An Interior Penalty Method for the Generalized Method of Moments

Abstract

The Generalized Method of Moments is a technique to discretize integral equations that permits integration of different types of basis functions as well as different geometric descriptions using a partition of unity framework. While accuracy and efficacy of the method have been demonstrated, the integration quadratures required to compute the inner-products are often high as they have to respect spatial variation of the integrand. To overcome this problem, we introduce an interior penalty function method within the GMM framework. The penalty formulation yields solutions that are smooth and accurate both in surface currents and fields with significantly lower numerical quadrature orders than would be required for the uncompensated operator. To demonstrate and analyze the method, we conduct an analytical and numerical investigation of the properties of the penalty method applied to the 2D TE z Electric Field Integral Equation operator.

Optimal Planned Electricity Allocation Model for Power Exchange Under the Plan-Market Double-Track Mechanism

“…In the upper level, the planned electricity is optimized by PX to minimize the CVaR of Lerner index in multiple scenarios, Bi-level nonlinear optimization is a relatively complex optimization problem. Common solving algorithms include the penalty method by Dault and Shanker (2015), tabu search by Wu and Soto (2020), the genetic algorithm by Silva et al (2019), the neural network by Zarco and Froese (2018)., etc. The proportion of planned electricity consumption is related to user structure, while the latter is related to market access conditions.…”