Pseudoparticle Multipole Method: A Simple Method to Implement High-Accuracy Treecode

In this letter we describe the pseudoparticle multipole method (P2M2), a new method to express multipole expansion by a distribution of pseudoparticles. We can use this distribution of particles to calculate high order terms in both the Barnes-Hut treecode and FMM. The primary advantage of P2M2 is that it works on GRAPE. GRAPE is a special-purpose hardware for the calculation of gravitational force between particles. Although the treecode has been implemented on GRAPE, we could handle terms only up to dipole, since GRAPE can calculate forces from point-mass particles only. Thus the calculation cost grows quickly when high accuracy is required. With P2M2, the multipole expansion is expressed by particles, and thus GRAPE can calculate high order terms. Using P2M2, we implemented an arbitrary-order treecode on GRAPE-4. Timing result shows GRAPE-4 accelerates the calculation by a factor between 10 (for low accuracy) to 150 (for high accuracy). Even on general-purpose programmable computers, our method offers the advantage that the mathematical formulae and therefore the actual program is much simpler than that of the direct implementation of multipole expansion.Comment: 6 pages, 4 figures, latex, submitted to ApJ Letter

PROGRAPE-1: A Programmable, Multi-Purpose Computer for Many-Body Simulations

We have developed PROGRAPE-1 (PROgrammable GRAPE-1), a programmable multi-purpose computer for many-body simulations. The main difference between PROGRAPE-1 and "traditional" GRAPE systems is that the former uses FPGA (Field Programmable Gate Array) chips as the processing elements, while the latter rely on the hardwired pipeline processor specialized to gravitational interactions. Since the logic implemented in FPGA chips can be reconfigured, we can use PROGRAPE-1 to calculate not only gravitational interactions but also other forms of interactions such as van der Waals force, hydrodynamical interactions in SPH calculation and so on. PROGRAPE-1 comprises two Altera EPF10K100 FPGA chips, each of which contains nominally 100,000 gates. To evaluate the programmability and performance of PROGRAPE-1, we implemented a pipeline for gravitational interaction similar to that of GRAPE-3. One pipeline fitted into a single FPGA chip, which operated at 16 MHz clock. Thus, for gravitational interaction, PROGRAPE-1 provided the speed of 0.96 Gflops-equivalent. PROGRAPE will prove to be useful for wide-range of particle-based simulations in which the calculation cost of interactions other than gravity is high, such as the evaluation of SPH interactions.Comment: 20 pages with 9 figures; submitted to PAS

GRAPE-5: A Special-Purpose Computer for N-body Simulation

We have developed a special-purpose computer for gravitational many-body simulations, GRAPE-5. GRAPE-5 is the successor of GRAPE-3. Both consist of eight custom pipeline chips (G5 chip and GRAPE chip). The difference between GRAPE-5 and GRAPE-3 are: (1) The G5 chip contains two pipelines operating at 80 MHz, while the GRAPE chip had one at 20 MHz. Thus, the calculation speed of the G5 chip and that of GRAPE-5 board are 8 times faster than that of GRAPE chip and GRAPE-3 board. (2) The GRAPE-5 board adopted PCI bus as the interface to the host computer instead of VME of GRAPE-3, resulting in the communication speed one order of magnitude faster. (3) In addition to the pure 1/r potential, the G5 chip can calculate forces with arbitrary cutoff functions, so that it can be applied to Ewald or P^3M methods. (4) The pairwise force calculated on GRAPE-5 is about 10 times more accurate than that on GRAPE-3. On one GRAPE-5 board, one timestep of 128k-body simulation with direct summation algorithm takes 14 seconds. With Barnes-Hut tree algorithm (theta = 0.75), one timestep of 10^6-body simulation can be done in 16 seconds.Comment: 19 pages, 24 Postscript figures, 3 tables, Latex, submitted to Publications of the Astronomical Society of Japa

GRAPE-6A: A single-card GRAPE-6 for parallel PC-GRAPE cluster system

In this paper, we describe the design and performance of GRAPE-6A, a special-purpose computer for gravitational many-body simulations. It was designed to be used with a PC cluster, in which each node has one GRAPE-6A. Such configuration is particularly effective in running parallel tree algorithm. Though the use of parallel tree algorithm was possible with the original GRAPE-6 hardware, it was not very cost-effective since a single GRAPE-6 board was still too fast and too expensive. Therefore, we designed GRAPE-6A as a single PCI card to minimize the reproduction cost and optimize the computing speed. The peak performance is 130 Gflops for one GRAPE-6A board and 3.1 Tflops for our 24 node cluster. We describe the implementation of the tree, TreePM and individual timestep algorithms on both a single GRAPE-6A system and GRAPE-6A cluster. Using the tree algorithm on our 16-node GRAPE-6A system, we can complete a collisionless simulation with 100 million particles (8000 steps) within 10 days.Comment: submitted to PAS

Long-term maintenance of hemoglobin levels in hemodialysis patients treated with bi-weekly epoetin beta pegol switched from darbepoetin alfa: a single-center, 12-month observational study in Japan

Recent evidence on maintenance administration of epoetin beta pegol, a continuous erythropoiesis receptor activator (CERA), in dialysis patients shows the clinical benefit of bi-weekly administration (Q2W) in improving hematopoiesis and iron use efficiency. We undertook a single-center observational study of 33 Japanese maintenance dialysis patients, whose anemia had been kept stable through weekly administration (Q1W) of darbepoetin (DA), to evaluate the effectiveness of CERA Q2W switched from DA in maintaining hemoglobin (Hb) levels over a 12-month period. The target Hb level was 10.0–12.0 g/dL. Throughout the 12-month period, the mean Hb was stably maintained at 10.5–10.8 g/dL, 69.7–87.9% of the patients achieving the target Hb level. The mean CERA dose was within the range of 62.9–78.8 µg/2 weeks. The average CERA dose adjustment frequency after switching was low at 0.42–0.67 times/3 months. In both subgroups stratified by the DA dose prior to the switch, Hb levels were kept stable during CERA administration; however, in the low-dose group (10–20 µg/week of DA), the CERA and iron doses decreased over time, whereas in the high-dose group (30–60 µg/week of DA) they remained unchanged. CERA Q2W achieved long-term successful anemia management in Japanese maintenance dialysis patients after switching from DA Q1W. CERA dose was adjusted based on an overall consideration of past changes in Hb levels, erythropoiesis-stimulating agent and iron doses. Subgroup analysis showed the CERA dose in the low-dose group decreased continuously, due possibly to a long-term improvement in iron use efficiency

Structure of Dark Matter Halos From Hierarchical Clustering. III. Shallowing of The Inner Cusp

We investigate the structure of the dark matter halo formed in the cold dark matter scenarios by N-body simulations with parallel treecode on GRAPE cluster systems. We simulated 8 halos with the mass of $4.4\times 10^{14}M_{\odot}$ to $1.6\times 10^{15}M_{\odot}$ in the SCDM and LCDM model using up to 30 million particles. With the resolution of our simulations, the density profile is reliable down to 0.2 percent of the virial radius. Our results show that the slope of inner cusp within 1 percent virial radius is shallower than -1.5, and the radius where the shallowing starts exhibits run-to-run variation, which means the innermost profile is not universal.Comment: 26 pages, 16 fugures, submitted to Ap