Deep submicron process technology is widely being used and interconnect structures are becoming more and more complex.This means that the resistance calculation based on two-dimensional models can no longer provide su...Deep submicron process technology is widely being used and interconnect structures are becoming more and more complex.This means that the resistance calculation based on two-dimensional models can no longer provide sufficiently accurate results.This paper presents a three-dimensional resistance calculation method called the combined analytical formula and boundary element method(ABEM).The method cuts selected interconnecting lines then it calculates the resistances of straight sections using an analytical formula and the resistances of the other sections using the boundary element method(BEM).The resistances of the different sub-regions are combined to calculate the resistance of the entire region.Experiments on actual layouts show that compared with the commercial software Raphael based on finite difference method,the proposed method is 2-3 orders of magnitude faster.The ABEM method uses much less memory(about 0.1%-1%),and is more accurate than Raphael with default mesh partitions.The results illustrate that the proposed method is efficient and accurate.展开更多
In this paper, the concept of k-submesh and k-submesh connectivity fault tolerance model is proposed. And the fault tolerance of 3-D mesh networks is studied under a more realistic model in which each network node has...In this paper, the concept of k-submesh and k-submesh connectivity fault tolerance model is proposed. And the fault tolerance of 3-D mesh networks is studied under a more realistic model in which each network node has an independent failure probability. It is first observed that if the node failure probability is fixed, then the connectivity probability of 3-D mesh networks can be arbitrarily small when the network size is sufficiently large. Thus, it is practically important for multicomputer system manufacturer to determine the upper bound for node failure probability when the probability of network connectivity and the network size are given. A novel technique is developed to formally derive lower bounds on the connectivity probability for 3-D mesh networks. The study shows that 3-D mesh networks of practical size can tolerate a large number of faulty nodes thus are reliable enough for multicomputer systems. A number of advantages of 3-D mesh networks over other popular network topologies are given. Compared to 2-D mesh networks, 3-D mesh networks are much stronger in tolerating faulty nodes, while for practical network size, the fault tolerance of 3-D mesh networks is comparable with that of hypercube networks but enjoys much lower node degree.展开更多
This paper describes an efficient improvement of the multipole accelerated boundary element method for 3-D capacitance extraction. The overall relations between the positions of 2-D boundary elements are considered in...This paper describes an efficient improvement of the multipole accelerated boundary element method for 3-D capacitance extraction. The overall relations between the positions of 2-D boundary elements are considered instead of only the relations between the center-points of the elements, and a new method of cube partitioning is introduced. Numerical results are presented to demonstrate that the method is accurate and has nearly linear computational growth as O(n), where n is the number of panels/boundary elements. The proposed method is more accurate and much faster than Fastcap.展开更多
基金supported by National Science Foundation of China(No.90407004).
文摘Deep submicron process technology is widely being used and interconnect structures are becoming more and more complex.This means that the resistance calculation based on two-dimensional models can no longer provide sufficiently accurate results.This paper presents a three-dimensional resistance calculation method called the combined analytical formula and boundary element method(ABEM).The method cuts selected interconnecting lines then it calculates the resistances of straight sections using an analytical formula and the resistances of the other sections using the boundary element method(BEM).The resistances of the different sub-regions are combined to calculate the resistance of the entire region.Experiments on actual layouts show that compared with the commercial software Raphael based on finite difference method,the proposed method is 2-3 orders of magnitude faster.The ABEM method uses much less memory(about 0.1%-1%),and is more accurate than Raphael with default mesh partitions.The results illustrate that the proposed method is efficient and accurate.
文摘In this paper, the concept of k-submesh and k-submesh connectivity fault tolerance model is proposed. And the fault tolerance of 3-D mesh networks is studied under a more realistic model in which each network node has an independent failure probability. It is first observed that if the node failure probability is fixed, then the connectivity probability of 3-D mesh networks can be arbitrarily small when the network size is sufficiently large. Thus, it is practically important for multicomputer system manufacturer to determine the upper bound for node failure probability when the probability of network connectivity and the network size are given. A novel technique is developed to formally derive lower bounds on the connectivity probability for 3-D mesh networks. The study shows that 3-D mesh networks of practical size can tolerate a large number of faulty nodes thus are reliable enough for multicomputer systems. A number of advantages of 3-D mesh networks over other popular network topologies are given. Compared to 2-D mesh networks, 3-D mesh networks are much stronger in tolerating faulty nodes, while for practical network size, the fault tolerance of 3-D mesh networks is comparable with that of hypercube networks but enjoys much lower node degree.
文摘This paper describes an efficient improvement of the multipole accelerated boundary element method for 3-D capacitance extraction. The overall relations between the positions of 2-D boundary elements are considered instead of only the relations between the center-points of the elements, and a new method of cube partitioning is introduced. Numerical results are presented to demonstrate that the method is accurate and has nearly linear computational growth as O(n), where n is the number of panels/boundary elements. The proposed method is more accurate and much faster than Fastcap.
