arXiv subjects

Atakan Koçyiğit

Publications and source records attributed to Atakan Koçyiğit.

3 recordsLinked to original sources

arXiv2025

Adaptive Wavelet-Galerkin Modelling of Heat Conduction in Heterogeneous Composite Materials

We present an adaptive wavelet Galerkin method for transient heat conduction in heterogeneous composite materials. The approach combines multiresolution wavelet bases with an implicit time discretization to efficiently resolve sharp temperature gradients near material interfaces and boundary layers. Adaptive refinement is driven by wavelet coefficients, significantly reducing the number of degrees of freedom compared to uniform discretizations. Numerical examples demonstrate accurate resolution of layered, inclusion-based, and functionally graded composites with improved computational efficiency.

math.NA↗

arXiv2025

Seismic wave propagation in viscoelastic media under Atangana-Baleanu fractional dynamics: Model formulation and numerical simulations

We propose a one-dimensional viscoelastic seismic-wave model driven by the Atangana-BaleanuCaputo fractional derivative with a non-singular Mittag-Leffler kernel. A finite-difference discretization in space and an Adams-Bashforth-Moulton predictor-corrector scheme in time are used to compute solutions for several fractional orders. Simulations indicate that fractional memory alters both attenuation and dispersion, leading to non-exponential energy decay compared with the classical integer-order case.

physics.geo-ph↗

arXiv2025

Atangana-Baleanu Regularized Wavelet Compression For Astronomical Time-Series

Astronomical light curves are noisy and irregular, so compression must reduce size without erasing weak transients. We propose a fractional wavelet compression method where wavelet coefficients are regularized via an Atangana Baleanu Caputo derivative with a nonsingular Mittag Leffler kernel. The induced long memory smoothing suppresses noise while preserving coherent transits, flares and oscillations. We give the coefficient level formulation, an efficient implementation, and comparisons with classical discrete wavelet thresholding, showing competitive compression with improved retention of low-amplitude events.

astro-ph.IM↗