Implementation of 2D Domain Decomposition in the UCAN Gyrokinetic Particle-in-Cell Code and Resulting Performance of UCAN2

The massively parallel, nonlinear, three-dimensional (3D), toroidal, electrostatic, gyrokinetic, particle-in-cell (PIC), Cartesian geometry UCAN code, with particle ions and adiabatic electrons, has been successfully exercised to identify non-diffusive transport characteristics in present day tokamak discharges. The limitation in applying UCAN to larger scale discharges is the 1D domain decomposition in the toroidal (or z-) direction for massively parallel implementation using MPI which has restricted the calculations to a few hundred ion Larmor radii or gyroradii per plasma minor radius. To exceed these sizes, we have implemented 2D domain decomposition in UCAN with the addition of the y-direction to the processor mix. This has been facilitated by use of relevant components in the P2LIB library of field and particle management routines developed for UCLA's UPIC Framework of conventional PIC codes. The gyro-averaging specific to gyrokinetic codes is simplified by the use of replicated arrays for efficient charge accumulation and force deposition. The 2D domain-decomposed UCAN2 code reproduces the original 1D domain nonlinear results within round-off. Benchmarks of UCAN2 on the Cray XC30 Edison at NERSC demonstrate ideal scaling when problem size is increased along with processor number up to the largest power of 2 available, namely 131,072 processors. These particle weak scaling benchmarks also indicate that the 1 nanosecond per particle per time step and 1 TFlops barriers are easily broken by UCAN2 with 1 billion particles or more and 2000 or more processors.     

Unified Gas-Kinetic Wave-Particle Methods VI: Disperse Dilute Gas-Particle Multiphase Flow

A coupled gas-kinetic scheme (GKS) and unified gas-kinetic wave-particle (UGKWP) method for the disperse dilute gas-particle multiphase flow is proposed. In the two-phase flow, the gas phase is always in the hydrodynamic regime and is followed by GKS for the Navier-Stokes solution. The particle phase is solved by UGKWP in all regimes from particle trajectory crossing to the hydrodynamic wave interaction with the variation of particle’s Knudsen number. In the intensive particle collision regime, the UGKWP gives a hydrodynamic wave representation for the particle phase and the GKS-UGKWP for the two-phase flow reduces to the two-fluid Eulerian-Eulerian (EE) model. In the rarefied regime, the UGKWP tracks individual particle and the GKS-UGKWP goes back to the Eulerian-Lagrangian (EL) formulation. In the transition regime for the solid particle, the GKS-UGKWP takes an optimal choice for the wave and particle decomposition for the solid particle phase and connects the EE and EL methods seamlessly. The GKS-UGKWP method will be tested in all flow regimes with a large variation of Knudsen number for the solid particle transport and Stokes number for the two-phase interaction. It is confirmed that GKS-UGKWP is an efficient and accurate multiscale method for the gas-particle two-phase flow.     

High-Order Interpolation Algorithms for Charge Conservation in Particle-in-Cell Simulations

High-order interpolation algorithms for charge conservation in Particle-in-Cell (PIC) simulations are presented. The methods are valid for the case that a particle trajectory is a zigzag line. The second-order and third-order algorithms which can be applied to any even-order and odd-order are discussed in this paper, respectively. Several test simulations are performed to demonstrate their validity in two-dimensional PIC code. Compared with the simulation results of one-order, high-order algorithms have advantages in computation precision and enlarging the grid scales which reduces the CPU time.     

Efficient Implementation of Smoothed Particle Hydrodynamics (SPH) with Plane Sweep Algorithm

Neighbour search (NS) is the core of any implementations of smoothed particle hydrodynamics (SPH). In this paper, we present an efficient$\mathcal{O}$($N$log$N$) neighbour search method based on the plane sweep (PW) algorithm with $N$ being the number of SPH particles. The resulting method, dubbed the PWNS method, is totally independent of grids (i.e., purely meshfree) and capable of treating variable smoothing length, arbitrary particle distribution and heterogenous kernels. Several state-of-the-art data structures and algorithms, e.g., the segment tree and the Morton code, are optimized and implemented. By simply allowing multiple lines to sweep the SPH particles simultaneously from different initial positions, a parallelization of the PWNS method with satisfactory speedup and load-balancing can be easily achieved. That is, the PWNS SPH solver has a great potential for large scale fluid dynamics simulations.     

An Implicit LU-SGS Scheme for the Spectral Volume Method on Unstructured Tetrahedral Grids

An efficient implicit lower-upper symmetric Gauss-Seidel (LU-SGS) solution approach has been applied to a high order spectral volume (SV) method for unstructured tetrahedral grids. The LU-SGS solver is preconditioned by the block element matrix, and the system of equations is then solved with a LU decomposition. The compact feature of SV reconstruction facilitates the efficient solution algorithm even for high order discretizations. The developed implicit solver has shown more than an order of magnitude of speed-up relative to the Runge-Kutta explicit scheme for typical inviscid and viscous problems. A convergence to a high order solution for high Reynolds number transonic flow over a 3D wing with a one equation turbulence model is also indicated.     

Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations

We propose a generalized space-time domain decomposition approach for the physics-informed neural networks (PINNs) to solve nonlinear partial differential equations (PDEs) on arbitrary complex-geometry domains. The proposed framework, named eXtended PINNs ($XPINNs$), further pushes the boundaries of both PINNs as well as conservative PINNs (cPINNs), which is a recently proposed domain decomposition approach in the PINN framework tailored to conservation laws. Compared to PINN, the XPINN method has large representation and parallelization capacity due to the inherent property of deployment of multiple neural networks in the smaller subdomains. Unlike cPINN, XPINN can be extended to any type of PDEs. Moreover, the domain can be decomposed in any arbitrary way (in space and time), which is not possible in cPINN. Thus, XPINN offers both space and time parallelization, thereby reducing the training cost more effectively. In each subdomain, a separate neural network is employed with optimally selected hyperparameters, e.g., depth/width of the network, number and location of residual points, activation function, optimization method, etc. A deep network can be employed in a subdomain with complex solution, whereas a shallow neural network can be used in a subdomain with relatively simple and smooth solutions. We demonstrate the versatility of XPINN by solving both forward and inverse PDE problems, ranging from one-dimensional to three-dimensional problems, from time-dependent to time-independent problems, and from continuous to discontinuous problems, which clearly shows that the XPINN method is promising in many practical problems. The proposed XPINN method is the generalization of PINN and cPINN methods, both in terms of applicability as well as domain decomposition approach, which efficiently lends itself to parallelized computation. The XPINN code is available on $https://github.com/AmeyaJagtap/XPINNs$.     

Prognostic factors of perforated sigmoid diverticulitis in the elderly

BACKGROUND: The Finnish population is aging fast and the prevalence of perforated sigmoid diverticulitis is simultaneously increasing in northern Finland. The fact that an increasing number of elderly patients, with their age-specific problems, are subjected to emergency surgery for acute diverticulitis underlines the importance of risk stratification. METHODS: One hundred and seventy-two patients admitted to Oulu University Hospital because of diverticular perforation from 1983 to 2002 were identified from the computer database. The clinical variables were evaluated as prognostic indicators of postoperative complications, mortality and time of hospitalization. RESULTS: The resection rate was 91%; 64 primary anastomoses, 93 Hartmann's procedures and two covering colostomies were performed. The overall complication rate was 33%. In patients under 70 years, a stepwise logistic regression analysis showed that the Mannheim Peritonitis Index (MPI) score and American Society of Anesthesiologists (ASA) score were independent prognostic factors. None of factors predicted morbidity in patients over 70 years. Overall mortality rate was 8%, without any significant difference between the procedures. Of the clinical variables, MPI score, ASA score, Hinchey classes and malnutrition correlated with mortality. All patients who died presented with ASA scores of III-IV, and 12 out of 14 patients had an MPI score of II. In a stepwise logistic regression analysis, only the MPI score seemed to be an independent predictor of mortality. CONCLUSIONS: Mortality is related to age but age alone is not an independent predictor of mortality. The MPI score is useful in predicting the risk of death in patients with perforated diverticulitis.     

Modeling of Bound Electron Effects in Particle-in-Cell Simulation

To include the bound electron effects in particle-in-cell (PIC) simulation, we propose a model in which the response of the dipole components of partially ionized ions to external electromagnetic fields can be included. Instead of treating the macroion particle as a single particle without an internal structure, the ions are considered to have a structure composed of a central nucleus and a bounded electron cloud in our model. The two parts experience the interactions of both the external electromagnetic fields and the internal Coulomb fields. In this way, the laser scattering effects by a partially ionized medium can be modeled properly in the PIC simulation. The laser propagation in a neutral medium and the Bragg scattering of the laser in crystal structure have been simulated with a PIC code modified based on our model as the benchmark. Our model may find applications to study some interesting problems, such as the x-ray laser-driven wakefield acceleration in crystals, the x-ray laser-driven high energy density physics, and intense laser propagation in partially ionized nonlinear optical materials, etc.     

Peritonitis in diverticulitis: the Bern concept

INTRODUCTION: The colon is the most frequent origine for a diffuse peritonitis and diverticular perforation is again the most common source of a spontaneous secondary peritonitis. This paper first focuses on the treatment of peritonitis and secondly on the strategies of source control in peritonitis with special emphasis on the tactics (primary anastomosis vs. Hartmann procedure with colostomy) for surgical source control. PATIENT AND METHODS: Prospective analysis of 404 patients suffering from peritonitis (11/93-2/98), treated with an uniform treatment concept including early operation, source control and extensive intraoperative lavage (20 to 30 liters) as a standard procedure. Other treatment measures were added in special indications "on demand" only. Peritonitis was graded with the Mannheim Peritonitis Index (MPI). Tactics of source control in peritonitis due to diverticulitis were performed according to "general condition" respectively the MPI of the patient. RESULTS: The 404 patients averaged a MPI of 19 (0-35) in "local" peritonitis and a MPI of 26 (11-43) in "diffuse" peritonitis. The colon as a source of peritonitis resulted in MPI of 16 (0-33) in the case of "local" respectively 27 (11-43) in "diffuse" peritonitis. From 181 patients suffering from diverticulitis 144 needed an operation and in 78 (54%) peritonitis was present. Fourty-six percent (36) of the patients suffered from "local", 54% (42) from "diffuse" peritonitis. Resection with primary anastomosis was performed in 26% (20/78) whereas in 74% (58/78) of the patients a Hartmann procedure with colostomy was performed. The correlating MPI was 16 (0-28) vs. 23 (16-27) respectively. The analysis of complications and mortality based on the MPI showed a decent discrimination potential for primary anastomosis vs Hartmann procedure: morbidity 35% vs. 41%; reoperation 5% vs. 5%; mortality 0% vs. 14%. CONCLUSION: In case of peritonitis due to diverticulitis the treatment of peritonitis comes first. Thanks to advances in intensive care and improved anti-inflammatory care, a more conservative surgical concept nowadays is accepted. In the case of diverticulitis the MPI is helpful to choose between primary anastomosis vs. Hartmann procedure with colostomy as source control. The MPI includes the "general condition" of the patient into the tactical decision how to attain source control.     

A study of patients with spinal disease using Maudsley Personality Inventory

We administered the Maudsley Personality Inventory (MPI) preoperatively to 303 patients with spinal diseases about to undergo surgery. Patients younger than 20 years, patients previously treated in the Department of Psychiatry, and patients with poor postoperative results were excluded. Patients with N-scores (neuroticism scale) of 39 points or greater or L-scores (lie scale) of 26 points or greater were regarded as "abnormal." Based on clinical definitions we identified 24 "problem patients" during the course and categorized them as "Unsatisfied," "Indecisive," "Doctor shoppers," or "Distrustful." Preoperative MPI categorized 26 patients as abnormal; 22 patients categorized as abnormal became problem patients (p<0.001). MPI sensitivity and specificity was 84.6% and 99.3%, respectively. Preoperative MPI to patients with spinal disease was found to be useful in detecting problem patients.

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Résumé Nous avons utilisé l'Inventaire de Personnalité de Maudsley (MPI) chez 303 malades avant qu'ils subissent une chirurgie vertébrale. Ont été exclus les patients de moins de 20 ans, les malades traités précédemment dans le Département de Psychiatrie, et les malades avec un mauvais résultat postopératoire. Les malades avec un "N Score" (échelle pour la névrose) de 39 points ou plus et/ou un "L-score" (échelle de situation) de 26 points ou plus ont été considérés comme "anormaux". Basé sur les définitions cliniques nous avons identifié 24 patients "à problème" pendant l'étude et les avons catégorisés comme "Insatisfait", Indécis", "acheteur du Docteur" ou "Méfiant". Le MPI pré-opératoire a catégorisé 26 malades comme "anormaux". Vingt deux d'entre eux sont devenus des malades à problèmes (p<0.001). La sensibilité et la spécificité du MPI étaient de 84.6% et 99.3%, respectivement. Le MPI pré-opératoire, appliqué à des malades avec une pathologie vertébrale a été utile pour détecter des malades "à problème".

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Multiscale Hemodynamics Using GPU Clusters

The parallel implementation of MUPHY, a concurrent multiscale code for large-scale hemodynamic simulations in anatomically realistic geometries, for multi-GPU platforms is presented. Performance tests show excellent results, with a nearly linear parallel speed-up on up to 32GPUs and a more than tenfold GPU/CPU acceleration, all across the range of GPUs. The basic MUPHY scheme combines a hydrokinetic (Lattice Boltzmann) representation of the blood plasma, with a Particle Dynamics treatment of suspended biological bodies, such as red blood cells. To the best of our knowledge, this represents the first effort in the direction of laying down general design principles for multiscale/physics parallel Particle Dynamics applications in non-ideal geometries. This configures the present multi-GPU version of MUPHY as one of the first examples of a high-performance parallel code for multiscale/physics biofluidic applications in realistically complex geometries.     

Computational Simulation of Flows in an Entire Centrifugal Heart Pump

A prototype computational code to numerically simulate the blood flows in an entire centrifugal heart pump has been developed. The unsteady incompressible Navier-Stokes equations are solved on a parallel computer, the Cray T3E. By domain decomposition, the whole flow space is decomposed to a number of subdomains for each of which a structured algebraic grid is assigned. The grids for the inlet eye and blade regions are on the rotating frame while grids for other regions are on the nonrotating frame, and the edge of the rotating grids slides over the edge of the nonrotating frame, and the edge of the rotating grids slides over the edge of the nonrotating grids. The code is able to simulate the flows in the rotor, volute, and diffuser as well as to find pump performance indicators. The present paper presents an overview of the code and describes a study on the effect of volute width.     

Evaluation of a prostate biopsy strategy for cancer detection using a computer simulation system with virtual needle biopsy for three-dimensional prostate models

AIM: We evaluated a prostate biopsy strategy for cancer detection using a computer simulation system with virtual needle biopsy for three-dimensional (3D) prostate models. METHODS: Two 3D prostate models with a volume of 25 cc or 50 cc were constructed from computed tomographic images of radical prostatectomy specimens. The peripheral zone (PZ) and transition zone (TZ) were arranged in the prostate models according to the anatomical information. Four thousand patterns of cancer lesions were automatically inserted into each prostate model with a proportion of 75% in PZ and 25% in TZ. Average hit rates (AHR) in prostate models were evaluated both with an increased number of biopsy cores and various angles of virtual needle biopsy. The influence of adding secondary tumors for hit rates was also evaluated. RESULTS: For both sizes, the laterally angled biopsy in 4-8 core biopsy schemes showed higher AHR than the vertical plane biopsy, while the vertical plane biopsy in 10-18 core biopsy schemes showed higher AHR than the laterally angled biopsy. A higher number of biopsy cores increased the AHR of secondary tumors. CONCLUSIONS: Our results suggest that it is important in prostate cancer detection to change the needle placement according to the number of biopsy cores and the size of the prostate.     

Heterogeneous LBM Simulation Code with LRnLA Algorithms

A design of a new heterogeneous code for LBM simulations is proposed. By heterogeneous computing we mean a collaborative computation on CPU and GPU, which is characterized by the following features: the data is distributed between CPU and GPU memory spaces taking advantage of both parallel hierarchies; the capabilities of both SIMT GPU and SIMD GPU parallelization are used for calculations; the algorithms in use efficiently conceal the CPU-GPU data exchange; the subdivision of the computing task is performed with an account for the strong points of both processing units: high performance of GPU, low latency, and advanced memory hierarchy of CPU. This code is a continuation of our work in the development of LRnLA codes for LBM. Previous LRnLA codes had good efficiency both for CPU and GPU computing, and allowed GPU simulation performed on data stored in CPU RAM without performance loss on CPU-GPU data transfer. In the new code, we use methods and instruments that can be flexibly adapted to GPU and CPU instruction sets. We present the theoretical study of the performance of the proposed code and suggest implementation techniques. The bottlenecks are identified. As a result, we conclude that larger problems can be simulated with higher efficiency in the heterogeneous system.     

A Kernel-Independent Treecode Based on Barycentric Lagrange Interpolation

A kernel-independent treecode (KITC) is presented for fast summation of particle interactions. The method employs barycentric Lagrange interpolation at Chebyshev points to approximate well-separated particle-cluster interactions. The KITC requires only kernel evaluations, is suitable for non-oscillatory kernels, and relies on the scale-invariance property of barycentric Lagrange interpolation. For a given level of accuracy, the treecode reduces the operation count for pairwise interactions from $\mathcal{O}$($N^2$) to $\mathcal{O}$($N$log$N$), where $N$ is the number of particles in the system. The algorithm is demonstrated for systems of regularized Stokeslets and rotlets in 3D, and numerical results show the treecode performance in terms of error, CPU time, and memory consumption. The KITC is a relatively simple algorithm with low memory consumption, and this enables a straightforward OpenMP parallelization.     

D3- versus D2-Dissektion beim Magenkarzinom Eine Fall-Kontroll-Studie hinsichtlich postoperativer Morbidität, Letalität und onkologischen Frühergebnissen

INTRODUCTION: In western countries, the benefit of the Japanese extended D3 lymph node dissection in gastric cancer patients who have been operated on in curative intent has not been proven and higher rates of side effects are expected. The present matched-pair study retrospectively compared the new D3 method (1995-1999) with the historic D2 dissection (1982-1995). METHODS: Two 1:1 matched-pair populations were created: (1) regarding intra- and postoperative course, morbidity and mortality, 2 x 67 patients stratified to "age", "gender", "surgical procedure", "splenectomy" and "extended resections"; and (2) regarding early oncologic outcome, 2 x 32 patients additionally stratified to "UICC-stage" and "Laurén-classification". The D3 dissection was performed according to the Japanese method without routine pancreaticosplenectomy. RESULTS: D3 dissection harvested significantly (P = 0.004) more lymph nodes per patient: 56.4 vs. 46.8. Postoperative mortality was 3% (n = 2) in both groups, the overall complication rate of 30% (D3) vs. 25% (D2) was equivalent (P = 0.678) and the rate of surgical complications was identical (21%). Non-surgical complications of 21% after D3 dissection were not significantly elevated (vs. 10%; P = 0.143). Operative time [289 min (D3) vs. 218 min (D2); P = 0.0001] and postoperative stay [17.4 days (D3) vs. 14.5 days (D2); P = 0.003] were significantly longer after the extended procedure. The were no statistically significant differences between 2-year overall survival, locoregional-, distant- and overall recurrence-free survival. CONCLUSIONS: Compared to the D2 method, D3 dissection is feasible without disadvantages in the patients. However, D3 dissection cannot routinely be recommended because--possibly due to the short follow-up period and the small number of patients so far observed--an oncologic benefit could not be shown.     

Parametric POD-Galerkin Model Order Reduction for Unsteady-State Heat Transfer Problems

A parametric reduced order model based on proper orthogonal decomposition with Galerkin projection has been developed and applied for the modeling of heat transport in T-junction pipes which are widely found in nuclear power reactor cooling systems. Thermal mixing of different temperature coolants in T-junction pipes leads to temperature fluctuations and this could potentially cause thermal fatigue in the pipe walls. The novelty of this paper is the development of a parametric ROM considering the three dimensional, incompressible, unsteady Navier-Stokes equations coupled with the heat transport equation in a finite volume regime. Two different parametric cases are presented in this paper: parametrization of the inlet temperatures and parametrization of the kinematic viscosity. Different training spaces are considered and the results are compared against the full order model. The first test case results to a computational speed-up factor of 374 while the second test case to one of 211.     

A High-Order Accurate Gas-Kinetic Scheme for One- and Two-Dimensional Flow Simulation

This paper develops a high-order accurate gas-kinetic scheme in the framework of the finite volume method for the one- and two-dimensional flow simulations, which is an extension of the third-order accurate gas-kinetic scheme [Q.B. Li, K. Xu, and S. Fu, J. Comput. Phys., 229(2010), 6715-6731] and the second-order accurate gas-kinetic scheme [K. Xu, J. Comput. Phys., 171(2001), 289-335]. It is formed by two parts: quartic polynomial reconstruction of the macroscopic variables and fourth-order accurate flux evolution. The first part reconstructs a piecewise cell-center based quartic polynomial and a cell-vertex based quartic polynomial according to the "initial" cell average approximation of macroscopic variables to recover locally the non-equilibrium and equilibrium single particle velocity distribution functions around the cell interface. It is in view of the fact that all macroscopic variables become moments of a single particle velocity distribution function in the gas-kinetic theory. The generalized moment limiter is employed there to suppress the possible numerical oscillation. In the second part, the macroscopic flux at the cell interface is evolved in fourth-order accuracy by means of the simple particle transport mechanism in the microscopic level, i.e. free transport and the Bhatnagar-Gross-Krook (BGK) collisions. In other words, the fourth-order flux evolution is based on the solution (i.e. the particle velocity distribution function) of the BGK model for the Boltzmann equation. Several 1D and 2D test problems are numerically solved by using the proposed high-order accurate gas-kinetic scheme. By comparing with the exact solutions or the numerical solutions obtained the second-order or third-order accurate gas-kinetic scheme, the computations demonstrate that our scheme is effective and accurate for simulating invisid and viscous fluid flows, and the accuracy of the high-order GKS depends on the choice of the (numerical) collision time.     

Incompatibility reactions in the intensive care unit. Five years after the implementation of a simple "colour code system"

In intensive care units (ICU) most of the drugs have to be administered by y-piece infusions or admixtures.Drug stability and compatibility are critical elements in the accurate and appropriate delivery of drug therapies to patients.Five years after the implementation of a simple "colour code system" in an attempt to minimize the number of incompatibilities, the situation has been re-examined. The clinical pharmacist collected 78 different medication regimes and the compatibility and incompatibilities were evaluated based on the available literature.Before initiating the "colour code system" in the ICU, 15% of the administered drugs were incompatible and afterwards the number decreased to 2%.This rate could be kept at 2%, even 5 years after the implementation of the system,without any further intervention. As a result of teamwork between nurses, doctors and clinical pharmacy a simple "colour system" was established to minimize incidences of drug incompatibility in the ICU. The system is highly accepted because the degree of uncertainty has been considerably reduced.     

A Code that Simulates Fast-Ion D_Alpha and Neutral Particle Measurements

A code that models signals produced by charge-exchange reactions between fast ions and injected neutral beams in tokamak plasmas is described. With the fastion distribution function as input, the code predicts the efflux to a neutral particle analyzer (NPA) diagnostic and the photon radiance of Balmer-alpha light to a fastion Dα (FIDA) diagnostic. Reactions with both the primary injected neutrals and with the cloud of secondary "halo" neutrals that surround the beam are treated. Accurate calculation of the fraction of neutrals that occupy excited atomic states (the collisional-radiative transition equations) is an important element of the code. Comparison with TRANSP output and other tests verify the solutions. Judicious selection of grid size and other parameters facilitate efficient solutions. The output of the code has been validated by FIDA measurements on DIII-D but further tests are warranted.