Nature

Finite Element Methods for Partial Differential Equations on Surfaces

The finite element method (FEM) has evolved into a robust and flexible tool for solving partial differential equations (PDEs) defined on surfaces. Its versatility allows for the treatment of complex ...
EDN

Finite-Difference Time-Domain Method using Yee’s Algorithm

Developed a CUDA version of the FDTD method and achieved a speedup 40x. Implemented on a NVIDIA Quadro FX 3800 GPU, which has 192 SPs, 1GB global memory, and a memory bandwidth of 51.2 GB/s.
Risk

Alternating direction implicit finite difference schemes for the Heston-Hull-White partial differential equation

In this paper we investigate the effectiveness of alternating direction implicit (ADI) time-discretization schemes in the numerical solution of the three-dimensional Heston-Hull-White partial ...
Risk

Finite-difference solution ansatz approach in least-squares Monte Carlo

This paper presents a simple but effective and efficient approach to improve the accuracy and stability of the least-squares Monte Carlo method. The key idea is to construct an ansatz for the ...
Nature

Finite Element Methods for Partial Differential Equations

Finite element methods (FEM) constitute a foundational numerical approach for solving partial differential equations by discretising complex domains into smaller, manageable subdomains known as ...