Professor! Today's topic is the thermal resistance (Rth) model, right? What exactly is it?

It's a series-parallel thermal resistance network. It's a standard method used for temperature prediction from the package level up to the system level.

What kind of equations are involved in the thermal resistance (Rth) model?

The thermal resistance (Rth) model.

How is this equation actually solved computationally?

We use spatial discretization via the Finite Element Method (FEM). This involves assembling the element stiffness matrices and constructing the global stiffness equation.

What specifically is meant by a matrix solution algorithm?

It solves the system of equations using either direct methods (LU decomposition, Cholesky decomposition) or iterative methods (Conjugate Gradient method, GMRES method). For large-scale problems, preconditioned iterative methods are particularly effective.

Thermal Resistance (Rth) Model

Category: 熱解析 | Integrated 2026-04-06

CAE visualization for thermal resistance rth theory - technical simulation diagram

熱抵抗（Rth）モデル

Theory and Physics

Overview

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Teacher! Today's topic is about thermal resistance (Rth) models, right? What are they like?

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Series and parallel thermal resistance networks. A standard method used for temperature prediction from package to system.

Governing Equations

$$ R_{\theta} = \frac{\Delta T}{P} $$

$$ R_{\theta,total} = \sum R_{\theta,i} + \frac{1}{\sum 1/R_{\theta,j}} $$

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So, if you cut corners on the thermal resistance part, you'll pay for it later. I'll keep that in mind!

Discretization Methods

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How do you actually solve these equations on a computer?

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We use spatial discretization by the Finite Element Method (FEM). We assemble the element stiffness matrix and construct the global stiffness equation.

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We perform transformation to the weak form (variational form) and use Galerkin method formulation using test functions and shape functions. The choice of element type (low-order elements vs. high-order elements, full integration vs. reduced integration) directly affects the trade-off between solution accuracy and computational cost.

Matrix Solution Algorithms

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What exactly are matrix solution algorithms?

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Solve the simultaneous equations using direct methods (LU decomposition, Cholesky decomposition) or iterative methods (CG method, GMRES method). For large-scale problems, preconditioned iterative methods are effective.

Solver	Classification	Memory Usage	Applicable Scale
LU decomposition	Direct Method	O(n²)	Small to Medium Scale
Cholesky decomposition	Direct Method (Symmetric Positive Definite)	O(n²)	Small to Medium Scale
PCG Method	Iterative Method	O(n)	Large Scale
GMRES method	Iterative Method	O(n·m)	Large Scale / Non-symmetric
AMG Preconditioner	Preprocessing	O(n)	Very Large Scale

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So, if you cut corners on the Finite Element Method part, you'll pay for it later. I'll keep that in mind!

Implementation in Commercial Tools

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So, what software can be used for thermal resistance (Rth) models?

Tool Name	Developer/Current	Main File Format
Ansys Mechanical (formerly ANSYS Structural)	Ansys Inc.	.cdb, .rst, .db, .ans, .mac
COMSOL Multiphysics	COMSOL AB	.mph
Ansys Fluent	Ansys Inc.	.cas, .dat, .msh, .jou
Simcenter STAR-CCM+	Siemens Digital Industries Software	.sim, .java, .csv

Vendor History and Product Integration Background

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Is the origin of each software quite dramatic?

Ansys Mechanical (formerly ANSYS Structural)

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Tell me about "Ansys Mechanical"!

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Developed in 1970 by Swanson Analysis Systems Inc. (SASI). APDL (Ansys Parametric Design Language) based.

Current affiliation: Ansys Inc.

COMSOL Multiphysics

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Tell me about "COMSOL Multiphysics"!

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Founded in Sweden in 1986. Started as FEMLAB with MATLAB integration, later renamed to COMSOL. Strong in multiphysics.

Current affiliation: COMSOL AB

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After hearing this, I finally understand why development is so important!

Ansys Fluent

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Next is the story about Ansys Fluent. What's it about?

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Developed by Fluent Inc. Acquired by Ansys in 2006. A general-purpose CFD solver based on unstructured grids.

Current affiliation: Ansys Inc.

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Wow, the story of development is super interesting! Tell me more.

File Formats and Interoperability

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Are there any points to note when transferring data between different software?

Format	Extension	Type	Overview
STEP	.stp/.step	Neutral CAD	ISO 10303 compliant 3D CAD data exchange format. Supports geometry + PMI.
IGES	.igs/.iges	Neutral CAD	Early CAD data exchange standard. Has issues with surface data compatibility. Transition to STEP is progressing.
VTK	.vtk/.vtu	Visualization	Visualization Toolkit format. Used by ParaView, etc.

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When converting models between different solvers, attention must be paid to element type correspondence, material model compatibility, and differences in load/boundary condition representation. Particularly, high-order elements and special elements (cohesive elements, user-defined elements, etc.) often cannot be directly converted between solvers.

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I see... Formats seem simple at first glance, but they're actually quite deep, aren't they?

Practical Considerations

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