The collocation method is a widely used numerical method for science and engineering
problems governed by partial differential equations. This paper provides a comprehensive …

We propose the variational collocation method for the numerical solution of partial
differential equations. The conceptual basis is the establishment of a direct connection …

We develop a new continuum mechanics modeling framework for liquid–vapor flows, with
particular focus on the van der Waals fluid. By invoking microforce theory, the Coleman–Noll …

We present a new computational framework of neuron growth based on the phase field
method and develop an open-source software package called “ …

This paper focuses on the employment of analysis-suitable T-spline surfaces of arbitrary
degree for performing structural analysis of fully nonlinear thin shells. Our aim is to bring …

Neuron growth is a complex, multi-stage process that neurons undergo to develop
sophisticated morphologies and interwoven neurite networks. Recent experimental research …

Moving interface problems are ubiquitous in science and engineering. To develop an
accurate and efficient methodology for this class of problems, we present algorithms for local …

Isogeometric analysis (IGA) is an effective numerical method for connecting computer-aided
design and engineering, which has been widely applied in various aspects of computational …

Computational fluid dynamics (CFD) is the cornerstone of the design and analysis process
in many engineering applications. Not only has it been applied in the design phase, but it …

The solution approximation for partial differential equations (PDEs) can be substantially
improved using smooth basis functions. The recently introduced mollified basis functions are …