Akselos provides fast and detailed digital twin simulations of large infrastructure using reduced basis finite element analysis (RB-FEA). RB-FEA uses divide-and-conquer algorithms and parameterized physics to simulate an entire asset 1,000x faster than traditional FEA for linear problems and 10-100x faster for localized nonlinearities. Akselos digital twins can incorporate real-time sensor data to enable predictive maintenance and condition-based analysis of assets like offshore structures.

1. Digital Twins for Offshore Infrastructure
Akselos Simulation Technology
North America – Akselos, Inc. ֎ Switzerland – Akselos S.A. Akselos.com

2. Akselos Enables Full Simulation of the
Largest Infrastructure
Globally linear 1000x faster
Localized nonlinearities 10x to 100x faster
Globally nonlinear 1x
Modern computational technologies (parallel, cloud)

3. Divide-and-Conquer Algorithms
(US Patent 9,213,788)
Set parameters
and solve
(2 seconds instead of 30
minutes)
Assemble model
Create/update
RB components
(similar to
parameterized
substructuring)
Parameterized
physics
Computational
Approx.

4. 15 Years of R&D Funded by US DoD.
More than 100 Publications
100+publications
100+Person years
Peer reviewed papers in top
journals. Two text books.
Two Akselos founders are patent
authors.
Reduced Basis Algorithms
Leading researchers from
major academic
institutions
US Patent 9,213,788Funded by US DoD + 20 other Universities

5. Fast FEA Enables Akselos Digital Twin
Digital Twin: Detailed virtual
replica of an entire asset, tracking
the current state of the asset
(including cracks, corrosion,
damage etc.)
Improved risk assessment
Simulate extreme events
Condition-based fatigue analysis
Predictive maintenance
Safe lean design

6. One Global Fine Model of your Entire
Asset (1/2)
Standard workflow: DNV-RP-C206
The standard
workflow
involves juggling
many models.
Slow and error
prone!

7. One Global Fine Model of your Entire
Asset (2/2)
Global mesh meets all requirements of DNV-RP-C206, e.g.
includes 1t x 1t mesh refinement in hot spot areas
Can incorporate condition-based data in the global model (hull
damage, corrosion, etc.)
Akselos provides one
global model that
uses a fine mesh
everywhere

8. We Provide the Full Range of Analysis…
Contact analysis
Geometric
nonlinearity
Buckling analysis
Plasticity
*Akselos’s RB-FEA solvers accelerate the linear
regions of the model. We use conventional FEA
for nonlinear regions. Akselos’s Hybrid solver
seamlessly couples RB-FEA and conventional FEA.

9. … and the Full Range of Elements
Shells
Beams
Solids
Hybrid

10. Solver Capabilities
Analysis Type RB-FEA FEA & Hybrid
Structural Steady-state linear
elasticity
Dynamic linear elasticity
Modal analysis
Node-to-node contact
The full range of
element types (springs,
beams, shells, solids)
Plasticity
Geometric nonlinearity
Surface-to-surface
contact
Buckling
Acoustics Frequency-domain
acoustics
Modal analysis
Time-domain acoustics
Thermal Steady-state and
dynamic linear thermal
analysis
Nonlinear
(temperature-
dependent materials)

11. Parallel Cloud-based Solver
Massively parallel
Cloud-based solver
which can efficiently
run 1000s of load
cases
Cloud data centerOne request
Code-based analysis
and fatigue analysis
can require 1000s of
solves

12. Digital Twin: Integration with
Sensors/ IoT (1/2)
Calibrated Digital Twin
Wind &
Seastates
Accelerometers
Strain
Corrosion
Wave
Sensors
Cloud-based Servers
Real-time risk-based
decisions

13. Digital Twin: Integration with
Sensors/ IoT (2/2)
Calibrated Digital Twin
Wind &
Seastates
Accelerometers
Strain
Corrosion
Wave
Sensors
Cloud-based Servers
Real-time risk-based
decisions
Akselos focuses on these
links in the value chain.
Partners provide the other
links.

14. The Akselos Digital Twin Safely Avoids
Unnecessary Downtime
2.
Akselos Digital Twin
used to quickly and
safely assess the
situation. First, the
Digital Twin is updated
to incorporate the
crack in full detail.
3. Thousands of simulations are run
on the updated Digital Twin. With
Akselos’s revolutionary simulation
algorithms and cloud-based platform,
this analysis can be performed within a
day.
1.During an inspection,
a crack is identified. The
impact and required action
are not clear. Is an
unplanned shutdown
required? Or, can the repair
be postponed until the
next planned shutdown?
4. Engineers can
then plan and execute
the appropriate
response based on
accurate simulation
data. The Digital Twin
stops unnecessary
downtime.

15. Akselos GUI
Client’s Model Library
The Akselos Simulation Platform
Simulation Engine
Decision Support System

16. Comparative Advantage
Example of a
Shiploader
Example of a
6,000 ton structure
Load combinations [lc] 100 lc. 30 lc.
Model degrees of
freedom[dof]
5 m. dof. 500 m. dof.
Image
Time for FEA, all load
combinations
3 days 7.5 hours Too large for FEA
Time for
RB-FEA, all load
combinations
8 min 20 seconds 1 hour 45 min

17. Digital Twin Examples
On-shore structures
Mining and
port infrastructure Pressure vessels
Wind turbines Offshore structures FPSO

18. Current Major Project:
FPSO Digital Twin

19. 5 Reasons Akselos is Unique
Akselos Reduced Basis
FEA is the next
generation simulation
technology: fast,
detailed, accurate.
Parameterized full 3D
models which can be
reconfigured and re-
solved in seconds.
Cloud-based solvers for
fast analysis, and
enhanced collaboration
between engineers.
Results from inspections
are incorporated into
Digital Twins, which are
then re-analyzed based
on preset decision
support system criteria.
Perform fast 3D solves of
entire assets, and
include localized
nonlinear analysis with
conventional FEA where
needed.

20. Appendix

21. Akselos’s Hybrid “Linear/Nonlinear”
Solver is Ideal for Push-over Analysis
Method:
1. Start with a fully linear
model, represented by RB-FEA
everywhere.
2. Apply load increments to it
as per standard push-over
analysis methodologies
3. Once any component that
has stress that exceeds yield, or
once a component requires
geometrically nonlinear
analysis, it is converted to an
FEA component.
4. Continue load-steps, modify
the nonlinear region adaptively
in each step.
This enables a fast, detailed,
parameterized approach to
push-over analysis.
Traditional Push-over Akselos Push-over
The user must specify plastic
regions ahead of time, based
on where they expect high
stresses to occur.
The approach is fully
adaptive and does not
require plastic regions to be
specified manually. This
means we cannot miss
critical regions due to “bad
guesses”.
Traditional push-over
analysis of large structures
relies extensively on beam
elements because it is too
computationally expensive to
use shell or solid elements.
Fast RB-FEA solvers make it
practical to use shell or solid
elements throughout the
entire model.
Plastification is assumed to
be concentrated at the
predefined plastic hinge
locations
Spread of plasticity is allowed
throughout the volume of
the structure

22. RB-FEA Components Consist of Two
Regions: Interior and Ports (1/2)
Interior: The Reduced Basis
Method is used to efficiently
represent component interiors.
This methodology is the product of
extensive published academic
research*.
The key idea is to create
a set of basis functions
that efficiently and
accurately represent the
component’s behavior
over the full parameter
range of interest. This is
achieved by the RB-FEA
Greedy Algorithm which
efficiently samples the
nonlinear parametric
manifold (see Figure on
the left). This yields a
basis that typically
converges at an
exponential rate, and
hence reproduces full
FEA at a small fraction of
the computational cost.
*E.g. see: G Rozza, DBP Huynh, and AT Patera, Reduced Basis Approximation and A Posteriori Error
Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations — Application to
Transport and Continuum Mechanics. Archives of Computational Methods in Engineering 15(3):229–275,
2008.

23. Ports: RB-FEA components
connect to each other on
ports. We use modes on
the ports to represent the
range of behaviors that can
be exhibited on component
interfaces. Similarly to
component interiors, a
reduction algorithm is used
to choose an efficient port
space. Once again, we
typically observe
exponential convergence
(See the right figure for an
example of rapid port
mode convergence) with
the number of modes,
using an optimal reduced
set of modes leads to fast
and accurate results. **.
**Port modeling is discussed in: Smetana and AT Patera, Optimal local approximation spaces for component-
based static condensation procedures. SIAM Journal on Scientific Computing
N=4 N=5 N=6
RB-FEA Components Consist of Two
Regions: Interior and Ports (2/2)

24. Standards-Based Analysis
Akselos component-based models enable standards-based
analysis, e.g. output from DNV-RP-C201 is shown below.