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The inverse one-phase Stefan problem in one dimension, aimed at identifying the unknown time-dependent heat flux P(t) with a known moving boundary position s(t), is investigated. A previous study [16] attempted to reconstruct the unknown…

We introduce the Closest Point Heat Method (CPHM), a novel approach for solving the surface Eikonal equation on general smooth surfaces. Building on the strengths of the classical heat method, such as simplicity of implementation and…

Knowing the exact 3D location of workers and robots in a collaborative environment enables several real applications, such as the detection of unsafe situations or the study of mutual interactions for statistical and social purposes. In…

In this paper, a meshless Hermite-HDMR finite difference method is proposed to solve high-dimensional Dirichlet problems. The approach is based on the local Hermite-HDMR expansion with an additional smoothing technique. First, we introduce…

In this paper we propose a collocation method for solving some well-known classes of Lane-Emden type equations which are nonlinear ordinary differential equations on the semi-infinite domain. They are categorized as singular initial value…

As is well-known, the advantage of the high-order compact difference scheme (H-OCD) is unconditionally stable and convergent with the order $O(\tau^2+h^4)$ under the maximum norm. In this article, a new numerical gradient scheme based on…

Adaptive methods for derivation of analytical and numerical solutions of heat diffusion in one dimensional thin rod have investigated. Comperhensive comparsion analysis based on the homotopy perturbation method (HPM) and finite difference…

The solution to the initial and Dirichlet boundary value problem for a semilinear, one dimensional heat equation is approximated by a numerical method that combines the Besse relaxation scheme in time (C. R. Acad. Sci. Paris S{\'e}r. I,…

A model order reduction technique is combined with an embedded boundary finite element method with a POD-Galerkin strategy. The proposed methodology is applied to parametrized heat transfer problems and we rely on a sufficiently refined…

This paper presents a steady-state and transient heat conduction analysis framework using the polygonal scaled boundary finite element method (PSBFEM) with polygon/quadtree meshes. The PSBFEM is implemented with commercial finite element…

This investigation is motivated by the problem of optimal design of cooling elements in modern battery systems. We consider a simple model of two-dimensional steady-state heat conduction described by elliptic partial differential equations…

High order accurate Hermite methods for the wave equation on curvilinear domains are presented. Boundaries are treated using centered compatibility conditions rather than more standard one-sided approximations. Both first-order-in-time…

In this work, we design and analyze a novel, provably conditionally stable, weakly coupled partitioned scheme to solve the conjugate heat transfer (CHT) problem. We consider a model CHT problem consisting of linear advection-diffusion and…

We propose an implementation of the Smooth Selection Embedding Method (SSEM) in the setting of Chebyshev polynomials. The SSEM is a hybrid fictitious domain / collocation method which solves boundary value problems in complex domains by…

In this paper, a well-conditioned collocation method is constructed for solving general $p$-th order linear differential equations with various types of boundary conditions. Based on a suitable Birkhoff interpolation, we obtain a new set of…

Localized representation of the Kohn-Sham subspace plays an important role in quantum chemistry and materials science. The recently developed selected columns of the density matrix (SCDM) method [J. Chem. Theory Comput. 11, 1463, 2015] is a…

Partial Differential Equations (PDEs) are widely used for modeling the physical phenomena and analyzing the dynamical behavior of many engineering and physical systems. The heat equation is one of the most well-known PDEs that captures the…

Efficiently enhancing heat conduction through optimized distribution of a limited quantity of high thermal conductivity material is paramount in cooling electronic devices and numerous other applications. This paper introduces a…

In this paper, a class of high-order compact finite difference Hermite scheme is presented for the simulation of double-diffusive convection. To maintain linear stability, the convective fluxes are split into positive and negative parts,…

In recent years, a variety of meshless methods have been developed to solve partial differential equations in complex domains. Meshless methods discretize the partial differential equations over scattered points instead of grids. Radial…