Large-scale Computational Applications Research Articles

Geometric constraints on two-electron reduced density matrices

For many-electron systems, the second-order reduced density matrix (2-RDM) provides sufficient information for characterizing their properties of interests in physics and chemistry, ranging from total energy, magnetism, quantum correlation and entanglement to long-range orders. Theoretical prediction of the structural properties of 2-RDM is an essential endeavor in quantum chemistry, condensed matter physics and, more recently, in quantum computation. Since 1960s, enormous progresses have been made in developing RDM-based electronic structure theories and their large-scale computational applications in predicting molecular structure and mechanical, electrical and optical properties of various materials. However, for strongly correlated systems, such as high-temperature superconductors, transition-metal-based biological catalysts and complex chemical bonds near dissociation limit, accurate approximation is still out of reach by currently most sophisticated approaches. This limitation highlights the elusive structural feature of 2-RDM that determines quantum correlation in many-electron system. Here, we present a set of constraints on 2-RDM based on the basic geometric property of Hilbert space and the commutation relations of operators. Numerical examples are provided to demonstrate the pronounced violation of these constraints by the variational 2-RDMs. It is shown that, for a strongly correlated model system, the constraint violation may be responsible for a considerable portion of the variational error in ground state energy. Our findings provide new insights into the structural subtlety of many-electron 2-RDMs.

Accurate and fast design algorithm for free-return lunar flyby trajectories

A linear approximation based fast prediction algorithm for the Earth–Moon transfer trajectory is proposed. Compared with the multi-conic technique, the algorithm dramatically improves the accuracy of the trajectory prediction results. Based on this prediction algorithm and the pseudostate theory, a preliminary design algorithm of the free-return lunar flyby trajectories between the Earth and the Moon is developed. Without numerical differential correction, an accurate solution can be obtained within a little computational time. A large number of numerical examples are carried out to examine the reliability and efficiency of this design algorithm. The results indicate that this design algorithm has a good balance between the accuracy and efficiency. It is valuable for the large-scale computational applications, such as the lunar exploration mission analysis.

Lean Algebraic Multigrid (LAMG): Fast Graph Laplacian Linear Solver

Laplacian matrices of graphs arise in large-scale computational applications such as semisupervised machine learning; spectral clustering of images, genetic data, and web pages; transportation network flows; electrical resistor circuits; and elliptic partial differential equations discretized on unstructured grids with finite elements. A lean algebraic multigrid (LAMG) solver of the symmetric linear system $Ax=b$ is presented, where $A$ is a graph Laplacian. LAMG's run time and storage are empirically demonstrated to scale linearly with the number of edges. LAMG consists of a setup phase, during which a sequence of increasingly coarser Laplacian systems is constructed, and an iterative solve phase using multigrid cycles. General graphs pose algorithmic challenges not encountered in traditional multigrid applications. LAMG combines a lean piecewise-constant interpolation, judicious node aggregation based on a new node proximity measure (the affinity), and an energy correction of coarse-level systems. This results in fast convergence and substantial setup and memory savings. A serial LAMG implementation scaled linearly for a diverse set of 3774 real-world graphs with up to 47 million edges, with no parameter tuning. LAMG was more robust than the UMFPACK direct solver and combinatorial multigrid (CMG), although CMG was faster than LAMG on average. Our methodology is extensible to eigenproblems and other graph computations.

Early parallelism with a loosely coupled array of processors: The ICAP experiment

The hardware, system software and Scientific application examples with relative performances are reported for the ICAP-1, ICAP-2, ICAP-3 and ICAP-3090 experimental systems, with emphases on motivation, strategy and accomplishments. These pioneering efforts are considered in the light of future large-scale computational applications, which will require parallel super computing power and also a new outlook to computational models.

Embedding languages within design environments

Large-scale computer applications reflect numerous sources of complexity: complexity originating in the constructs of the application domain, complexity of feature-rich interfaces, and (in many cases) complexity arising from the inclusion of enduser programming environments. The paper discusses a software design strategy for the creation of programmable design environments (PDEs); such environments are geared toward alleviating, for users, the negative effects of various sources of complexity. The paper illustrates this notion of PDEs with a description of a charting/graphing application named SchemeChart.

Gallium arsenide digital integrated circuits

The motivations behind the development of GaAs integrated circuits (IC) are two-fold: to integrate high speed logic with optical sources and to meet the increasing demand of realising LSI/VLSI with higher speed and lower power dissipation for large scale computer applications. GaAs gigabit circuits have been growing in complexity to more than 3000 gates on a single chip. Although this is encouraging, more efforts are needed to improve production yield. By far the most work on GaAs digital IC has been done using MESFET as the active devices. MOSFET technology is yet to mature from the practical IC point of view. The logic gate types used in circuits are predominantly of the enhancement-mode driver and depletion-mode load configuration (E/D).

Large-scale scientific application programs in chemistry and physics on an experimental parallel computer system

We present and discuss an experimental distributed system consisting of two IBM 4341s, an IBM 4381, and ten FPS-164 attached processors, configured to allow parallel execution of a single large-scale calculation on multiple processors. A number of our application programs have been converted to run on this system, and the strategy for this conversion is outlined in sufficient detail to facilitate the development of tests using other scientific and engineering computer application programs. Our tests, though limited to certain biochemical and physicochemical problems, demonstrate the versatility, flexibility, and accessibility of this system, and we find performance comparable to that of today's supercomputers, which suggests that our approach can provide a practical answer to many large-scale computer applications.

New technology towards GaAs LSI/VLSI for computer applications

For future large-scale computer applications, new device technologies towards GaAs LSI/VLSI have been developed: self-aligned fully implanted planar GaAs MESFET technology and high electron mobility transistor (HEMT) technology by molecular beam epitaxy (MBE). The self-aligned GaAs MESFET logic with 1.5-µm gate length exhibits a minimum switching time of 50 ps and the lowest power-delay product of 14.5 fJ at room temperature. The enhancement/depletion (E/D) type direct coupled HEMT logic has achieved a switching time of 17.1 ps with 1.7-µm gate length at liquid nitrogen temperature and more recently a switching time of 12.8 ps with 1.1-µm gate HEMT logic, which exceeds the top speed of Josephson Junction logic and shows the highest speed of any device logic ever reported. Optimized system performances are also projected to system delay of 200 ps at 10-kilogate integration with GaAs MESFET VLSI, and 100 ps at 100-kilogate with HEMT VLSI. These values of system delay correspond to the computer performance of over 100 million instructions per second (MIPS).

New Technology Towards GaAs LSI/VLSI for Computer Applications

For future large-scale computer applications, new device technologies towards GaAs LSI/VLSI have been developed self-aligned fully implanted planar GaAs MESFET technology and high electron mobility transistor (HFMT) technology by molecular beam epitaxy (MBE). The self-aligned GaAs MESFET logic with 1.5-µm gate length exhibits a minimum switching time of 50 ps and the lowest power-delay product of 14.5 fJ at room temperature. The enhancement/depletion (E/D) type direct coupled HEMT logic has achieved a switching time of 17.1 ps with 1.7-µm gate length at liquid nitrogen temperature and more recently a switching time of 12.8 ps with 1.1-µm gate HEMT logic, which exceeds the top speed of Josephson Junction logic and shows the highest speed of any device logic ever reported. Optimized system performances are also projected to system delay of 200 ps at 10-kilogate integration with GaAs MESFET VLSI, and 100 ps at 100-kilogate with HEMT VLSI. These values of system delay correspond to the computer performance of over 100 million instructions per second (MIPS).