To solve electrically large scattering problems with limited memory, a Gauss-Seidel iteration scheme is applied to solve the interior penalty integral equation domain decomposition method. Since the original stabiliza...To solve electrically large scattering problems with limited memory, a Gauss-Seidel iteration scheme is applied to solve the interior penalty integral equation domain decomposition method. Since the original stabilization parameter in this method is frequency-dependent, the convergence of stationary iterations shows obvious dependence on frequency and slow convergence can be observed in some frequency bands. To avoid this dependence and obtain fast convergence in a wide frequency band, a frequency-independent stabilization parameter is introduced. This parameter is chosen proportionally to the average mesh length and inversely proportionally to the wavelength. Numerical examples are proposed to verify the effectiveness of the proposed approach.展开更多
PoW(Proof of Work)plays a significant role in most blockchain systems to grant an accounting right over decentralized participants and ensure tamper resistance.Though hash functions are generally exploited for PoW due...PoW(Proof of Work)plays a significant role in most blockchain systems to grant an accounting right over decentralized participants and ensure tamper resistance.Though hash functions are generally exploited for PoW due to their merits on summering,anti-collision,and irreversibility,they cannot certify that the bookkeeper is exactly the worker.Thereafter,such insistence may lead to abuse or even embezzlement of computing power for the benefit of malicious miners.To preserve the functionality of PoW but also bind the miners’signing keys with their works,we build a post-quantum PoW scheme by changing the approximate closest vector norm for probabilistic NTRUSign.Different from the schemes based on hash functions,our scheme takes signing as the proof of work where signature verification is just the evidence of block reward.We also presented a method to adjust the difficulty of signing by modifying the probability of generating a correct signature.The performance of our scheme is also analyzed theoretically and experimentally,which implies its practicability and advantages.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.11647095
文摘To solve electrically large scattering problems with limited memory, a Gauss-Seidel iteration scheme is applied to solve the interior penalty integral equation domain decomposition method. Since the original stabilization parameter in this method is frequency-dependent, the convergence of stationary iterations shows obvious dependence on frequency and slow convergence can be observed in some frequency bands. To avoid this dependence and obtain fast convergence in a wide frequency band, a frequency-independent stabilization parameter is introduced. This parameter is chosen proportionally to the average mesh length and inversely proportionally to the wavelength. Numerical examples are proposed to verify the effectiveness of the proposed approach.
基金This work was supported in part by the National Natural Science Foundation of P.R.China under Grants[61573076,61703063,61903053]the Science and Technology Research Project of the Chongqing Municipal Education Commission of P.R.China under Grants[KJZD-K201800701,KJQN201900702,KJ1705121,KJ1705139]+1 种基金the Program of Chongqing innovation and entrepreneurship for Returned Overseas Scholars of P.R.China under Grant cx20181102018 Team Building Project for Graduate Tutors in Chongqing under Grant JDDSTD2018001.
文摘PoW(Proof of Work)plays a significant role in most blockchain systems to grant an accounting right over decentralized participants and ensure tamper resistance.Though hash functions are generally exploited for PoW due to their merits on summering,anti-collision,and irreversibility,they cannot certify that the bookkeeper is exactly the worker.Thereafter,such insistence may lead to abuse or even embezzlement of computing power for the benefit of malicious miners.To preserve the functionality of PoW but also bind the miners’signing keys with their works,we build a post-quantum PoW scheme by changing the approximate closest vector norm for probabilistic NTRUSign.Different from the schemes based on hash functions,our scheme takes signing as the proof of work where signature verification is just the evidence of block reward.We also presented a method to adjust the difficulty of signing by modifying the probability of generating a correct signature.The performance of our scheme is also analyzed theoretically and experimentally,which implies its practicability and advantages.
