# FEM Simulation Vs BEM Simulation (What is the difference?)

A career in the world of FEA (Finite Element Analysis), is both exciting and daunting. FEA offers such design potential, but the level of knowledge required to understand how FEA works mathematically can be overwhelming.

Many terms and acronyms get used in the world of design analysis and it is important to know what these terms mean, in particular, FEM and BEM, and how these methods work within the world of FEA.

FEM stands for Finite Element Method. It is a numerical method that solves a design problem by the approximate solution of partial differential equations. BEM stands for Boundary Element Method, which is also a numerical method but works by solving a design problem by approximating boundary integral equations.

FEA stands for Finite Element Analysis. The term FEA refers to the overarching world of FEA. It is the term used to describe the simulation design tool.

FEM and BEM are numerical methods (ways to solve simulation problems) within the world of FEA.

I like to imagine that FEA is the car and FEM and BEM are the gears. You can drive a car, but what gear you are in will determine how fast you get to your destination and how effectively you get to your destination.

For the simulation purists out there, this might seem like an oversimplification, but when starting out in the world of FEA, we need some basic analogy to grasp the concepts.

Within the simulation industry, the terms FEM and FEA can get used interchangeably, as often FEM is implied when stating something like “I have done a structural FEA analysis”.

For example, going back to the car analogy, you can say that you are driving a car (doing FEA) and that you are doing this means that using gears is implied (you are using the FEM or BEM method).

In this article, I want to break down these terms to simplify the concepts, as understood from my experience of working as a simulation engineer in the acoustics industry.

I will cover:

• What is the difference between BEM and FEM?
• How does FEM compare to BEM? (Pros & Cons)
• Examples of a FEM Simulation
• Examples of a BEM Simulation

## What Is The Difference Between BEM And FEM?

To understand the difference between BEM and FEM, we must first understand what each numerical method means.

### What Is A FEM Simulation?

FEM stands for Finite Element Method and is a numerical method for solving design methods.

The principle of FEM is to divide up a structure or design problem into smaller building blocks, which we call finite elements.

These finite elements, or building blocks, have mathematical properties of the physical characteristics that they represent.

For example, let’s say you are trying to analyse how strong the steel chassis of a speaker is. Using FEM, we divide this large and possibly complex structure up into smaller building blocks, each of which has the physical properties of steel.

Using FEM, we have divided up the speaker chassis geometry into smaller blocks, each with the mathematical behaviour of steel. We then performed an analysis on each individual building block, which is called a finite element.

We combine the boundary conditions and interactions between all these smaller finite elements to create an overall picture (approximation) of how the whole steel chassis performs.

From these building blocks, we can build up a full picture of how strong the speaker’s steel chassis is and how it could react to stress and fatigue.

In FEM, we calculate all these interactions between elements using partial differential equations

### What Is A BEM Simulation?

BEM stands for Boundary Element Method, which, like FEM, is also a numerical method within FEA but is focused on the boundary.

Unlike FEM, which approximates partial differential equations, BEM solves boundary integral equations.

As the name pimples, BEM is more concerned with the boundary of the design problem to be solved. A boundary is the physical limitations of the simulation or how it interacts with the world around it.

BEM is useful where we understand and have a lot of knowledge about our simulation boundary conditions. For example, a component which is restrained and loaded on its surface.

## How Does FEM Compare To BEM? (Pros & Cons)

FEM simulations and BEM simulations both have their advantages and disadvantages and will each have their rightful place in the world of finite element analysis.

The following table lists the pros and cons of both FEM simulations and BEM simulations.

## Examples Of FEM Simulations

Because of advances in computer processing power, we find applications of FEM and BEM simulations in small design offices across the globe.

Some examples of FEM simulations in practice are:

• Stress and fatigue analysis
• Vibrational analysis
• Modal analysis

## Examples Of BEM Simulation

The great thing about BEM is that you do not need to create the large volumetric meshes that are required by FEM. BEM is boundary focused.

For simulations that require large 3D meshes, BEM is very useful. Here are some applications of BEM simulations:

• Acoustic analysis
• Loudspeaker horn design
• Car Audio
• Simulations with radiation or scattering (temperature, air)
• Underwater acoustics
• Infinite baffles or walls

## Final Thoughts

FEM simulations and BEM simulations are both powerful numerical solving methods within the world of finite element analysis.

While FEM simulations have a wide variety of applications, we can use BEM simulations for problems where the boundary conditions are well understood.

Each tool has its own advantages and disadvantages, which you should consider when choosing a simulation type.