Professor! Today's topic is the compact thermal model (Delphi/JEDEC), right? What exactly is it?

It's a simplified model that represents the thermal characteristics of a package using a small number of nodes. It's based on the Delphi methodology, which complies with JEDEC standards, and is essential for system-level thermal design.

What kind of equations are involved in the compact thermal model (Delphi/JEDEC)?

The compact thermal model (Delphi/JEDEC) is governed by the steady-state heat conduction equation, which is discretized into a system of linear equations.

How is this equation actually solved computationally?

It's solved using spatial discretization via the Finite Element Method (FEM). This involves assembling the element stiffness matrices to construct the global stiffness equation.

What specifically is meant by matrix solution algorithms?

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

Compact Thermal Model (Delphi/JEDEC)

Category: 熱解析 | Integrated 2026-04-06

CAE visualization for compact thermal model theory - technical simulation diagram

コンパクト熱モデル（Delphi/JEDEC）

Theory and Physics

Overview

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Teacher! Today's topic is about compact thermal models (Delphi/JEDEC), right? What are they?

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A simplified model representing the thermal characteristics of a package with a small number of nodes. It's the Delphi method compliant with JEDEC standards. Essential for system-level thermal design.

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Wait, wait, representing the thermal characteristics of a package... so, can it be used in cases like this too?

Governing Equations

$$ R_{\theta,jb} = \frac{T_j - T_{board}}{P} $$

$$ \Psi_{jt} = \frac{T_j - T_{top}}{P} $$

Discretization Method

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How do you actually solve this equation 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 a transformation to the weak form (variational form) and use formulation by the Galerkin method using test functions and shape functions. The choice of element type (low-order elements vs. higher-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 do you mean by matrix solution algorithms?

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We 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.

Solution Method	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 to work with compact thermal models (Delphi/JEDEC)?

Tool Name	Developer/Current	Main File Formats
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 Lineage and Product Integration History

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Is the background story 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). Based on APDL (Ansys Parametric Design Language).

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 is needed to the correspondence of element types, compatibility of material models, and differences in the representation of loads and boundary conditions. Especially, higher-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 very deep, aren't they?