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DOE OSTI2015

Gregarious Data Re-structuring in a Many Core Architecture

this paper, we have developed a new methodology that takes in consideration the access patterns from a single parallel actor (e.g. a thread), as well as, the access patterns of “grouped” parallel actors that share a resource (e.g. a distributed Level 3 cache). We start with a hierarchical tile code for our target machine and apply a series of transformations at the tile level to improve data residence in a given memory hierarchy level. The contribution of this paper includes (a) collaborative data restructuring for group reuse and (b) low overhead transformation technique to improve access pattern and bring closely connected data elements together. Preliminary results in a many core architecture, Tilera TileGX, shows promising improvements over optimized OpenMP code (up to 31% increase in GFLOPS) and over our own previous work on fine grained runtimes (up to 16%) for selected kernels

data restructuring↗

DOE OSTI2016

Composition and Realization of Source-to-Sink High-Performance Flows: File Systems, Storage, Hosts, LAN and WAN

A number of Department of Energy (DOE) science applications, involving exascale computing systems and large experimental facilities, are expected to generate large volumes of data, in the range of petabytes to exabytes, which will be transported over wide-area networks for the purpose of storage, visualization, and analysis. To support such capabilities, significant progress has been made in various components including the deployment of 100 Gbps networks with future 1 Tbps bandwidth, increases in end-host capabilities with multiple cores and buses, capacity improvements in large disk arrays, and deployment of parallel file systems such as Lustre and GPFS. High-performance source-to-sink data flows must be composed of these component systems, which requires significant optimizations of the storage-to-host data and execution paths to match the edge and long-haul network connections. In particular, end systems are currently supported by 10-40 Gbps Network Interface Cards (NIC) and 8-32 Gbps storage Host Channel Adapters (HCAs), which carry the individual flows that collectively must reach network speeds of 100 Gbps and higher. Indeed, such data flows must be synthesized using multicore, multibus hosts connected to high-performance storage systems on one side and to the network on the other side. Current experimental results show that the constituent flows must be optimally composed and preserved from storage systems, across the hosts and the networks with minimal interference. Furthermore, such a capability must be made available transparently to the science users without placing undue demands on them to account for the details of underlying systems and networks. And, this task is expected to become even more complex in the future due to the increasing sophistication of hosts, storage systems, and networks that constitute the high-performance flows. The objectives of this proposal are to (1) develop and test the component technologies and their synthesis methods to achieve source-to-sink high-performance flows, and (2) develop tools that provide these capabilities through simple interfaces to users and applications. In terms of the former, we propose to develop (1) optimization methods that align and transition multiple storage flows to multiple network flows on multicore, multibus hosts; and (2) edge and long-haul network path realization and maintenance using advanced provisioning methods including OSCARS and OpenFlow. We also propose synthesis methods that combine these individual technologies to compose high-performance flows using a collection of constituent storage-network flows, and realize them across the storage and local network connections as well as long-haul connections. We propose to develop automated user tools that profile the hosts, storage systems, and network connections; compose the source-to-sink complex flows; and set up and maintain the needed network connections. These solutions will be tested using (1) 100 Gbps connection(s) between Oak Ridge National Laboratory (ORNL) and Argonne National Laboratory (ANL) with storage systems supported by Lustre and GPFS file systems with an asymmetric connection to University of Memphis (UM); (2) ORNL testbed with multicore and multibus hosts, switches with OpenFlow capabilities, and network emulators; and (3) 100 Gbps connections from ESnet and their Openflow testbed, and other experimental connections. This proposal brings together the expertise and facilities of the two national laboratories, ORNL and ANL, and UM. It also represents a collaboration between DOE and the Department of Defense (DOD) projects at ORNL by sharing technical expertise and personnel costs, and leveraging the existing DOD Extreme Scale Systems Center (ESSC) facilities at ORNL.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

WE-AB-207B-10: On Spinal Nerve Toxicity from Single-Session SAbR in Pigs and the Translation of Small Animal NTCP Models

Purpose: The incidence of peripheral neuropathy has risen with increased utilization of SAbR. There is no consensus regarding the dose-tolerance of the peripheral nervous system. In 2015, we commenced an investigation to test the hypotheses that single-session irradiation to the pig spinal nerves exhibit a similar dose-tolerance as that of the spinal cord and that a dose-length effect exists. This work evaluates the direct application of small animal NTCP models to both large animal spinal cord and preliminary peripheral nerve data. Methods: To date, 16 of 25 Yucatan minipigs have received single-session SAbR to a 1.5cm length and 4 of 25 have received irradiation to a 0.5cm length of left-sided C6-C8 spinal nerves. Toxicity related gait change has been observed in 13 animals (9 from the long length group and 4 from the short). This preliminary data is overlaid on several dose-response models which have been fit to rodent spinal cord tolerance experiments. Model parameters define a toxicity profile between a completely serial or parallel behaving organ. Adequacy of model application, including how length effects are handled, to published minipig spinal cord dose-response data and to preliminary peripheral nerve response data was evaluated through residual analysis. Results: No rodent-derived dose-response models were directly applicable to all pig data for the different lengths irradiated. Several models fit the long-length irradiated spinal cord data well, with the more serial-like models fitting best. Preliminary data on the short-length irradiation suggests no length effect exists, disproving our hypothesis. Conclusion: Direct application of small-animal NTCP models to pig data suggests dose-length effect predictions from small animal data may not translate clinically. However, the small animal models used have not considered dose heterogeneity and it is expected that including the low-to-mid dose levels in the penumbral region will improve this match. This work was funded by the Cancer Prevention Research Institute of Texas (CPRIT).

60 APPLIED LIFE SCIENCES↗

DOE OSTI2025

Leveraging the Run 3 experience for the evolution of the ATLAS software-based readout towards HL-LHC

The High-Luminosity Large Hadron Collider (HL-LHC), scheduled to start operating in 2030, aims to increase the instantaneous luminosity by a factor of 10 compared to the LHC. To match this increase, the ATLAS experiment has been implementing a major upgrade program divided into two phases. The first phase (Phase-I), completed in 2022, introduced new trigger and detector systems that have been used during the Run 3 data taking period which began in July 2022. These systems have been used in conjunction with the new Data Acquisition (DAQ) Readout system, based on a software application called Software Readout Driver (SW ROD). SW ROD receives and aggregates data from the front-end electronics via the Front-End Link eXchange (FELIX) system and passes aggregated data fragments to the High-Level Trigger (HLT) system. During Run 3, SW ROD operates in parallel with the legacy Readout System (ROS) at an input rate of 100 kHz. For the Phase-II, the legacy ROS will be completely replaced with a new system based on the next generation of FELIX and an evolution of the SW ROD application called Data Handler. Data Handler has the same functional requirements as SW ROD but must be able to operate at an input rate of 1 MHz. To facilitate this evolution the SW ROD has been implemented using plugin architecture. This contribution presents the design and implementation of the SW ROD application for Run 3, along with the strategy for its evolution to the Phase-II Readout system. It discusses the lessons learned during Run 3 and describes the challenges that have been addressed to accomplish the demanding performance requirements of HL-LHC.

Kolos, Serguei [Univ. of California, Irvine, CA (U↗

DOE OSTI2015

Methods and apparatus for capture and storage of semantic information with sub-files in a parallel computing system

Techniques are provided for storing files in a parallel computing system using sub-files with semantically meaningful boundaries. A method is provided for storing at least one file generated by a distributed application in a parallel computing system. The file comprises one or more of a complete file and a plurality of sub-files. The method comprises the steps of obtaining a user specification of semantic information related to the file; providing the semantic information as a data structure description to a data formatting library write function; and storing the semantic information related to the file with one or more of the sub-files in one or more storage nodes of the parallel computing system. The semantic information provides a description of data in the file. The sub-files can be replicated based on semantically meaningful boundaries.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Evidence of the ion cyclotron resonance at proton kinetic scales in the solar wind

The k-filtering and wave polarization techniques are applied to Cluster magnetic field data at four intervals of fast free (not connected to Earth's foreshock) solar wind. In addition to the commonly observed population of magnetic field fluctuations propagating at quasi-perpendicular angles to the global mean field B{sub 0}, a population of fluctuations propagating at quasi-parallel angles are also observed when no local plasma instability can be identified. At low wavenumbers (kv{sub A}/Ω{sub p} ≤ 0.6) both components are present, and have powers of similar strength, while at higher wavenumbers (kv{sub A}Ω{sub p} > 0.6) only the perpendicular component can be identified. Here v{sub A} and Ω{sub p} are the Alfvén speed and the proton (angular) gyration frequency, k denotes the wavenumber. The dispersion curve obtained (and the ratio of the magnitudes of left and right hand polarized fluctuations) shows a sharp transition (and decrease) at (kv{sub A}/Ω{sub p}) ∼ 0.6, which corresponds to a spacecraft frequency f {sub sc} = 0.32 Hz. At higher wavenumbers the measurements agree with previous studies indicating the presence of kinetic Alfvén wave (KAW) turbulence or a mixture of KAW turbulence and convected structures. The parallel component displays a scaling of k{sub ∥}{sup −δ} where the spectral index δ ranges between about 5/3 and 2 although the number of data points does not warrant an accurate determination. The origins of the observed parallel component are unclear. The presence of a parallel component is consistent with ion cyclotron waves, and we interpret the sharp drop of this component at higher wavenumbers as evidence that the ion cyclotron resonance is occurring in the solar wind intervals studied.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2022

Surrogate models for plasma displacement and current in 3D perturbed magnetohydrodynamic equilibria in tokamaks

Abstract A numerical database of over one thousand perturbed three-dimensional (3D) equilibria has been generated, constructed based on the MARS-F (Liu et al 2000 Phys. Plasmas 7 3681) computed plasma response to the externally applied 3D field sources in multiple tokamak devices. Perturbed 3D equilibria with the n = 1–4 ( n is the toroidal mode number) toroidal periodicity are computed. Surrogate models are created for the computed perturbed 3D equilibrium utilizing model order reduction (MOR) techniques. In particular, retaining the first few eigenstates from the singular value decomposition (SVD) of the data is found to produce reasonably accurate MOR-representations for the key perturbed quantities, such as the perturbed parallel plasma current density and the plasma radial displacement. SVD also helps to reveal the core versus edge plasma response to the applied 3D field. For the database covering the conventional aspect ratio devices, about 95% of data can be represented by the truncated SVD-series with inclusion of only the first five eigenstates, achieving a relative error (RE) below 20%. The MOR-data is further utilized to train neural networks (NNs) to enable fast reconstruction of perturbed 3D equilibria, based on the two-dimensional equilibrium input and the 3D source field. The best NN-training is achieved for the MOR-data obtained with a global SVD approach, where the full set of samples used for NN training and testing are stretched and form a large matrix which is then subject to SVD. The fully connected multi-layer perceptron, with one or two hidden layers, can be trained to predict the MOR-data with less than 10% RE. As a key insight, a better strategy is to train separate NNs for the plasma response fields with different toroidal mode numbers. It is also better to apply MOR and to subsequently train NNs separately for conventional and low aspect ratio devices, due to enhanced toroidal coupling of Fourier spectra in the plasma response in the latter case.

3D equilibrium↗

DOE OSTI2017

Effective Vectorization with OpenMP 4.5

This paper describes how the Single Instruction Multiple Data (SIMD) model and its extensions in OpenMP work, and how these are implemented in different compilers. Modern processors are highly parallel computational machines which often include multiple processors capable of executing several instructions in parallel. Understanding SIMD and executing instructions in parallel allows the processor to achieve higher performance without increasing the power required to run it. SIMD instructions can significantly reduce the runtime of code by executing a single operation on large groups of data. The SIMD model is so integral to the processor s potential performance that, if SIMD is not utilized, less than half of the processor is ever actually used. Unfortunately, using SIMD instructions is a challenge in higher level languages because most programming languages do not have a way to describe them. Most compilers are capable of vectorizing code by using the SIMD instructions, but there are many code features important for SIMD vectorization that the compiler cannot determine at compile time. OpenMP attempts to solve this by extending the C++/C and Fortran programming languages with compiler directives that express SIMD parallelism. OpenMP is used to pass hints to the compiler about the code to be executed in SIMD. This is a key resource for making optimized code, but it does not change whether or not the code can use SIMD operations. However, in many cases critical functions are limited by a poor understanding of how SIMD instructions are actually implemented, as SIMD can be implemented through vector instructions or simultaneous multi-threading (SMT). We have found that it is often the case that code cannot be vectorized, or is vectorized poorly, because the programmer does not have sufficient knowledge of how SIMD instructions work.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

An Accelerated Clip Algorithm for Unstructured Meshes: A Batch-Driven Approach

The clip technique is a popular method for visualizing complex structures and phenomena within 3D unstructured meshes. Meshes can be clipped by specifying a scalar isovalue to produce an output unstructured mesh with its external surface as the isovalue. Similar to isocontouring, the clipping process relies on scalar data associated with the mesh points, including scalar data generated by implicit functions such as planes, boxes, and spheres, which facilitates the visualization of results interior to the grid. In this paper, we introduce a novel batch-driven parallel algorithm based on a sequential clip algorithm designed for high-quality results in partial volume extraction. Our algorithm comprises five passes, each progressively processing data to generate the resulting clipped unstructured mesh. The novelty lies in the use of fixed-size batches of points and cells, which enable rapid workload trimming and parallel processing, leading to a significantly improved memory footprint and run-time performance compared to the original version. On a 32-core CPU, the proposed batch-driven parallel algorithm demonstrates a run-time speed-up of up to 32.6x and a memory footprint reduction of up to 4.37x compared to the existing sequential algorithm. The software is currently available under an open-source license in the VTK visualization system.

Tsalikis, Spiros↗

DOE OSTI2019

Tail queues: A multi-threaded matching architecture

As we approach exascale, computational parallelism will have to drastically increase in order to meet throughput targets. Many–core architectures have exacerbated this problem by trading reduced clock speeds, core complexity, and computation throughput for increasing parallelism. This presents two major challenges for communication libraries such as MPI: the library must leverage the performance advantages of thread level parallelism and avoid the scalability problems associated with increasing the number of processes to that scale. Hybrid programming models, such as MPI+X, have been proposed to address these challenges. MPI THREAD MULTIPLE is MPI's thread safe mode. While there has been work to optimize it, it largely remains non–performant in most implementations. While current applications avoid MPI multithreading due to performance concerns, it is expected to be utilized in future applications. One of the major synchronous data structures required by MPI is the matching engine. In this paper, we present a parallel matching algorithm that can improve MPI matching for multithreaded applications. We then perform a feasibility study to demonstrate the performance benefit of the technique.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Fast and Accurate Core Analysis by the Full-Immersion Pressure-Pulse Decay: Part 1—Theory

Summary Core-scale measurements are considered the ground truth that oil and gas or electric utility companies use to predict the migration of fluids such as oil, natural gas, carbon dioxide, or brine deep underground during their extraction or injection operations. To provide a greater understanding of petrophysical properties of low-permeability geologic formations such as shales and tight gas sandstones, this study introduces a novel core-analysis procedure. The technique follows conventional pressure-pulse-decay permeametry, where the pressure in an inlet chamber adjacent to a cylindrical core plug undergoes a rapid pressurization, the system is shut in, and the pressure reaches a new equilibrium. However, unlike a standard unidirectional pressure-pulse decay, the full-immersion pressure-pulse decay (Hannon 2019) applies a pressure disturbance to the entire outer surface area of the sample. This article covers the numerical simulator designed to model flow through an anisotropic porous sample in this scenario. The model assumes distinct but uniform permeabilities along the radial and axial directions of the cylindrical plug sample. When extracting a plug vertically (or perpendicular to bedding), the permeability along the radial direction associates with the horizontal permeability (i.e., parallel to bedding), whereas in the axial direction, flow occurs perpendicular to bedding (a vertical permeability). Investigations of these model outputs demonstrate an approximately 20-fold decrease in time to complete a full-immersion experiment compared with conventional pressure-pulse decay. Furthermore, the pressure-decay curves resulting from the full-immersion method have slightly different shapes than those resulting from other unidimensional transient methods. These differences begin to demonstrate that, under achievable experimental conditions, the analysis of pressure data from one full-immersion test could enable the simultaneous estimation of the apparent permeabilities parallel and perpendicular to bedding of a cylindrical sample in addition to its porosity. A follow-up article finalizes the proof of this capability with a parameter-estimation procedure and presents experimental verification through a proof-of-concept study. Described in greater detail in that article, the parameter estimator requires multiple forward simulations to analyze the data, which behooves minimizing the compute time for each simulation. By using an alternating direction implicit time-marching scheme and a structured but variably spaced grid, the numerical simulator built for this purpose provides a forward model output with suitable accuracy in approximately 0.5 seconds.

Energy & Fuels↗

DOE OSTI2020

Distributed Berkeley Efficient Long-Read to Long-Read Aligner and Overlapper (DiBELLA) v1.0.0

We present a parallel algorithm and scalable implementation for genome analysis, specifically the problem of finding overlaps and alignments for data from "third generation" long read sequencers. While long sequences of DNA offer enormous advantages for biological analysis and insight, current long read sequencing instruments have high error rates and therefore require different approaches to analysis than their short read counterparts. Our work focuses on an efficient distributed-memory parallelization of an accurate single-node algorithm for overlapping and aligning long reads. We achieve scalability of this irregular algorithm by addressing the competing issues of increasing parallelism, minimizing communication, constraining the memory footprint, and ensuring good load balance. The resulting application, DiBELLA, is the first distributed memory overlapper and aligner specifically designed for long reads and parallel scalability.

Ellis, Marquita↗

DOE OSTI2017

Insight into 3D micro-CT data: exploring segmentation algorithms through performance metrics

Three-dimensional (3D) micro-tomography (µ-CT) has proven to be an important imaging modality in industry and scientific domains. Understanding the properties of material structure and behavior has produced many scientific advances. An important component of the 3D µ-CT pipeline is image partitioning (or image segmentation), a step that is used to separate various phases or components in an image. Image partitioning schemes require specific rules for different scientific fields, but a common strategy consists of devising metrics to quantify performance and accuracy. The present article proposes a set of protocols to systematically analyze and compare the results of unsupervised classification methods used for segmentation of synchrotron-based data. Additionally, the proposed dataflow for Materials Segmentation and Metrics (MSM) provides 3D micro-tomography image segmentation algorithms, such as statistical region merging (SRM), k-means algorithm and parallel Markov random field (PMRF), while offering different metrics to evaluate segmentation quality, confidence and conformity with standards. Both experimental and synthetic data are assessed, illustrating quantitative results through the MSM dashboard, which can return sample information such as media porosity and permeability. The main contributions of this work are: (i) to deliver tools to improve material design and quality control; (ii) to provide datasets for benchmarking and reproducibility; (iii) to yield good practices in the absence of standards or ground-truth for ceramic composite analysis.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Utilizing ensemble learning for performance and power modeling and improvement of parallel cancer deep learning CANDLE benchmarks

Abstract Machine learning (ML) continues to grow in importance across nearly all domains in modeling to learn from data. Often a tradeoff exists between a model's ability to minimize bias and variance. In this article, we utilize ensemble learning to combine linear, nonlinear, and tree‐/rule‐based ML methods to cope with the bias‐variance tradeoff and result in more accurate models. We use the datasets collected for two parallel cancer deep learning CANDLE benchmarks, NT3 and P1B2, to build performance and power models based on hardware performance counters using single‐object and multiple‐objects ensemble learning to identify the most important counters for improvement on the Cray XC40 Theta at Argonne National Laboratory. Based on the insights from these models, we improve the performance and energy of P1B2 and NT3 by optimizing the deep learning environments TensorFlow, Keras, Horovod, and Python under the huge page size of 8 MB. Experimental results show that ensemble learning not only produces more accurate models but also provides more robust performance counter ranking. We achieve up to 61.15% performance improvement and up to 62.58% energy saving for P1B2 and up to 55.81% performance improvement and up to 52.60% energy saving for NT3 on up to 24,576 cores.

Wu, Xingfu↗

DOE OSTI2019

diBELLA: Distributed Long Read to Long Read Alignment

© 2019 ACM. We present a parallel algorithm and scalable implementation for genome analysis, specifically the problem of finding overlaps and alignments for data from "third generation" long read sequencers [29]. While long sequences of DNA offer enormous advantages for biological analysis and insight, current long read sequencing instruments have high error rates and therefore require different approaches to analysis than their short read counterparts. Our work focuses on an efficient distributed-memory parallelization of an accurate single-node algorithm for overlapping and aligning long reads. We achieve scalability of this irregular algorithm by addressing the competing issues of increasing parallelism, minimizing communication, constraining the memory footprint, and ensuring good load balance. The resulting application, diBELLA, is the first distributed memory overlapper and aligner specifically designed for long reads and parallel scalability. We describe and present analyses for high level design trade-offs and conduct an extensive empirical analysis that compares performance characteristics across state-of-the-art HPC systems as well as a commercial cloud architectures, highlighting the advantages of state-of-the-art network technologies.

Ellis, Marquita↗

DOE OSTI2017

Parallel Asynchronous Distributed-Memory Maximal Independent Set Algorithm with Work Ordering

The maximal independent set (MIS) graph problem arises in many applications such as computer vision, information theory, molecular biology, and process scheduling. The growing scale of graph data suggests the use of distributed memory hardware as a cost-effective approach to providing necessary compute and memory resources. Existing distributed memory parallel MIS algorithms rely on synchronous communication and use techniques such as subgraph computations. In this paper, we present an asynchronous distributed-memory parallel graph algorithm that relies on a virtual directed acyclic graph (DAG) that is created during the algorithm execution. We introduce two additional algorithms that save computations by ordering generated work. The first algorithm applies ordering globally to reduce computations, and the second algorithm applies ordering locally at the level of threads to minimize the synchronization overhead. We use two different implementations of Luby’s algorithm variants as baseline to compare the performance of the presented algorithms: (1) vertex-centric Luby A and Luby B implementations, and (2) the CombBLAS linear-algebra Luby A implementation. Results show that proposed algorithms outperform both implementations of Luby algorithms, especially in distributed execution. Furthermore, we show that for low-diameter graphs the algorithm that applies global ordering scales better than other algorithms and for high diameter graphs the original asynchronous algorithm and thread-level ordering algorithm show better performance.

maximal independent set (MIS), distributed memory ↗

DOE OSTI2026

Uncertainty quantification of fireball features extracted from nuclear test films using computer vision

Films from the US’s historic nuclear testing era comprise the only extensive collection of imagery depicting high-yield detonations. These films offer unique insights into the characteristics of flows occurring on scales that are difficult to replicate experimentally, and they are a valuable source of data for the validation of models used to describe nuclear detonations. In recent work, we implemented modern computer vision and machine learning techniques to extract features of the fireball following nuclear detonation. With a training dataset of fireball films, we fine-tuned a You Only Look Once 11 (YOLO11) model to detect and track the fireball. Applied to a video, the outer bounding box produced in each frame by YOLO11 is used as an input prompt to Meta’s Segment Anything Model 2 (SAM2), which is shown to accurately predict the boundary of the fireball over time with high resolution. These state-of-the-art computer vision foundation models exhibit impressive visual accuracy in their results but lack an output of values that robustly quantify uncertainty in scientific applications. In this paper, we develop procedures for uncertainty quantification of extracted fireball features. We outline the application of a parallel attention mechanism to calculate uncertainty ranges that complement and better pose model validation data. This higher quality fireball validation data may serve to improve prognostic models describing nuclear detonations in support of nuclear forensic and emergency response activities.

Khristy, Joel [ORNL] (ORCID:0000000209963060)↗

DOE OSTI2021

Coupling Surface Flow with High-performance Subsurface Reactive Flow and Transport Code PFLOTRAN

Water exchange between the surface and subsurface is important for both water resource management and environmental protection. In this paper, we develop coupled surface and subsurface flow simulation capability in a parallel subsurface flow and reactive transport code PFLOTRAN. We sequentially couple the diffusion wave-based surface flow with the subsurface flow governedby the Richards equation in PFLOTRAN. These two flow domains are linked with a boundary condition switching method that ensures continuity of pressure and flux at the surface-subsurface interface. We verify the coupled code against other existing hydrologic models and observation data using a number of numerical experiments. The coupled hydrological model exhibits good performance in strong parallel scaling tests. The new coupled surface and subsurface simulator significantly advance community simulation capability towards improving integrated hydrologic and biogeochemical understanding of complex systems such as watersheds and river corridors. Keywords: Surface flow, Integrated hydrological modeling, Boundary condition switching, Parallel computing

Wu, Runjian↗