9429067
Frequency domain wavelet method with GMRES for large-scale linear circuit simulation
In this paper, a frequency domain fast wavelet collocation method with GMRES (FFWCM-G) is proposed for the simulation of high-speed large-scale linear VLSI circuits. Taking advantages of wavelet expansion and adaptive scheme, the number of frequency points for calculating frequency response is minimized. Moreover, due to the efficiency of GMRES as the internal iterative solver, the proposed method can achieve nearly linear time complexity, which undoubtedly would be more promising to simulate large-scale integrated circuits.
7673603
Wirelength reduction by using diagonal wire
We study the octilinear Steiner tree to evaluate the rectilinear Steiner tree based router. First, we give the worst and average case wirelength for rectilinear routing and octilinear routing for two terminals net. Next, we show the octilinear Steiner trees have smaller wirelength reduction for multiterminal net than that of rectilinear Steiner tree. Then, we propose an O(|V|+|E|) algorithm to construct an isomorphic octilinear Steiner tree from a rectilinear Steiner tree G = (V, E) and prove the wirelength of the isomorphic octilinear Steiner tree is the lower bound. In the end, we show two types of experiment of wirelength reduction results by using diagonal wire The octilinear Steiner tree reduces 9.201% and 6.63% of the wirelength over rectilinear Steiner tree on a set of nets generated at random and on 15 VLSI designs, respectively.
11957537
Revisiting variable radius circles in constructive geometric constraint solving
Variable-radius circles are common constructs in planar constraint solving and are usually not handled completely by algebraic constraint solvers.This work offers a set of basic constructive methods for the complete treatment of variable radius circles determined by the simultaneous placement of two other rigid geometric objects. The variable radius circle is defined by geometric constraints that determine both the circumference and the center point. There are two constraints between the variable radius circle and each of the rigid geometric objects. The problem has been classified into two groups according to whether the relative movement between the two rigid objects is a translation or a rotation. The number of solutions in each case is also given.