Pub Date : 2023-06-01DOI: 10.4208/cicp.oa-2023-0152
Lulu Zhang, Wei Cai null, Z. Xu
{"title":"A Correction and Comments on “Multi-Scale Deep Neural Network (MscaleDNN) for Solving Poisson-Boltzmann Equation in Complex Domains CiCP, 28(5):1970–2001,2020”","authors":"Lulu Zhang, Wei Cai null, Z. Xu","doi":"10.4208/cicp.oa-2023-0152","DOIUrl":"https://doi.org/10.4208/cicp.oa-2023-0152","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47168126","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-01DOI: 10.4208/cicp.oa-2023-0062
Qiwei Feng, Bin Han null, Michelle Michelle
Due to its highly oscillating solution, the Helmholtz equation is numerically challenging to solve. To obtain a reasonable solution, a mesh size that is much smaller than the reciprocal of the wavenumber is typically required (known as the pollution effect). High order schemes are desirable, because they are better in mitigating the pollution effect. In this paper, we present a high order compact finite difference method for 2D Helmholtz equations with singular sources, which can also handle any possible combinations of boundary conditions (Dirichlet, Neumann, and impedance) on a rectangular domain. Our method achieves a sixth order consistency for a constant wavenumber, and a fifth order consistency for a piecewise constant wavenumber. To reduce the pollution effect, we propose a new pollution minimization strategy that is based on the average truncation error of plane waves. Our numerical experiments demonstrate the superiority of our proposed finite difference scheme with reduced pollution effect to several state-of-the-art finite difference schemes, particularly in the critical pre-asymptotic region where $textsf{k} h$ is near $1$ with $textsf{k}$ being the wavenumber and $h$ the mesh size.
{"title":"Sixth-Order Compact Finite Difference Method for 2D Helmholtz Equations with Singular Sources and Reduced Pollution Effect","authors":"Qiwei Feng, Bin Han null, Michelle Michelle","doi":"10.4208/cicp.oa-2023-0062","DOIUrl":"https://doi.org/10.4208/cicp.oa-2023-0062","url":null,"abstract":"Due to its highly oscillating solution, the Helmholtz equation is numerically challenging to solve. To obtain a reasonable solution, a mesh size that is much smaller than the reciprocal of the wavenumber is typically required (known as the pollution effect). High order schemes are desirable, because they are better in mitigating the pollution effect. In this paper, we present a high order compact finite difference method for 2D Helmholtz equations with singular sources, which can also handle any possible combinations of boundary conditions (Dirichlet, Neumann, and impedance) on a rectangular domain. Our method achieves a sixth order consistency for a constant wavenumber, and a fifth order consistency for a piecewise constant wavenumber. To reduce the pollution effect, we propose a new pollution minimization strategy that is based on the average truncation error of plane waves. Our numerical experiments demonstrate the superiority of our proposed finite difference scheme with reduced pollution effect to several state-of-the-art finite difference schemes, particularly in the critical pre-asymptotic region where $textsf{k} h$ is near $1$ with $textsf{k}$ being the wavenumber and $h$ the mesh size.","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135145208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-01DOI: 10.4208/cicp.oa-2023-0012
Yanyan Wang, Qiang Li null, Liang Yan
. The ensemble Kalman inversion (EKI), inspired by the well-known ensemble Kalman filter, is a derivative-free and parallelizable method for solving inverse problems. The method is appealing for applications in a variety of fields due to its low computational cost and simple implementation. In this paper, we propose an adaptive ensemble Kalman inversion with statistical linearization (AEKI-SL) method for solving inverse problems from a hierarchical Bayesian perspective. Specifically, by adaptively updating the unknown with an EKI and updating the hyper-parameter in the prior model, the method can improve the accuracy of the solutions to the inverse problem. To avoid semi-convergence, we employ Morozov’s discrepancy principle as a stopping criterion. Furthermore, we extend the method to simultaneous estimation of noise levels in order to reduce the randomness of artificially ensemble noise levels. The convergence of the hyper-parameter in prior model is investigated theoretically. Numerical experiments show that our proposed methods outperform the traditional EKI and EKI with statistical linearization (EKI-SL) methods.
{"title":"Adaptive Ensemble Kalman Inversion with Statistical Linearization","authors":"Yanyan Wang, Qiang Li null, Liang Yan","doi":"10.4208/cicp.oa-2023-0012","DOIUrl":"https://doi.org/10.4208/cicp.oa-2023-0012","url":null,"abstract":". The ensemble Kalman inversion (EKI), inspired by the well-known ensemble Kalman filter, is a derivative-free and parallelizable method for solving inverse problems. The method is appealing for applications in a variety of fields due to its low computational cost and simple implementation. In this paper, we propose an adaptive ensemble Kalman inversion with statistical linearization (AEKI-SL) method for solving inverse problems from a hierarchical Bayesian perspective. Specifically, by adaptively updating the unknown with an EKI and updating the hyper-parameter in the prior model, the method can improve the accuracy of the solutions to the inverse problem. To avoid semi-convergence, we employ Morozov’s discrepancy principle as a stopping criterion. Furthermore, we extend the method to simultaneous estimation of noise levels in order to reduce the randomness of artificially ensemble noise levels. The convergence of the hyper-parameter in prior model is investigated theoretically. Numerical experiments show that our proposed methods outperform the traditional EKI and EKI with statistical linearization (EKI-SL) methods.","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43176196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-01DOI: 10.4208/cicp.oa-2022-0122
Wenhua Ma, Dongmi Luo, W. Ying, Guoxi Ni, M. null, Yibing Chen
{"title":"Adaptive Multi-Resolution Method for 3D Reactive Flows with Level Set Front Capturing","authors":"Wenhua Ma, Dongmi Luo, W. Ying, Guoxi Ni, M. null, Yibing Chen","doi":"10.4208/cicp.oa-2022-0122","DOIUrl":"https://doi.org/10.4208/cicp.oa-2022-0122","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41931216","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-01DOI: 10.4208/cicp.oa-2023-0053
Jia Liu null, L. Wu
{"title":"Fast-Converging and Asymptotic-Preserving Simulation of Frequency Domain Thermoreflectance","authors":"Jia Liu null, L. Wu","doi":"10.4208/cicp.oa-2023-0053","DOIUrl":"https://doi.org/10.4208/cicp.oa-2023-0053","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45831934","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-01DOI: 10.4208/cicp.oa-2023-0080
Hao Zhang, Yidao Dong, Shichao Zheng null, Xiaogang Deng
. In this paper, we present a hybrid form of weighted compact nonlinear scheme (WCNS) for hyperbolic conservation laws by applying linear and nonlinear methods for smooth and discontinuous zones individually. To fulfill this algorithm, it is inseparable from the recognition ability of the discontinuity detector adopted. In specific, a troubled-cell indicator is utilized to recognize unsmooth areas such as shock waves and contact discontinuities, while avoiding misjudgments of smooth structures. Some classical detectors are classified into three basic types: derivative combination, smoothness indicators and characteristic decomposition. Meanwhile, a new improved detector is proposed for comparison. Then they are analyzed through identifying a series of waveforms firstly. After that, hybrid schemes using such indicators, as well as different detection variables, are examined with Euler equations, so as to investigate their ability to distinguish practical discontinuities on various levels. Simulation results demonstrate that the proposed algorithm has similar performances to pure WCNS, while it generally saves 50 percent of CPU time for 1D cases and about 40 percent for 2D Euler equations. Current research is in the hope of providing some reference and establishing some standards for judging existing discontinuity detectors and developing novel ones.
{"title":"Analysis of Discontinuity Detectors and Hybrid WCNS Schemes Based on Waveform Recognition","authors":"Hao Zhang, Yidao Dong, Shichao Zheng null, Xiaogang Deng","doi":"10.4208/cicp.oa-2023-0080","DOIUrl":"https://doi.org/10.4208/cicp.oa-2023-0080","url":null,"abstract":". In this paper, we present a hybrid form of weighted compact nonlinear scheme (WCNS) for hyperbolic conservation laws by applying linear and nonlinear methods for smooth and discontinuous zones individually. To fulfill this algorithm, it is inseparable from the recognition ability of the discontinuity detector adopted. In specific, a troubled-cell indicator is utilized to recognize unsmooth areas such as shock waves and contact discontinuities, while avoiding misjudgments of smooth structures. Some classical detectors are classified into three basic types: derivative combination, smoothness indicators and characteristic decomposition. Meanwhile, a new improved detector is proposed for comparison. Then they are analyzed through identifying a series of waveforms firstly. After that, hybrid schemes using such indicators, as well as different detection variables, are examined with Euler equations, so as to investigate their ability to distinguish practical discontinuities on various levels. Simulation results demonstrate that the proposed algorithm has similar performances to pure WCNS, while it generally saves 50 percent of CPU time for 1D cases and about 40 percent for 2D Euler equations. Current research is in the hope of providing some reference and establishing some standards for judging existing discontinuity detectors and developing novel ones.","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48515102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-01DOI: 10.4208/cicp.oa-2022-0181
K. Datadien, G. D. Staso, C. Diddens, H. W. null, F. Toschi
{"title":"Comparison of Lattice Boltzmann, Finite Element and Volume of Fluid Multicomponent Methods for Microfluidic Flow Problems and the Jetting of Microdroplets","authors":"K. Datadien, G. D. Staso, C. Diddens, H. W. null, F. Toschi","doi":"10.4208/cicp.oa-2022-0181","DOIUrl":"https://doi.org/10.4208/cicp.oa-2022-0181","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45562431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-01DOI: 10.4208/cicp.oa-2021-0209
L. Chai, Lorin Emmanuel null, Xu Yang
{"title":"Frozen Gaussian Approximation for the Dirac Equation in Curved Space with Application to Strained Graphene","authors":"L. Chai, Lorin Emmanuel null, Xu Yang","doi":"10.4208/cicp.oa-2021-0209","DOIUrl":"https://doi.org/10.4208/cicp.oa-2021-0209","url":null,"abstract":"","PeriodicalId":50661,"journal":{"name":"Communications in Computational Physics","volume":null,"pages":null},"PeriodicalIF":3.7,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46271065","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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