Pub Date : 2025-04-07DOI: 10.1109/JMMCT.2025.3558662
Nikolas Hadjiantoni;Dou Feng;Miguel Navarro-Cía;Stephen M. Hanham
Electromagnetic topological optimization holds the promise of the fully automated design of electromagnetic structures such as antennas, waveguides, metasurfaces and metamaterials; however, it often yields designs that are incompatible with fabrication processes. In this work, we describe a topological optimization framework that combines structural finite element analysis and electromagnetic finite-difference time-domain simulation to realize fabricable structures which meet specified electromagnetic design objectives. As a demonstration, the framework is applied towards the design of G-band low-profile leaky lens antennas suitable for future 6G communication applications. The 5$lambda _{0}$ radius, 2$lambda _{0}$ thick leaky lens antenna is compatible with stereolithography 3D printing and displays a realized gain of 23 dBi at 0.2 THz with a low side-lobe level of −20 dB. We foresee the proposed framework being applicable to a wide range of electromagnetic design problems intended for fabrication using additive manufacturing techniques.
{"title":"Topological Optimization Framework for the Automated Design of 3D Printable THz Lens Antennas","authors":"Nikolas Hadjiantoni;Dou Feng;Miguel Navarro-Cía;Stephen M. Hanham","doi":"10.1109/JMMCT.2025.3558662","DOIUrl":"https://doi.org/10.1109/JMMCT.2025.3558662","url":null,"abstract":"Electromagnetic topological optimization holds the promise of the fully automated design of electromagnetic structures such as antennas, waveguides, metasurfaces and metamaterials; however, it often yields designs that are incompatible with fabrication processes. In this work, we describe a topological optimization framework that combines structural finite element analysis and electromagnetic finite-difference time-domain simulation to realize fabricable structures which meet specified electromagnetic design objectives. As a demonstration, the framework is applied towards the design of G-band low-profile leaky lens antennas suitable for future 6G communication applications. The 5<inline-formula><tex-math>$lambda _{0}$</tex-math></inline-formula> radius, 2<inline-formula><tex-math>$lambda _{0}$</tex-math></inline-formula> thick leaky lens antenna is compatible with stereolithography 3D printing and displays a realized gain of 23 dBi at 0.2 THz with a low side-lobe level of −20 dB. We foresee the proposed framework being applicable to a wide range of electromagnetic design problems intended for fabrication using additive manufacturing techniques.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":"10 ","pages":"218-226"},"PeriodicalIF":1.8,"publicationDate":"2025-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143900506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Conventionally, the large sparse matrix equation ($Ax=b$) generated by the Laguerre-FDTD method is computed using direct matrix solvers, which is often numerically expensive and computationally slow. In this work, we demonstrate an innovative approach to replace direct matrix solver with an iterative algorithm for the Laguerre-FDTD method. A novel preconditioner, specifically targeted to improve the convergence rate of biconjugate gradient stabilized solver (BiCGSTAB), is derived and implemented in the Laguerre-FDTD method. Compared with the classical Jacobi preconditioner, the proposed preconditioner achieves on average an improvement of more than 1.3× in the convergence rate. To further leverage the computational efficiency, a modified sparse matrix-vector multiplication algorithm is proposed and implemented using a General-Purpose Graphics Processing Unit (GPGPU). The new algorithm ensures that all computations are performed within the GPU, with minimum number of device-to-host data transfer and global memory access. With GPU's accelerated computing capability, the proposed solver achieves more than 5× computational speed up with respect to a high performance CPU-based direct solver on average. In addition, due to the intrinsic memory efficient nature of iterative solver, our approach also shows maximally more than 31× reduction in memory consumption against the direct solver. Various numerical examples are simulated to validate the capability and improvement of the proposed method.
{"title":"GPU Accelerated Matrix Solution Using Novel Preconditioner for Three Dimensional Laguerre-FDTD Method","authors":"Yifan Wang;Yiliang Guo;Joshua Corsello;Madhavan Swaminathan","doi":"10.1109/JMMCT.2025.3572490","DOIUrl":"https://doi.org/10.1109/JMMCT.2025.3572490","url":null,"abstract":"Conventionally, the large sparse matrix equation (<inline-formula><tex-math>$Ax=b$</tex-math></inline-formula>) generated by the Laguerre-FDTD method is computed using direct matrix solvers, which is often numerically expensive and computationally slow. In this work, we demonstrate an innovative approach to replace direct matrix solver with an iterative algorithm for the Laguerre-FDTD method. A novel preconditioner, specifically targeted to improve the convergence rate of biconjugate gradient stabilized solver (BiCGSTAB), is derived and implemented in the Laguerre-FDTD method. Compared with the classical Jacobi preconditioner, the proposed preconditioner achieves on average an improvement of more than 1.3× in the convergence rate. To further leverage the computational efficiency, a modified sparse matrix-vector multiplication algorithm is proposed and implemented using a General-Purpose Graphics Processing Unit (GPGPU). The new algorithm ensures that all computations are performed within the GPU, with minimum number of device-to-host data transfer and global memory access. With GPU's accelerated computing capability, the proposed solver achieves more than 5× computational speed up with respect to a high performance CPU-based direct solver on average. In addition, due to the intrinsic memory efficient nature of iterative solver, our approach also shows maximally more than 31× reduction in memory consumption against the direct solver. Various numerical examples are simulated to validate the capability and improvement of the proposed method.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":"10 ","pages":"259-270"},"PeriodicalIF":1.8,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144213617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-12DOI: 10.1109/JMMCT.2025.3569766
Rui Fang;Yu Mao Wu;Hongxia Ye
The optimization of radar cross section (RCS) is now a significant issue in the designation of military and civilian equipment. Comparing with the expensive material approaches, changing the geometry of an object is a relatively flexible and low-cost way. However, the RCS optimization of large-scale models often faces two major problems: too large optimization space and slow RCS calculation, which caused by increasing geometry parameters and iterative numerical computation, respectively. In addition, secondary problems such as geometric information loss and RCS results lacking of gaurantees always remain even if dimensionality reduction has been carried out for alleviating these two problems. In this paper, we propose a novel end-to-end differentiable RCS optimization framework based on the physical optics (PO) method. The proposed framework utilize the differentiability of the PO method, and realize an efficient and interpretable RCS optimization without dimension reduction. The innovation of this paper lies in the combination of PO method and gradient-based optimization to achieve RCS optimization of large-scale complex 3D geometries. Experiments show that in ordinary 2D scenarios, our method achieves at least 16 times higher efficiency than the mainstream optimization method. Meanwhile, the optimization error of RCS has been reduced by 75.29$%$ compared to traditional methods (0.0515vs. 0.2084). We further validate the performance of the framework on more complex tasks such as 3D plane model and analyzed the effectiveness of the overall framework. The proposed optimization method is expected to be widely used in applications such as stealth and aircraft designs.
{"title":"End-to-End Differentiable RCS Optimization on 3D Geometry Based on Physical Optics Method","authors":"Rui Fang;Yu Mao Wu;Hongxia Ye","doi":"10.1109/JMMCT.2025.3569766","DOIUrl":"https://doi.org/10.1109/JMMCT.2025.3569766","url":null,"abstract":"The optimization of radar cross section (RCS) is now a significant issue in the designation of military and civilian equipment. Comparing with the expensive material approaches, changing the geometry of an object is a relatively flexible and low-cost way. However, the RCS optimization of large-scale models often faces two major problems: too large optimization space and slow RCS calculation, which caused by increasing geometry parameters and iterative numerical computation, respectively. In addition, secondary problems such as geometric information loss and RCS results lacking of gaurantees always remain even if dimensionality reduction has been carried out for alleviating these two problems. In this paper, we propose a novel end-to-end differentiable RCS optimization framework based on the physical optics (PO) method. The proposed framework utilize the differentiability of the PO method, and realize an efficient and interpretable RCS optimization without dimension reduction. The innovation of this paper lies in the combination of PO method and gradient-based optimization to achieve RCS optimization of large-scale complex 3D geometries. Experiments show that in ordinary 2D scenarios, our method achieves at least 16 times higher efficiency than the mainstream optimization method. Meanwhile, the optimization error of RCS has been reduced by 75.29<inline-formula><tex-math>$%$</tex-math></inline-formula> compared to traditional methods (0.0515vs. 0.2084). We further validate the performance of the framework on more complex tasks such as 3D plane model and analyzed the effectiveness of the overall framework. The proposed optimization method is expected to be widely used in applications such as stealth and aircraft designs.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":"10 ","pages":"246-258"},"PeriodicalIF":1.8,"publicationDate":"2025-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144196910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-11DOI: 10.1109/JMMCT.2025.3550117
Runwei Zhou;Dan Jiao
Solid-state spin qubits are one of the candidate platforms for future quantum computers due to their long coherence time and good controllability. However, qubits are susceptible to noise generated from external magnetic fields. In this paper, we present a fast and accurate volume integral equation solver for analyzing local/nonlocal optical responses in quantum nano-electromagnetic gate circuitry. Due to small electric sizes of quantum circuitry, conventional volume integral equation (VIE) solvers suffer from both numerical difficulties and deteriorated accuracy since the underlying numerical system is highly ill-conditioned. To overcome this problem, we introduce a well-conditioned VIE formulation. We further accelerate the VIE solution by transforming the six-dimensional integral arising from the nonlocal constitutive relation to the spectral domain using fast Fourier transform (FFT). The same FFT is also applied to efficiently compute the convolution of Green's function with equivalent volumetric currents. The resultant fast and robust VIE solver has been applied to analyze large-scale 3-D quantum gate devices. Both local and nonlocal optical responses of the devices are captured accurately and efficiently. This work offers a fast and accurate approach to guide the noise control of high-fidelity quantum gate circuitry design.
{"title":"Fast Well-Conditioned Volume Integral Equation Solver for Analyzing Nonlocal Optical Responses in Quantum Nanostructures","authors":"Runwei Zhou;Dan Jiao","doi":"10.1109/JMMCT.2025.3550117","DOIUrl":"https://doi.org/10.1109/JMMCT.2025.3550117","url":null,"abstract":"Solid-state spin qubits are one of the candidate platforms for future quantum computers due to their long coherence time and good controllability. However, qubits are susceptible to noise generated from external magnetic fields. In this paper, we present a fast and accurate volume integral equation solver for analyzing local/nonlocal optical responses in quantum nano-electromagnetic gate circuitry. Due to small electric sizes of quantum circuitry, conventional volume integral equation (VIE) solvers suffer from both numerical difficulties and deteriorated accuracy since the underlying numerical system is highly ill-conditioned. To overcome this problem, we introduce a well-conditioned VIE formulation. We further accelerate the VIE solution by transforming the six-dimensional integral arising from the nonlocal constitutive relation to the spectral domain using fast Fourier transform (FFT). The same FFT is also applied to efficiently compute the convolution of Green's function with equivalent volumetric currents. The resultant fast and robust VIE solver has been applied to analyze large-scale 3-D quantum gate devices. Both local and nonlocal optical responses of the devices are captured accurately and efficiently. This work offers a fast and accurate approach to guide the noise control of high-fidelity quantum gate circuitry design.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":"10 ","pages":"209-217"},"PeriodicalIF":1.8,"publicationDate":"2025-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143761369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-07DOI: 10.1109/JMMCT.2025.3563480
Boyuan Zhang;Weng Cho Chew
The discrete exterior calculus (DEC) $mathbf {A}$-$Phi$ solver is a broadband stable solver in computational electromagnetics which can work from DC to optics. In order to solve practical problems, which are often multi-scale ones with large number of unknowns and condition number, a broadband preconditioner to the DEC $mathbf {A}$-$Phi$ solver is proposed in this paper. The proposed preconditioner is based on sparsified nested dissection ordering (spa-NDO) technique. In this paper, introductions to the DEC $mathbf {A}$-$Phi$ solver and NDO technique are provided, as well as detailed implementation flow of the proposed modified spa-NDO preconditioner. Through numerical examples, it reveals that the proposed preconditioned solver has $O(N log N)$ computational complexity. The efficiency of the proposed preconditioner is almost independent of parameters such as frequency and conductivity in the problem, which indicates its broadband nature.
{"title":"A Broadband Preconditioner Based on Sparsified Nested Dissection Ordering Technique for the Vector-Scalar Potential Discrete Exterior Calculus Solver","authors":"Boyuan Zhang;Weng Cho Chew","doi":"10.1109/JMMCT.2025.3563480","DOIUrl":"https://doi.org/10.1109/JMMCT.2025.3563480","url":null,"abstract":"The discrete exterior calculus (DEC) <inline-formula><tex-math>$mathbf {A}$</tex-math></inline-formula>-<inline-formula><tex-math>$Phi$</tex-math></inline-formula> solver is a broadband stable solver in computational electromagnetics which can work from DC to optics. In order to solve practical problems, which are often multi-scale ones with large number of unknowns and condition number, a broadband preconditioner to the DEC <inline-formula><tex-math>$mathbf {A}$</tex-math></inline-formula>-<inline-formula><tex-math>$Phi$</tex-math></inline-formula> solver is proposed in this paper. The proposed preconditioner is based on sparsified nested dissection ordering (spa-NDO) technique. In this paper, introductions to the DEC <inline-formula><tex-math>$mathbf {A}$</tex-math></inline-formula>-<inline-formula><tex-math>$Phi$</tex-math></inline-formula> solver and NDO technique are provided, as well as detailed implementation flow of the proposed modified spa-NDO preconditioner. Through numerical examples, it reveals that the proposed preconditioned solver has <inline-formula><tex-math>$O(N log N)$</tex-math></inline-formula> computational complexity. The efficiency of the proposed preconditioner is almost independent of parameters such as frequency and conductivity in the problem, which indicates its broadband nature.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":"10 ","pages":"235-245"},"PeriodicalIF":1.5,"publicationDate":"2025-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145051026","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-05DOI: 10.1109/JMMCT.2025.3567252
Takaya Sugiura
Loss visualization and analysis of 4H-silicon carbide (4H-SiC) power diodes were performed using the free energy loss analysis (FELA) method that was originally developed for photovoltaic cells. The FELA approach features several advantages, including the direct expression of loss in W/cm$^{2}$, representation of each electron- and hole-induced loss, and internal loss visualization by calculating the free energy at each point. Four 4H-SiC power diodes, including two PiN diodes, a Schottky barrier diode (SBD), and a junction-barrier Schottky diode (JBSD), were evaluated. The PiN diodes exhibited significant Joule losses owing to the inherently high recombination heating associated with these bipolar devices. In contrast, the SBD e$^-$-induced Joule loss, whereas h$^+$-induced Joule and recombination losses were negligible for this unipolar device. The JBSD exhibited a high allowable current density with low self-heating and was determined to be the best power diode. The FELA visualization of the e$^-$-induced Joule loss of this device revealed that the SBD interface, particularly the p$^+$-region, is the dominant source of Joule loss. Applying FELA to reversed characteristics revealed several insightful device phenomena and which physics were responsible for the loss in different situations.
{"title":"Internal Loss Analysis and Visualization of 4H-Silicon Carbide Power Diodes: Free Energy Loss Analysis Under the Static Condition","authors":"Takaya Sugiura","doi":"10.1109/JMMCT.2025.3567252","DOIUrl":"https://doi.org/10.1109/JMMCT.2025.3567252","url":null,"abstract":"Loss visualization and analysis of 4H-silicon carbide (4H-SiC) power diodes were performed using the free energy loss analysis (FELA) method that was originally developed for photovoltaic cells. The FELA approach features several advantages, including the direct expression of loss in W/cm<inline-formula><tex-math>$^{2}$</tex-math></inline-formula>, representation of each electron- and hole-induced loss, and internal loss visualization by calculating the free energy at each point. Four 4H-SiC power diodes, including two PiN diodes, a Schottky barrier diode (SBD), and a junction-barrier Schottky diode (JBSD), were evaluated. The PiN diodes exhibited significant Joule losses owing to the inherently high recombination heating associated with these bipolar devices. In contrast, the SBD e<inline-formula><tex-math>$^-$</tex-math></inline-formula>-induced Joule loss, whereas h<inline-formula><tex-math>$^+$</tex-math></inline-formula>-induced Joule and recombination losses were negligible for this unipolar device. The JBSD exhibited <bold>a high allowable current density with</b> low self-heating and was determined to be the best power diode. The FELA visualization of the e<inline-formula><tex-math>$^-$</tex-math></inline-formula>-induced Joule loss of this device revealed that the SBD interface, particularly the p<inline-formula><tex-math>$^+$</tex-math></inline-formula>-region, is the dominant source of Joule loss. Applying FELA to reversed characteristics revealed several insightful device phenomena and which physics were responsible for the loss in different situations.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":"10 ","pages":"227-234"},"PeriodicalIF":1.8,"publicationDate":"2025-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143949153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The paper proposes a new approach to the fast solution of matrix equations resulting from boundary element discretization of integral equations. By hybridizing fast iterative $mathcal {H}$-matrix solvers with a fast direct $mathcal {H}$-matrix preconditioner factorization, we create a framework that can be tuned between the extremes of a direct solver and a unpreconditioned iterative solver. This tuning is largely achieved using a single numerical parameter representing the preconditioner tolerance. A more complicated scheme involving two different tolerances is also briefly considered. The proposed framework is demonstrated on a high-order accurate Locally Corrected Nyström solution of surface integral equations for PEC targets. Examples consider various scattering problems including those featuring strong physical resonances. We show that appropriately choosing the preconditioner tolerance achieves the prescribed solution accuracy with minimal CPU time. Expanding from one to two tolerance parameters further enhances the framework by providing the flexibility to dynamically adjust tolerance, enabling higher compression while maintaining accuracy and fast convergence. This adaptive strategy offers significant potential for optimizing the balance between memory usage and CPU time in the future.
{"title":"Optimal Preconditioners for Hybrid Direct-Iterative $mathcal {H}$-Matrix Solvers in Boundary Element Methods","authors":"Omid Babazadeh;Emrah Sever;Jin Hu;Ian Jeffrey;Constantine Sideris;Vladimir Okhmatovski","doi":"10.1109/JMMCT.2025.3547827","DOIUrl":"https://doi.org/10.1109/JMMCT.2025.3547827","url":null,"abstract":"The paper proposes a new approach to the fast solution of matrix equations resulting from boundary element discretization of integral equations. By hybridizing fast iterative <inline-formula><tex-math>$mathcal {H}$</tex-math></inline-formula>-matrix solvers with a fast direct <inline-formula><tex-math>$mathcal {H}$</tex-math></inline-formula>-matrix preconditioner factorization, we create a framework that can be tuned between the extremes of a direct solver and a unpreconditioned iterative solver. This tuning is largely achieved using a single numerical parameter representing the preconditioner tolerance. A more complicated scheme involving two different tolerances is also briefly considered. The proposed framework is demonstrated on a high-order accurate Locally Corrected Nyström solution of surface integral equations for PEC targets. Examples consider various scattering problems including those featuring strong physical resonances. We show that appropriately choosing the preconditioner tolerance achieves the prescribed solution accuracy with minimal CPU time. Expanding from one to two tolerance parameters further enhances the framework by providing the flexibility to dynamically adjust tolerance, enabling higher compression while maintaining accuracy and fast convergence. This adaptive strategy offers significant potential for optimizing the balance between memory usage and CPU time in the future.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":"10 ","pages":"187-197"},"PeriodicalIF":1.8,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143698349","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-03-04DOI: 10.1109/JMMCT.2025.3547852
Nils Kielian;Marcus Stiemer
A robust data-transfer process for balanced domain decomposition is presented. This algorithm reduces the number of mesh elements required to solve certain 3D multiscale problems with the finite element method. In some examples, a reduction factor of up to 5 has been observed. The reduction is achieved by introducing an overlapping auxiliary domain to an originally non-overlapping domain decomposition scheme, allowing for individual meshing of the subdomains. The data transfer to couple the individually meshed subdomains is performed with the help of barycentric interpolation. Hence, the advantages of parallel solution of subdomain problems is combined with a stable inter-subdomain data transfer. The developed algorithm can be applied on problems with a scalar valued second order spatial elliptic differential operator in various fields of engineering, such as semiconductors, huge and complex biological cell clusters, heat conducting and pressure problems on multiple scales.
{"title":"Fast Domain Decomposition Algorithm Using Barycentric Interpolation and Overlapping Subdomains for 3D Multiscale Problems","authors":"Nils Kielian;Marcus Stiemer","doi":"10.1109/JMMCT.2025.3547852","DOIUrl":"https://doi.org/10.1109/JMMCT.2025.3547852","url":null,"abstract":"A robust data-transfer process for balanced domain decomposition is presented. This algorithm reduces the number of mesh elements required to solve certain 3D multiscale problems with the finite element method. In some examples, a reduction factor of up to 5 has been observed. The reduction is achieved by introducing an overlapping auxiliary domain to an originally non-overlapping domain decomposition scheme, allowing for individual meshing of the subdomains. The data transfer to couple the individually meshed subdomains is performed with the help of barycentric interpolation. Hence, the advantages of parallel solution of subdomain problems is combined with a stable inter-subdomain data transfer. The developed algorithm can be applied on problems with a scalar valued second order spatial elliptic differential operator in various fields of engineering, such as semiconductors, huge and complex biological cell clusters, heat conducting and pressure problems on multiple scales.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":"10 ","pages":"198-208"},"PeriodicalIF":1.8,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=10909529","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143698294","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-20DOI: 10.1109/JMMCT.2025.3544143
Yifan Wang;Dan Jiao
In this paper, we develop a new one-stage $ O(N log N)$ algorithm to generate a rank-minimized $mathcal {H}^{2}$-representation of electrically large volume integral equations (VIEs), which significantly reduces the CPU run time of state-of-the-art algorithms for completing the same task. Unlike existing two-stage algorithms, this new algorithm requires only one stage to build nested cluster bases. The cluster basis is obtained directly from the interaction between a cluster and its admissible clusters composed of real or auxiliary ones that cover all interaction directions. Furthermore, the row and column pivots of the resultant low-rank representation are chosen from the source and observer points in an analytical way without the need for numerically finding them. This further speeds up the computation. Numerical experiments on a suite of electrically large 3D scattering problems have demonstrated the efficiency and accuracy of the proposed new algorithm.
{"title":"One-Stage $ O(N log N)$ Algorithm for Generating Nested Rank-Minimized Representation of Electrically Large Volume Integral Equations","authors":"Yifan Wang;Dan Jiao","doi":"10.1109/JMMCT.2025.3544143","DOIUrl":"https://doi.org/10.1109/JMMCT.2025.3544143","url":null,"abstract":"In this paper, we develop a new one-stage <inline-formula><tex-math>$ O(N log N)$</tex-math></inline-formula> algorithm to generate a rank-minimized <inline-formula><tex-math>$mathcal {H}^{2}$</tex-math></inline-formula>-representation of electrically large volume integral equations (VIEs), which significantly reduces the CPU run time of state-of-the-art algorithms for completing the same task. Unlike existing two-stage algorithms, this new algorithm requires only one stage to build nested cluster bases. The cluster basis is obtained directly from the interaction between a cluster and its admissible clusters composed of real or auxiliary ones that cover all interaction directions. Furthermore, the row and column pivots of the resultant low-rank representation are chosen from the source and observer points in an analytical way without the need for numerically finding them. This further speeds up the computation. Numerical experiments on a suite of electrically large 3D scattering problems have demonstrated the efficiency and accuracy of the proposed new algorithm.","PeriodicalId":52176,"journal":{"name":"IEEE Journal on Multiscale and Multiphysics Computational Techniques","volume":"10 ","pages":"169-178"},"PeriodicalIF":1.8,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-02-20DOI: 10.1109/JMMCT.2025.3544270
Praveen Singh;Soumyashree S. Panda;Jogesh C. Dash;Bright Riscob;Surya K. Pathak;Ravi S. Hegde
Antenna synthesis is becoming increasingly challenging with tight requirements for C-SWAP (cost, size, weight and power) reduction while maintaining stringent electromagnetic performance specifications. While machine learning approaches are increasingly being explored for antenna synthesis, they are still not capable of handling large shape sets with diverse responses. We propose a branched deep convolutional neural network architecture that can serve as a drop-in replacement for a full-wave simulator (it can predict the full spectral response of reflection co-efficient, input impedance and radiation pattern). We show the utility of such models in surrogate-assisted evolutionary optimization for antenna synthesis with arbitrary specification of targeted response. Specifically, we consider the large shape set defined by the set of 16-vertexes polygonal patch antennas and consider antenna synthesis by specifying independent constraints on return loss, radiation pattern and gain. In contrast to online surrogates, our approach is an offline surrogate that is objective-agnostic; trained once, it can be used over multiple optimizations whereby the model training costs become amortized across multiple synthesis requests. Our approach outperforms evolutionary optimizations relying on full-wave solver-based fitness estimation. Specifically, we report the design, fabrication and experimental characterization of three polygon-shaped patch antennas, each fulfilling different objectives (narrow band, dual-band & wide-band). The reported methodology enables rapid synthesis (in seconds), produces verifiable sound designs and is promising for furthering data-driven design methodologies for electromagnetic wave device synthesis.
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