Related papers: An Online Generalized Multiscale finite element me…
Reservoir simulators utilize numerical techniques to solve the governing equations of fluid flow in porous media and they are essential tool for oil and gas fields development. In practical reservoir simulation, the finite difference method…
Real-time analysis of bio-heat transfer is very beneficial in improving clinical outcomes of hyperthermia and thermal ablative treatments but challenging to achieve due to large computational costs. This paper presents a fast numerical…
We present a multiscale mixed finite element method for solving second order elliptic equations with general $L^{\infty}$-coefficients arising from flow in highly heterogeneous porous media. Our approach is based on a multiscale spectral…
Boiling is a complex phenomenon where different non-linear physical interactions take place and for which the quantitative modeling of the mechanism involved is not fully developed yet. In the last years, many works have been published…
In this paper, we propose a deep learning based reduced order modeling method for stochastic underground flow problems in highly heterogeneous media. We aim to utilize supervised learning to build a reduced surrogate model from the…
We proposed a structure-preserving stabilized parametric finite element method (SPFEM) for the evolution of closed curves under anisotropic surface diffusion with an arbitrary surface energy $\hat{\gamma}(\theta)$. By introducing a…
We propose a parametric finite element method (PFEM) for efficiently solving the morphological evolution of solid-state dewetting of thin films on a flat rigid substrate in three dimensions (3D). The interface evolution of the dewetting…
In this work we address the Multiscale Spectral Generalized Finite Element Method (MS-GFEM) developed in [I. Babu\v{s}ka and R. Lipton, Multiscale Modeling and Simulation 9 (2011), pp. 373--406]. We outline the numerical implementation of…
In this paper a generalized fundamental solution using the boundary element method to solve the Helmholtz equation is proposed. It is observed that the commonly used fundamental solution is only valid for good conductors since the…
We develop a cut finite element method (CutFEM) for the convection problem in a so called fractured domain which is a union of manifolds of different dimensions such that a $d$ dimensional component always resides on the boundary of a $d+1$…
Long simulation times in climate sciences typically require coarse grids due to computational constraints. Nonetheless, unresolved subscale information significantly influences the prognostic variables and can not be neglected for reliable…
We present an immersed boundary method to simulate the creeping motion of a rigid particle in a fluid described by the Stokes equations discretized thanks to a finite element strategy on unfitted meshes, called Phi-FEM, that uses the…
Many problems in physics are inherently of multi-scale nature. The issues of MHD turbulence or magnetic reconnection, namely in the hot and sparse, almost collision-less astrophysical plasmas, can stand as clear examples. The Finite Element…
Advancement in manufacturing methods enable designing so called metamaterials with a tailor-made microstructure. Microstructure affects materials response within a length-scale, where we model this behavior by using the generalized…
A finite element model and its equivalent electronic analogue circuit of hydraulic transmission lines have been developed. Basic equations are approximated to be a set of ordinary differential equations that can be represented in state…
Numerical analytical heat transfer models play a critical role in geothermal design and feasibility studies. Classical solutions, such as those proposed by Gringarten et al. 1975, rely on simplified assumptions and systematically…
In energy science, Darcy flow in heterogeneous porous media is a central problem in reservoir sim-ulation. However, the pronounced multiscale characteristics of such media pose significant challenges to conventional numerical methods in…
This work deals with numerical simulation of water freezing and thawing in a complex three-dimensional geometry of a porous medium. The porous structure is represented by a virtual container filled with glass beads. Phase transition…
A modeling of metasurfaces in the finite element method (FEM) based on generalized sheet transition conditions (GSTCs) is presented. The discontinuities in electromagnetic fields across a metasurface as represented by the GSTC are modeled…
The study of the continuum radiative transfer problem inside circumstellar envelopes is both a theoretical and numerical challenge, especially in the frequency-dependent and multi-dimensional case. While approximate methods are easier to…