arXiv subjects

August Johansson

Publications and source records attributed to August Johansson.

8 recordsLinked to original sources

arXiv2026

Comprehensive parameter and electrochemical dataset for a 1 Ah graphite/LNMO battery cell for physical modelling as a blueprint for data reporting in battery research

While current technology has enabled their widespread use, further improvements are needed for stationary, portable, and mobile applications, for example by the development of novel cathode materials. Digitalization of battery development, combining both experimental and modelling efforts is extremely valuable in this development. This is addressed in the present paper, where the authors present a comprehensive dataset for a graphite/LNMO 1 Ah pouch cell, including material, design, and electrochemical data. The dataset, validated through the BattMo modelling framework, supports physical modelling and aims to benefit the battery modelling community by offering a comprehensive resource for future studies. Both the dataset and the accompanying software for numerical validation is openly available and processed in such a way that it can serve as blueprint for reporting of comparable research data.

cond-mat.mtrl-sci↗

arXiv2025

BattMo -- Battery Modelling Toolbox

This paper presents the Battery Modelling Toolbox (BattMo), a flexible finite volume continuum modelling framework in MATLAB\textsuperscript{\textregistered} (\citeproc{ref-MATLAB}{The MathWorks Inc., 2025}) for simulating the performance of electro-chemical cells. BattMo can quickly setup and solve models for a variety of battery chemistries, even considering 3D designs such as cylindrical and prismatic cells. The simulation input parameters, including the material parameters and geometric descriptions, are specified through JSON schemas. In this respect, we follow the guidelines of the Battery Interface Ontology (BattINFO) to support semantic interoperability in accordance with the FAIR principles (\citeproc{ref-fair}{Wilkinson et al., 2016}). The Doyle-Fuller-Newman (DFN) (\citeproc{ref-Doyle1993ModelingCell}{Doyle et al., 1993}) approach is used as a base model. We include fully coupled thermal simulations. It is possible to include degradation mechanisms such as SEI layer growth, and the use of composite material, such as a mixture of Silicon and graphite. The models are setup in a hierarchical way, for clarity and modularity. Each model corresponds to a computational graph, which introduces a set of variables (the nodes) and functional relationship (the edges). This design enables the flexibility for changing and designing new models. The solver in BattMo uses automatic differentiation and support adjoint computation. We can therefore compute the derivative of objective functions with respect to all parameters efficiently. Gradient-based optimization routines can be used to calibrate parameters from experimental data.

physics.comp-ph↗

arXiv2020

MultiMesh Finite Elements with Flexible Mesh Sizes

We analyze a new framework for expressing finite element methods on arbitrarily many intersecting meshes: multimesh finite element methods. The multimesh finite element method, first presented in [40], enables the use of separate meshes to discretize parts of a computational domain that are naturally separate; such as the components of an engine, the domains of a multiphysics problem, or solid bodies interacting under the influence of forces from surrounding fluids or other physical fields. Furthermore, each of these meshes may have its own mesh parameter. In the present paper we study the Poisson equation and show that the proposed formulation is stable without assumptions on the relative sizes of the mesh parameters. In particular, we prove optimal order a priori error estimates as well as optimal order estimates of the condition number. Throughout the analysis, we trace the dependence of the number of intersecting meshes. Numerical examples are included to illustrate the stability of the method.

math.NA↗

arXiv2019

A multimesh finite element method for the Navier-Stokes equations based on projection methods

The multimesh finite element method is a technique for solving partial differential equations on multiple non-matching meshes by enforcing interface conditions using Nitsche's method. Since the non-matching meshes can result in arbitrarily cut cells, additional stabilization terms are needed to obtain a stable variational formulation. In this contribution we extend the multimesh finite element method to the Navier-Stokes equations based on the incremental pressure correction scheme. For each step in the pressure correction scheme, we derive a multimesh finite element formulation with suitable stabilization terms. The overall scheme yields expected spatial and temporal convergence rates on the Taylor-Green problem, and demonstrates good agreement for the drag and lift coefficients on the Turek-Schafer benchmark (DFG benchmark 2D-3). Finally, we illustrate the capabilities of the proposed scheme by optimizing the layout of obstacles in a channel.

math.NA↗

arXiv2018

Shape Optimization using the Finite Element Method on Multiple Meshes

An important step in shape optimization with partial differential equation constraints is to adapt the geometry during each optimization iteration. Common strategies are to employ mesh-deformation or re-meshing, where one or the other typically lacks robustness or is computationally expensive. This paper proposes a different approach, in which the computational domain is represented by multiple, independent meshes. A Nitsche based finite element method is used to weakly enforce continuity over the non-matching mesh interfaces. The optimization is preformed using an iterative gradient method, in which the shape-sensitivities are obtained by employing the Hadamard formulas and the adjoint approach. An optimize-then-discretize approach is chosen due to its independence of the FEM framework. Since the individual meshes may be moved freely, re-meshing or mesh deformations can be entirely avoided in cases where the geometry changes consists of rigid motions or scaling. By this free movement, we obtain robust and computational cheap mesh adaptation for optimization problems even for large domain changes. For general geometry changes, the method can be combined with mesh-deformation or re-meshing techniques to reduce the amount of deformation required. We demonstrate the capabilities of the method on several examples, including the optimal placement of heat emitting wires in a cable to minimize the chance of overheating, the drag minimization in Stokes flow, and the orientation of 25 objects in a Stokes flow.

math.NA↗

arXiv2018

A MultiMesh Finite Element Method for the Stokes Problem

The multimesh finite element method enables the solution of partial differential equations on a computational mesh composed by multiple arbitrarily overlapping meshes. The discretization is based on a continuous--discontinuous function space with interface conditions enforced by means of Nitsche's method. In this contribution, we consider the Stokes problem as a first step towards flow applications. The multimesh formulation leads to so called cut elements in the underlying meshes close to overlaps. These demand stabilization to ensure coercivity and stability of the stiffness matrix. We employ a consistent least-squares term on the overlap to ensure that the inf-sup condition holds. We here present the method for the Stokes problem, discuss the implementation, and verify that we have optimal convergence.

math.NA↗

arXiv2018

MultiMesh Finite Element Methods: Solving PDEs on Multiple Intersecting Meshes

We present a new framework for expressing finite element methods on multiple intersecting meshes: multimesh finite element methods. The framework enables the use of separate meshes to discretize parts of a computational domain that are naturally separate; such as the components of an engine, the domains of a multiphysics problem, or solid bodies interacting under the influence of forces from surrounding fluids or other physical fields. Such multimesh finite element methods are particularly well suited to problems in which the computational domain undergoes large deformations as a result of the relative motion of the separate components of a multi-body system. In the present paper, we formulate the multimesh finite element method for the Poisson equation. Numerical examples demonstrate the optimal order convergence, the numerical robustness of the formulation and implementation in the face of thin intersections and rounding errors, as well as the applicability of the methodology. In the accompanying paper~\cite{mmfem-2}, we analyze the proposed method and prove optimal order convergence and stability.

math.NA↗

arXiv2015

High Order Cut Finite Element Methods for the Stokes Problem

We develop a high order cut finite element method for the Stokes problem based on general inf-sup stable finite element spaces. We focus in particular on composite meshes consisting of one mesh that overlaps another. The method is based on a Nitsche formulation of the interface condition together with a stabilization term. Starting from inf-sup stable spaces on the two meshes, we prove that the resulting composite method is indeed inf-sup stable and as a consequence optimal \emph{a~priori} error estimates hold.

math.NA↗