Figure 1: Simulation results for 40,960 RBCs in a complex vessel geometry. For our strong scaling experiments, we use the vessel geometry shown on the left, with inflow-outflow boundary conditions at various regions of the vessel geometry. To setup the problem, we fill the vessel with nearly-touching RBCs of different sizes. The figure above shows a setup with overall 40,960 RBCs at a volume fraction of 19%, and 40,960 polynomial patches. The full simulation video is available at https://vimeo.com/329509229.
ABSTRACTHigh-resolution blood flow simulations have potential for developing better understanding biophysical phenomena at the microscale, such as vasodilation, vasoconstriction and overall vascular resistance. To this end, we present a scalable platform for the simulation of red blood cell (RBC) flows through complex capillaries by modeling the physical system as a viscous fluid with immersed deformable particles. We describe a parallel boundary integral equation solver for general elliptic partial differential equations, which we apply to Stokes flow through blood vessels. We also detail a parallel collision avoiding algorithm to ensure RBCs and the blood vessel remain contact-free. We have scaled our code on Stampede2 at the Texas Advanced Computing Center up to 34,816 cores. Our largest simulation enforces a contact-free state between four billion surface * Both authors contributed equally to this research. elements and solves for three billion degrees of freedom on one million RBCs and a blood vessel composed from two million patches.
Abstract. The complex of curves C(Sg) of a closed orientable surface of genus g ≥ 2 is the simplicial complex whose vertices, C 0 (Sg), are isotopy classes of essential simple closed curves in Sg. Two vertices co-bound an edge of the 1-skeleton, C 1 (Sg), if there are disjoint representatives in Sg. A metric is obtained on C 0 (Sg) by assigning unit length to each edge of C 1 (Sg). Thus, the distance between two vertices, d(v, w), corresponds to the length of a geodesic-a shortest edge-path between v and w in C 1 (Sg). In (4), Birman, Margalit and the second author introduced the concept of efficient geodesics in C 1 (Sg) and used them to give a new algorithm for computing the distance between vertices. In this note, we introduce the software package MICC (Metric in the Curve Complex), a partial implementation of the efficient geodesic algorithm. We discuss the mathematics underlying MICC and give applications. In particular, up to an action of an element of the mapping class group, we give a calculation which produces all distance 4 vertex pairs for g = 2 that intersect 12 times, the minimal number of intersections needed for this distance and genus.
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