An Algorithmic Framework for Efficient Large-Scale Circuit Simulation Using Exponential Integrators

We propose an efficient algorithmic framework for time domain circuit simulation using exponential integrator. This work addresses several critical issues exposed by previous matrix exponential based circuit simulation research, and makes it capable of simulating stiff nonlinear circuit system at a large scale. In this framework, the system's nonlinearity is treated with exponential Rosenbrock-Euler formulation. The matrix exponential and vector product is computed using invert Krylov subspace method. Our proposed method has several distinguished advantages over conventional formulations (e.g., the well-known backward Euler with Newton-Raphson method). The matrix factorization is performed only for the conductance/resistance matrix G, without being performed for the combinations of the capacitance/inductance matrix C and matrix G, which are used in traditional implicit formulations. Furthermore, due to the explicit nature of our formulation, we do not need to repeat LU decompositions when adjusting the length of time steps for error controls. Our algorithm is better suited to solving tightly coupled post-layout circuits in the pursuit for full-chip simulation. Our experimental results validate the advantages of our framework.Comment: 6 pages; ACM/IEEE DAC 201

Simplicity of AdS Super Yang-Mills at One Loop

We perform a systematic bootstrap analysis of four-point one-loop Mellin amplitudes for super gluons in $\mathrm{AdS}_5\times\mathrm{S}^3$ with arbitrary Kaluza-Klein weights. The analysis produces the general expressions for these amplitudes at extremalities two and three, as well as analytic results for many other special cases. From these results we observe remarkable simplicity. We find that the Mellin amplitudes always contain only simultaneous poles in two Mellin-Mandelstam variables, extending a previous observation in the simplest case with the lowest Kaluza-Klein weights. Moreover, we discover a substantial extension of the implication of the eight-dimensional hidden conformal symmetry, which goes far beyond the Mellin poles associated with the leading logarithmic singularities. This leaves only a small finite set of poles which can be determined on a case-by-case basis from the contributions of protected operators in the OPE.Comment: 62 pages, 9 figures and 1 auxiliary fil