A Cut Finite Element Method for Transient Thermal Simulation in Multi-material Electronic Packaging Structures
Abstract
Advanced electronic packaging structures represent a key technological approach for extending Moore's Law. An electronic packaging structure consists of multiple materials with distinct properties, constituting a composite structure with complex spatial architecture. This paper develops an unfitted cut finite element method (CutFEM) for transient heat conduction simulation in multi-material electronic packaging structures with complex material interfaces. In the proposed computational framework, the heterogeneous spatial geometric features of electronic packaging structures is embedded and characterized in a regular background mesh, thereby avoiding the generation of body-fitted meshes on complicated interfaces. Interface temperature and heat-flux transmission conditions are imposed by a coefficient-weighted symmetric Nitsche formulation. In addition, a ghost-penalty stabilization controls arbitrarily small intersections between the physical materials and background meshes. Furthermore, the semi-discrete and fully-discrete numerical schemes are proposed, and an explicit energy estimate is derived in detail. Finally, two-dimensional and three-dimensional electronic packaging structures containing substrate, molding compound, die, and solder balls are designed to validate its accuracy, efficiency, and scalability in simulating challenging transient thermal problems.
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BibTeX
@misc{dong2026finite,
title = {{A Cut Finite Element Method for Transient Thermal Simulation in Multi-material Electronic Packaging Structures}},
author = {Hao Dong},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08543},
eprint = {2610.08543},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08543},
}
RIS
TY - UNPB
TI - A Cut Finite Element Method for Transient Thermal Simulation in Multi-material Electronic Packaging Structures
AU - Hao Dong
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08543
UR - https://arxiv.org/abs/2610.08543
AB - Advanced electronic packaging structures represent a key technological approach for extending Moore's Law. An electronic packaging structure consists of multiple materials with distinct properties, constituting a composite structure with complex spatial architecture. This paper develops an unfitted cut finite element method (CutFEM) for transient heat conduction simulation in multi-material electronic packaging structures with complex material interfaces. In the proposed computational framework, the heterogeneous spatial geometric features of electronic packaging structures is embedded and characterized in a regular background mesh, thereby avoiding the generation of body-fitted meshes on complicated interfaces. Interface temperature and heat-flux transmission conditions are imposed by a coefficient-weighted symmetric Nitsche formulation. In addition, a ghost-penalty stabilization controls arbitrarily small intersections between the physical materials and background meshes. Furthermore, the semi-discrete and fully-discrete numerical schemes are proposed, and an explicit energy estimate is derived in detail. Finally, two-dimensional and three-dimensional electronic packaging structures containing substrate, molding compound, die, and solder balls are designed to validate its accuracy, efficiency, and scalability in simulating challenging transient thermal problems.
ER -