Tsogtgerel Gantumur

Mathematician. Analysis, computation, geometry, and mathematical physics.

Publications

arXiv Google Scholar

Preprints

  1. Projection geometry and relaxed quasi-orthogonality for inf-sup stable Galerkin methods arXiv:2609.16265 (2026).
  2. Exact ReLU realization of binary affine refinement iterates via reflection folding and cone switching with Boldsaikhan Bolorkhuu. arXiv:2609.11962 (2026).
  3. Exact ReLU realization of affine one-dimensional refinement iterates via residual memory and offset frames with Boldsaikhan Bolorkhuu. arXiv:2607.20586 (2026).
  4. Conditional Euclidean-Hamiltonian reductions for sign-problem toy models arXiv:2607.15950 (2026).
  5. Exact ReLU realization of tensor-product refinement iterates arXiv:2605.03917 (2026).
  6. Exact Loop Controllers for ReLU Realization of Homogeneous Curve Refinements with Boldsaikhan Bolorkhuu. arXiv:2605.01655 (2026).
  7. Possible Reforms of the Tibetan Lunisolar Calendar arXiv:2604.01233 (2026).
  8. An expository review of the Chebyshev-Sylvester method in prime number theory arXiv:2512.02466 (2025).
  9. A direct proof of the equivalence between Dirichlet's principle and Perron's method arXiv:2511.18762 (2025).
  10. A scaling approach to elliptic theory for geometrically-natural differential operators with Sobolev-type coefficients with Michael Holst and David Maxwell. arXiv:2306.15842 (2023).
  11. A prescribed scalar and boundary mean curvature problem on compact manifolds with boundary with Vladmir Sicca Gonçalves. arXiv:2102.11236 (2021).
  12. Local convergence of adaptive methods for nonlinear partial differential equations with Michael Holst and Yunrong Zhu. arXiv:1001.1382 (2010).

Published and accepted

  1. TCubes: Non-privacy invasive dataset for activities of daily living as thermal cubes with Luubaatar Badarch, Dorj Byambaa, Hansaem Park, Fady Alnajjar, and Munkhjargal Gochoo. Expert Systems with Applications, 333, 133943 (2027). journal · DOI
  2. Projectional continuous data assimilation on the torus: Resonant and kernel-free regimes 2026. Journal of Mathematical Fluid Mechanics, Accepted for publication. arXiv
  3. Rotationally invariant dynamical lattice regulators for Euclidean quantum field theories J. High Energ. Phys. 2026, 36 (2026). arXiv · journal · DOI
  4. Regularity of solutions of the Navier-Stokes-alpha-beta equations with wall-eddy boundary conditions with Nella Rotundo. 2025. Zeitschrift für angewandte Mathematik und Physik, Accepted for publication in Zeitschrift für angewandte Mathematik und Physik. arXiv
  5. Relaxation Time Limits of Subsonic Steady States for Multidimensional Hydrodynamic Model of Semiconductors with Yue-Hong Feng, Haifeng Hu, Ming Mei, and Guojing Zhang. SIAM Journal on Mathematical Analysis, 56(5), 6933-6962 (2024). journal · DOI
  6. Convergence Theory of Adaptive Mixed Finite Element Methods for the Stokes Problem Journal of Mathematical Sciences, 279, 794-813 (2024). arXiv · journal · DOI
  7. Polyharmonic splines interpolation on scattered data in 2D and 3D with applications with Kalani Rubasinghe, Guangming Yao, and Jing Niu. Engineering Analysis with Boundary Elements, 156, 240-250 (2023). journal · DOI · corrigendum
  8. A prescribed scalar and boundary mean curvature problem and the Yamabe classification on asymptotically Euclidean manifolds with inner boundary with Vladmir Sicca Gonçalves. J. Geom. Anal. 33, 342 (2023). arXiv · journal · DOI · correction
  9. Solving Nonlinear Elliptic PDEs in 2D and 3D Using Polyharmonic Splines and Low-Degree of Polynomials with Kalani Rubasinghe, Guangming Yao, and Wen Li. International Journal of Computational Methods, 20(8), 2250051 (2023). journal · DOI
  10. Uniqueness of Weak Solutions to Second Boundary Value Problems for Generated Prescribed Jacobian Equations with Gerard Awanou. Electronic Journal of Differential Equations, Accepted for publication in Electronic Journal of Differential Equations, Special Issue 03 (2026). arXiv
  11. Convergence of discrete exterior calculus approximations for Poisson problems with Erick Schulz. Discrete & Computational Geometry, 63(2):346-376 (2020). arXiv · DOI
  12. A posteriori analysis of a B-spline based finite-element method for the stationary quasi-geostrophic equations of the ocean with Ibrahim Al Balushi, Wen Jiang, and Tae-Yeon Kim. Computer Methods in Applied Mechanics and Engineering, 371:113317 (2020). journal · DOI
  13. Non-CMC solutions of the Einstein constraint equations on compact manifolds with apparent horizon boundaries with Michael Holst and Caleb Meier. Communications in Mathematical Physics, 357(2):467-517 (2018). arXiv · DOI
  14. Adaptivity of a B-spline based finite element method for modeling wind-driven ocean circulation with Ibrahim Al Balushi, Wen Jiang, and Tae-Yeon Kim. Computer Methods in Applied Mechanics and Engineering, 332:1-24 (2018). journal · DOI
  15. Convergence rates of adaptive methods, Besov spaces, and multilevel approximation Foundations of Computational Mathematics, 17(4), 917-956 (2017). arXiv · DOI
  16. Axisymmetric critical points of a nonlocal isoperimetric problem on the two-sphere with Rustum Choksi and Ihsan Topaloglu. ESAIM: Control, Optimisation and Calculus of Variations, 21(1), 247-270 (2015). arXiv · DOI
  17. On the consistency of the combinatorial codifferential with Douglas N. Arnold, Richard S. Falk, and Johnny Guzmán. Transactions of the American Mathematical Society, 366, 5487-5502 (2014). arXiv · DOI
  18. The Lichnerowicz equation on compact manifolds with boundary with Michael Holst. Classical and Quantum Gravity, 30, 205011 (2013); selected as a journal highlight in 2013-2014. arXiv · highlight · DOI
  19. Adaptive boundary element methods with convergence rates Numerische Mathematik, 124(3), 471-516 (2013). arXiv · DOI
  20. Analysis of a general family of regularized Navier-Stokes and magnetohydrodynamics models with Michael Holst and Evelyn Lunasin. Journal of Nonlinear Science, 20(5), 523-567 (2010). arXiv · DOI
  21. Rough solutions of the Einstein constraints on closed manifolds without near-CMC conditions with Michael Holst and Gabriel Nagy. Communications in Mathematical Physics, 288, 547-613 (2009). arXiv · DOI
  22. Far-from-constant mean curvature solutions of Einstein's constraint equations with positive Yamabe metrics with Michael Holst and Gabriel Nagy. Physical Review Letters, 100, 161101 (2008). arXiv · DOI
  23. An optimal adaptive wavelet method for nonsymmetric and indefinite elliptic problems Journal of Computational and Applied Mathematics, 211(1), 90-102 (2008). DOI · pdf
  24. An optimal adaptive wavelet method without coarsening of the iterands with Helmut Harbrecht and Rob Stevenson. Mathematics of Computation, 76, 615-629 (2007). DOI · pdf
  25. Computation of differential operators in wavelet coordinates with Rob Stevenson. Mathematics of Computation, 75, 697-709 (2006). DOI · pdf
  26. Computation of singular integral operators in wavelet coordinates with Rob Stevenson. Computing, 76, 77-107 (2006). DOI · pdf

Thesis

  1. Adaptive wavelet algorithms for solving operator equations PhD thesis. Department of Mathematics, Utrecht University. August 2006. ISBN 90-393-4365-9. summary · samenvatting · main part · errata