Nonuniform Integrated Photonics Waveguide Bragg Gratings Numerical Modeling

Authors: Andrade-Fonseca, Leandro, Hernandez-Figueroa, Hugo E.

Source: 2026 40th Symposium on Microelectronics Technology and Devices (SBMicro) Microelectronics Technology and Devices (SBMicro), 2026 40th Symposium on. :1-4 Aug, 2026

Relation: 2026 40th Symposium on Microelectronics Technology and Devices (SBMicro)

A stochastic Galerkin method for optimal Dirichlet boundary control problems with uncertain data.

Authors: Winkler, Max¹ (AUTHOR) max.winkler@mathematik.tu-chemnitz.de, Yücel, Hamdullah² (AUTHOR) yucelh@metu.edu.tr

Source: Computational Optimization & Applications. Oct2026, p1-35. 35p.

Subject Terms: *Optimal control theory, *Stochastic analysis, Galerkin methods, Approximation error, Numerical analysis, Elliptic differential equations

Well-posedness and error analysis for semilinear stochastic fractional diffusion-wave equations with multiplicative noise.

Authors: Yang, Jinping¹ (AUTHOR) yjpll0627@163.com, Li, Zhiqiang¹ (AUTHOR) lizhiqiang0914@126.com, Yan, Yubin^1,2 (AUTHOR) y.yan@chester.ac.uk

Source: Computers & Mathematics with Applications. Oct2026, Vol. 220, p266-292. 27p.

Subject Terms: *Caputo fractional derivatives, *Galerkin methods, *Stochastic partial differential equations, *Error analysis in mathematics, *Numerical integration, *Fractional differential equations

Robust globally divergence-free weak Galerkin methods for the steady Boussinesq system with damping.

Authors: Wang, Xiaojuan¹ (AUTHOR) xiaojuanwang@sxau.edu.cn, Xie, Xiaoping² (AUTHOR) xpxie@scu.edu.cn, Zhang, Shiquan^1,2 (AUTHOR) shiquanzhang@scu.edu.cn

Source: Computers & Mathematics with Applications. Oct2026, Vol. 220, p237-265. 29p.

Subject Terms: *Boussinesq equations, *Galerkin methods, *Polynomial approximation, *Damping (Mechanics), *Iterative methods (Mathematics), *Error analysis in mathematics

Dynamic Characteristics of Conveying Fluid Pipe Under Thermal Load and Axial Force by Galerkin-Eigenvalue Method.

Authors: Xie, Liang¹ (AUTHOR), Jiang, Zequn¹ (AUTHOR), He, Zhenzhao¹ (AUTHOR), Yu, Hui¹ (AUTHOR), Qu, Wei¹ (AUTHOR) 563493574@qq.com

Source: International Journal of Structural Stability & Dynamics. 10/15/2026, Vol. 26 Issue 22, p1-23. 23p.

Subject Terms: *Galerkin methods, *Eigenvalues, *Compressive force, *Eigenfrequencies, *Pipeline transportation, *Fluid-structure interaction, *Mechanical vibration research, *Thermal stresses

A local discontinuous Galerkin method for Dirichlet boundary control problems.

Authors: Benner, Peter¹ (AUTHOR) benner@mpi-magdeburg.mpg.de, Hinze, Michael² (AUTHOR) hinze@uni-koblenz.de, Yücel, Hamdullah³ (AUTHOR) yucelh@metu.edu.tr

Source: Journal of Numerical Mathematics. Oct2026, p1. 22p. 5 Illustrations.

Subject Terms: *Galerkin methods, *Piecewise linear approximation, *Variational approach (Mathematics), *Advection-diffusion equations, *Computer simulation

Provably positivity-preserving, globally divergence-free central DG methods for ideal MHD system.

Authors: Yan, Ruifang^1,2,3 (AUTHOR) yanrf@hust.edu.cn, Cao, Huihui^4,5 (AUTHOR) caohh@sustech.edu.cn, Wu, Kailiang³ (AUTHOR) wukl@sustech.edu.cn

Source: Mathematical Models & Methods in Applied Sciences. Oct2026, p1-40. 40p.

Subject Terms: *Magnetohydrodynamics, *Galerkin methods, *Quasilinearization, *Magnetic flux

An enhanced hybrid fractional order modified Taylor wavelets Galerkin approach for the numerical simulation of fractal-fractional integro-differential equations.

Authors: Anand, Monika¹ (AUTHOR) monikaanand895@gmail.com, Srivastava, Vineet Kishore² (AUTHOR)

Source: International Journal of Computer Mathematics. Oct2026, Vol. 103 Issue 10, p2125-2164. 40p.

Subject Terms: *Galerkin methods, *Wavelets (Mathematics), *Fractional calculus, *Computer simulation, *Mathematical optimization, *Integro-differential equations, *Algebraic equations

Optimal order error estimates of a mixed discontinuous Galerkin method with BDF-2 scheme for transient Darcy flow.

Authors: Shah, Sheheryar¹ (AUTHOR) shayree007@yahoo.com, He, Limin² (AUTHOR), Cai, Wentao³ (AUTHOR), Khattak, Shahzad⁴ (AUTHOR)

Source: Waves in Random & Complex Media. Oct2026, Vol. 36 Issue 5, p7872-7892. 21p.

Subject Terms: *Time integration scheme, *Galerkin methods, *Computer simulation, *Groundwater flow, *Flow velocity, *Stability (Mechanics)

Finite element Galerkin methods for plate vibration problems: error analysis and efficient implementation.

Authors: Khebchareon, Morrakot^1,2,3 (AUTHOR) morrakot.k@cmu.ac.th, Pani, Amiya K.⁴ (AUTHOR) amiyap@goa.bits-pilani.ac.in, Fairweather, Graeme⁵ (AUTHOR) graeme.fairweather@gmail.com

Source: Numerical Algorithms. Oct2026, Vol. 103 Issue 2, p1263-1294. 32p.

Subject Terms: *Galerkin methods, *Crank-Nicolson method, *Flexural vibrations (Mechanics), *Error analysis in mathematics, *Partial differential equations, *Boundary value problems

A computational space-time spectral method for solving high–dimensional fractional Fokker–Planck Equations.

Authors: Khasi, Manoochehr¹ (AUTHOR) mkhasi81math@gmail.com, Rashidinia, Jalil¹ (AUTHOR) rashidinia@iust.ac.ir

Source: Numerical Algorithms. Oct2026, Vol. 103 Issue 2, p807-848. 42p.

Subject Terms: *Galerkin methods, *Fokker-Planck equation, *Spectral element method, *High-dimensional model representation, *Jacobi polynomials, *Eigenanalysis

Asymptotic estimate of solutions to a fourth-order parabolic equation with double logarithm terms¹.

Authors: Li, Ruixi¹ (AUTHOR) ruixili0321@163.com, Feng, Tingfu² (AUTHOR) fengtingfu@kmu.edu.cn, Zhai, Xia¹ (AUTHOR) zhaixia924@163.com

Source: QM - Quaestiones Mathematicae. Oct2026, Vol. 49 Issue 10, p1471-1498. 28p.

Subject Terms: *Partial differential equations, *Galerkin methods, *Nonlinear theories, *Asymptotic analysis

Superconvergence analysis of an energy-preserving Galerkin method for a class of nonlinear wave equation.

Authors: Liao, Xin¹ (AUTHOR), Wang, Lele¹ (AUTHOR) wanglele@zua.edu.cn, Yang, Huaijun¹ (AUTHOR)

Source: Computers & Mathematics with Applications. Oct2026, Vol. 219, p150-162. 13p.

Subject Terms: *Galerkin methods, *Nonlinear wave equations, *Energy conservation, *Time integration scheme, *Numerical analysis, *Approximation error, *Finite element method

The discontinuous Galerkin method for solving the two-dimensional transport equation with distributed-order memory kernel on triangular meshes.

Authors: Wei, Leilei^1,2 (AUTHOR) leileiwei@haut.edu.cn, Chen, Yanping^1,3 (AUTHOR) ypchen@njupt.edu.cn, Qin, Fangfang³ (AUTHOR) ffqin@njupt.edu.cn, Huang, Jian⁴ (AUTHOR) huangjian213@xtu.edu.cn, Li, Peng⁵ (AUTHOR) lipeng@haut.edu.cn

Source: Applied Numerical Mathematics. Oct2026, Vol. 228, p57-70. 14p.

Subject Terms: *Galerkin methods, *Transport equation, *Numerical analysis, *Transport theory, *Numerical calculations

A mixed [formula omitted] Galerkin method using mixed partial derivative intermediate function for fourth order Rosenau equation.

Authors: Doss, L. Jones Tarcius¹ (AUTHOR) jones@annauniv.edu, L․, Aishwarya¹ (AUTHOR)

Source: Applied Numerical Mathematics. Oct2026, Vol. 228, p117-131. 15p.

Subject Terms: *Galerkin methods, *Partial differential equations, *Nonlinear evolution equations, *Discretization methods, *Approximation error, *Numerical calculations, *Partial differential operators

Sequential symmetric interior penalty discontinuous Galerkin method for fully coupled quasi-static thermo-poroelasticity problems.

Authors: Chen, Fan¹ (AUTHOR) ChenFan2021@emails.bjut.edu.cn, Cui, Ming² (AUTHOR) mingcui@bjut.edu.cn, Zhou, Chenguang^1,2 (AUTHOR) zhoucg@bjut.edu.cn

Source: Computers & Mathematics with Applications. Sep2026, Vol. 218, p67-88. 22p.

Subject Terms: *Galerkin methods, *Euler method, *Thermoelasticity, *Convective flow, *Numerical analysis, *Stability theory

Exponential Runge-Kutta Galerkin finite element method for a reaction-diffusion system with nonsmooth initial data.

Authors: Zhang, Runjie¹ (AUTHOR) 2112314030@mail2.gdut.edu.cn, Yang, Shuo¹ (AUTHOR) 2112414027@mail2.gdut.edu.cn, Fang, Jinwei¹ (AUTHOR) fangjinwei@gdut.edu.cn

Source: Computers & Mathematics with Applications. Sep2026, Vol. 218, p30-46. 17p.

Subject Terms: *Galerkin methods, *Reaction-diffusion equations, *Numerical analysis, *Function spaces, *Runge-Kutta formulas, *Error analysis in mathematics

Optimized staggered multistep discontinuous Galerkin method for wavefield simulation.

Authors: Zhu, Si-biao¹ (AUTHOR), Huang, Jian-dong^2,3 (AUTHOR) huangjd_zljs@sina.com, Fang, Zhi-long⁴ (AUTHOR), He, Xi-jun⁵ (AUTHOR), Wen, Jin¹ (AUTHOR), Wang, Yong-fei¹ (AUTHOR), Xu, Xiao-bing¹ (AUTHOR)

Source: Applied Geophysics: Bulletin of Chinese Geophysical Society. Sep2026, p1-13. 13p.

Subject Terms: *Galerkin methods, *Wave equation, *Numerical grid generation (Numerical analysis), *Numerical analysis, *Theory of wave motion, *Time integration scheme, *Optimization algorithms

Error estimate of the operator splitting L2-NIPG method for two-dimensional time-fractional diffusion equations.

Authors: Maji, Sandip^1,2 (AUTHOR) smaji@shu.edu.cn, Natesan, Srinivasan¹ (AUTHOR) natesan@iitg.ac.in

Source: Numerical Algorithms. Sep2026, Vol. 103 Issue 1, p389-407. 19p.

Subject Terms: *Galerkin methods, *Caputo fractional derivatives, *Approximation error, *Partial differential equations, *Stability (Mechanics), *Fick's laws of diffusion, *Iterative methods (Mathematics)

Error estimate of the spectral Galerkin method for the steady convection diffusion problem with variable coefficients based on the least-squares method.

Authors: Qin, Yonghui^1,2,3 (AUTHOR) yonghui1676@163.com, Huang, Jiaoxia¹ (AUTHOR)

Source: Computers & Mathematics with Applications. Sep2026, Vol. 217, p315-330. 16p.

Subject Terms: *Galerkin methods, *Least squares, *Numerical analysis, *Approximation error, *Spectral element method, *Iterative methods (Mathematics), *Transport equation