A Turning Band Approach to Kernel Convolution for Arbitrary Surfaces

TL;DR

This paper introduces a nonstationary kernel convolution method for data on arbitrary surfaces, enabling efficient simulations where traditional FFT-based spectral methods are not applicable due to irregular geometries.

Contribution

It presents a novel kernel convolution approach tailored for arbitrary surfaces, extending the applicability of simulation techniques beyond regular grids.

Findings

Enables simulation on arbitrary surfaces

Provides a nonstationary kernel convolution framework

Improves flexibility over traditional spectral methods

Abstract

One of the most efficient ways to produce unconditional simulations is with the spectral method using fast Fourier transform (FFT) [1]. But this approach is not applicable to arbitrary surfaces because no regular grid exists. However, points on the arbitrary surface can be generated randomly using uniform distribution to replace a regular grid. This paper will describe a nonstationary kernel convolution approach for data on arbitrary surfaces.