Kirill Serkh's Home Page

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Selected Papers:

• Zewen Shen and Kirill Serkh. Rapid Evaluation of Newtonian Potentials on Planar Domains. SIAM J. Sci. Comput. 46.1 (2024): A609–A628. Data
• Seungbae Bang, Kirill Serkh, Oded Stein, and Alec Jacobson. An adaptive fast-multipole-accelerated hybrid boundary integral equation method for accurate diffusion curves. SIGGRAPH Asia 2023. Confer. arXiv
• Kirill Serkh and James Bremer. Phase function methods for second order inhomogeneous linear ordinary differential equations. J. Sci. Comput. 98.1 (2024): 14.
• Dawei Wang, Kirill Serkh, and Christina Christara. A high-order deferred correction method for the solution of free boundary problems using penalty iteration, with an application to American option pricing. J. Comput. Appl. Math. 432 (2023): 115272.
• James Garritano, Yuval Kluger, Vladimir Rokhlin, and Kirill Serkh. On the efficient evaluation of the azimuthal Fourier components of the Green's function for Helmholtz's equation in cylindrical coordinates. J. Comput. Phys. 471 (2022): 111585. Code
• Zewen Shen and Kirill Serkh. On the evaluation of the eigendecomposition of the Airy integral operator. App. Comput. Harmon. Anal. 57 (2022): 105–150.
• Manas Rachh and Kirill Serkh. On the Solution of the Stokes Equation on Regions with Corners. Commun. Pur. Appl. Math. 73.11 (2020): 2295–2369.
• Kirill Serkh. On the Solution of Elliptic Partial Differential Equations on Regions with Corners II: Detailed Analysis. App. Comput. Harmon. Anal. 46.2 (2019): 250–287.
• Kirill Serkh and Vladimir Rokhlin. On the Solution of the Helmholtz Equation on Regions with Corners. PNAS 113.33 (2016): 9171–9176.
• Kirill Serkh and Vladimir Rokhlin. On the Solution of Elliptic Partial Differential Equations on Regions with Corners. J. Comput. Phys. 305 (2016): 150–171.

Selected Preprints:

• Andreas A. Buchheit, Torsten Keßler, and Kirill Serkh. On the computation of lattice sums without translational invariance. arXiv Preprint (2024). Code
• Dawei Wang, Christina Christara, and Kirill Serkh. Analysis of high-order time-stepping schemes for nonsmooth initial conditions in financial pricing. University of Toronto NA Technical Report (2023).
• Mohan Zhao and Kirill Serkh. On the Approximation of Singular Functions by Series of Non-integer Powers. 2nd ver. University of Toronto NA Technical Report (2023). arXiv Data
• Mohan Zhao and Kirill Serkh. A Continuation Method for Fitting a Bandlimited Curve to Points in the Plane. University of Toronto NA Technical Report (2023). arXiv Code
• Zewen Shen and Kirill Serkh. On polynomial interpolation in the monomial basis 4th ver. University of Toronto NA Technical Report (2023). arXiv Demo
• Kirill Serkh and James Bremer. Phase function methods for second order inhomogeneous linear ordinary differential equations. arXiv Preprint (2022).
• Shukui Chen, Kirill Serkh, and James Bremer. On the adaptive Levin method. 3rd ver. arXiv Preprint (2024).
• Zewen Shen and Kirill Serkh. Rapid evaluation of Newtonian potentials on planar domains. 4th ver. University of Toronto NA Technical Report (2023). arXiv Data
• Zewen Shen and Kirill Serkh. Accelerating potential evaluation over unstructured meshes in two dimensions. University of Toronto NA Technical Report (2022). arXiv
• Dawei Wang, Kirill Serkh, and Christina Christara. A high-order deferred correction method for the solution of free boundary problems using penalty iteration, with an application to American option pricing. University of Toronto NA Technical Report (2022). arXiv
• Zewen Shen and Kirill Serkh. On the Evaluation of the Eigendecomposition of the Airy Integral Operator. 4th ver. University of Toronto NA Technical Report (2021). arXiv
• James Garritano, Yuval Kluger, Vladimir Rokhlin, and Kirill Serkh. On the Efficient Evaluation of the Azimuthal Fourier Components of the Green's Function for Helmholtz's Equation in Cylindrical Coordinates. University of Toronto NA Technical Report (2021). arXiv
• Kirill Serkh and Vladimir Rokhlin. A Provably Componentwise Backward Stable O(n²) QR Algorithm for the Diagonalization of Colleague Matrices. University of Toronto NA Technical Report (2021). arXiv
• Kirill Serkh. A Note on the Use of the Spectra of Multiplication Operators as a Numerical Tool. Yale Technical Report YALEU/DCS/TR-1541 (2018).
• Kirill Serkh. On the Solution of Elliptic Partial Differential Equations on Regions with Corners III: Curved Boundaries. New York University Technical Report NYU/CIMS/TR2018-989 (2018).
• Manas Rachh and Kirill Serkh. On the Solution of the Stokes Equation on Regions with Corners. Yale Technical Report YALEU/DCS/TR-1536 (2017).
• Kirill Serkh. On Generalized Prolate Spheroidal Functions. Yale Technical Report YALEU/DCS/TR-1519 (2015).