shape between the parallelepipedonal processor domain and the rhombohedral finite elements with arbitrary crystallographic orientations, the latter of which also results in the jagged simulation cell boundaries. Instead of having all relevant processors calculate the same quantities (e.g., force, energy, and virial) within a shared element, in the PyCAC code, each relevant processor only calculates quantities of the integration points its domain contains. Then these quantities are summed in the processor_equiv.f90 subroutine, after which all relevant processors have the same nodal quantities. This simple summation is feasible because of the trilinear shape function employed in the finite elements.

To facilitate the shared element-related calculations, a public array tag_shared_ele and a public variable ele_shared_num are introduced. For example, processor 3 has 6 local elements, with the 2nd, 4th, and 5th elements shared with other processors, then

tag_ele_shared(1) = 0
tag_ele_shared(2) = 1
tag_ele_shared(3) = 0
tag_ele_shared(4) = 2
tag_ele_shared(5) = 3
tag_ele_shared(6) = 0

and

ele_shared_num = 3

The array and the variable, defined in processor_scatter_cg.f90 and updated in update_neighbor_cg.f90, are used in these three subroutines: processor_edenshost_intpo.f90, processor_equiv.f90, and processor_langevin_cg.f90.

Note that in current PyCAC code, the "shared element communication" process mentioned above does NOT involve a host processor as described in page 123 of Xu et al., which was for a previous version. The host processor, which has the highest rank among all processors that share the same element, is indeed used in the code, but only for the purposes of (i) sending the element/node information to the root processor for output, e.g., in all_to_one_cg.f90 and all_to_one_group_cg.f90, and (ii) calculating certain variables based on the global arrays, e.g., the global force norm force_norm calculated in conjugate_gradient.f90, fire.f90, langevin_vel.f90, quenched_vel.f90, quick_mini.f90, steepest_descent.f90, and update_vel.f90. For example, when processor 2 and processor 3 share the same element (and thus have the same relevant nodal information), only one of them needs to send the information to root. The host processor is set in the processor_scatter_cg.f90 subroutine, in which the array who_has_ele(ie) = .true. for the host processor and .false. for non-host processors, where ie is the local element id.

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