The non-Hermitian skin effect has been applied in multiple fields.However,there are relatively few models in the field of thermal diffusion that utilize the non-Hermitian skin effect for achieving thermal regulation.H...The non-Hermitian skin effect has been applied in multiple fields.However,there are relatively few models in the field of thermal diffusion that utilize the non-Hermitian skin effect for achieving thermal regulation.Here,we propose two non-Hermitian Su-Schrieffer-Heeger(SSH)models for thermal regulation:one capable of achieving edge states,and the other capable of achieving corner states within the thermal field.By analyzing the energy band structures and the generalized Brillouin zone,we predict the appearance of the non-Hermitian skin effect in these two models.Furthermore,we analyze the time-dependent evolution results and assess the robustness of the models.The results indicate that the localized thermal effects of the models align with our predictions.In a word,this work presents two models based on the non-Hermitian skin effect for regulating the thermal field,injecting vitality into the design of non-Hermitian thermal diffusion systems.展开更多
In this paper,a two-step semi-regularized Hermitian and skew-Hermitian splitting(SHSS)iteration method is constructed by introducing a regularization matrix in the(1,1)-block of the first iteration step,to solve the s...In this paper,a two-step semi-regularized Hermitian and skew-Hermitian splitting(SHSS)iteration method is constructed by introducing a regularization matrix in the(1,1)-block of the first iteration step,to solve the saddle-point linear system.By carefully selecting two different regularization matrices,two kinds of SHSS preconditioners are proposed to accelerate the convergence rates of the Krylov subspace iteration methods.Theoretical analysis about the eigenvalue distribution demonstrates that the proposed SHSS preconditioners can make the eigenvalues of the corresponding preconditioned matrices be clustered around 1 and uniformly bounded away from 0.The eigenvector distribution and the upper bound on the degree of the minimal polynomial of the SHSS-preconditioned matrices indicate that the SHSS-preconditioned Krylov subspace iterative methods can converge to the true solution within finite steps in exact arithmetic.In addition,the numerical example derived from the optimal control problem shows that the SHSS preconditioners can significantly improve the convergence speeds of the Krylov subspace iteration methods,and their convergence rates are independent of the discrete mesh size.展开更多
基金supported by the Key Research and Development Program of China(Grant No.2022YFA1405200)the National Natural Science Foundation of China(Grant Nos.92163123 and 52250191)。
文摘The non-Hermitian skin effect has been applied in multiple fields.However,there are relatively few models in the field of thermal diffusion that utilize the non-Hermitian skin effect for achieving thermal regulation.Here,we propose two non-Hermitian Su-Schrieffer-Heeger(SSH)models for thermal regulation:one capable of achieving edge states,and the other capable of achieving corner states within the thermal field.By analyzing the energy band structures and the generalized Brillouin zone,we predict the appearance of the non-Hermitian skin effect in these two models.Furthermore,we analyze the time-dependent evolution results and assess the robustness of the models.The results indicate that the localized thermal effects of the models align with our predictions.In a word,this work presents two models based on the non-Hermitian skin effect for regulating the thermal field,injecting vitality into the design of non-Hermitian thermal diffusion systems.
基金the National Natural Science Foundation of China(No.12001048)R&D Program of Beijing Municipal Education Commission(No.KM202011232019),China.
文摘In this paper,a two-step semi-regularized Hermitian and skew-Hermitian splitting(SHSS)iteration method is constructed by introducing a regularization matrix in the(1,1)-block of the first iteration step,to solve the saddle-point linear system.By carefully selecting two different regularization matrices,two kinds of SHSS preconditioners are proposed to accelerate the convergence rates of the Krylov subspace iteration methods.Theoretical analysis about the eigenvalue distribution demonstrates that the proposed SHSS preconditioners can make the eigenvalues of the corresponding preconditioned matrices be clustered around 1 and uniformly bounded away from 0.The eigenvector distribution and the upper bound on the degree of the minimal polynomial of the SHSS-preconditioned matrices indicate that the SHSS-preconditioned Krylov subspace iterative methods can converge to the true solution within finite steps in exact arithmetic.In addition,the numerical example derived from the optimal control problem shows that the SHSS preconditioners can significantly improve the convergence speeds of the Krylov subspace iteration methods,and their convergence rates are independent of the discrete mesh size.
