Nicodemus Banagaaya

INDEX-AWARE MODEL ORDER REDUCTION FOR LINEAR INDEX-2 DAES WITH CONSTANT COEFFICIENTS ∗

A model order reduction method for index-2 differential-algebraic equations (DAEs) is introduced, which is based on the intrinsic differential equations and on the remaining algebraic constraints. This extends the method introduced in a previous paper for index-1 DAEs. This procedure is implemented numerically and the results show numerical evidence of its robustness over the traditional methods.

Model Order Reduction for nanoelectronics coupled problems with many inputs

This paper is concerned with Model Order Reduction (MOR) for nanoelectronics coupled problems with many inputs. Our main applications are electro-thermal coupled problems described by nonlinear quadratic differential-algebraic systems (DAEs). We present algorithms that combine the advantages of the splitting techniques for DAEs and the existing MOR methods for systems with many inputs such as sparse implicit projection (SIP) for RC/RLC networks and MOR based on the superposition principle.

An index-aware parametric model order reduction method for parameterized quadratic differential–algebraic equations

Modeling of sophisticated applications, such as coupled problems arising from nanoelectronics can lead to quadratic differential algebraic equations (DAEs). The quadratic DAEs may also be parameterized, due to variations in material properties, system configurations, etc., and they are usually subject to multi-query tasks, such as optimization, or uncertainty quantification. Model order reduction (MOR), specifically parametric model order reduction (pMOR), is known as a useful tool for accelerating the simulations in a multi-query context. However, pMOR dedicated to this particular structure, has not yet been systematically studied. Directly applying the existing pMOR methods may produce parametric reduced-order models (pROMs) which are less accurate, or may be very difficult to simulate. The same problem was already observed for linear DAEs, and could be eliminated by introducing splitting MOR techniques such as the index-aware MOR (IMOR) methods. We extend the IMOR methods to parameterized quadratic DAEs, thereby producing accurate and easy to simulate index-aware parametric reduced-order models (IpROMs). The proposed approach is so far limited to index-1 one-way coupled problems, but these often appear in computational nanoelectronics. We illustrate the performance of the new approach using industrial models for nanoelectronic structures.

Sparse Model Order Reduction for Electro-Thermal Problems with Many Inputs

Recently, the block-diagonal structured model order reduction method for electro-thermal coupled problems with many inputs (BDSM-ET) was proposed in Banagaaya et al. (Model order reduction for nanoelectronics coupled problems with many inputs. In: Proceedings 2016 design, automation & test in Europe conference & exhibition, DATE 2016, Dresden, March 14–16, pp 313–318, 2016). After splitting the electro-thermal (ET) coupled problems into electrical and thermal subsystems, the BDSM-ET method reduces both subsystems separately, using Gaussian elimination and the block-diagonal structured MOR (BDSM) method, respectively. However, the reduced electrical subsystem has dense matrices and the nonlinear part of the reduced-order thermal subsystem is computationally expensive. We propose a modified BDSM-ET method which leads to sparser reduced-order models (ROMs) for both the electrical and thermal subsystems. Simulation of a very large-scale model with up to one million state variables shows that the proposed method achieves significant speed-up as compared with the BDSM-ET method.

Parametric Model Order Reduction for Electro-Thermal Coupled Problems with Many Inputs

The modified BDSM-ET method is a model order reduction (MOR) technique which was developed to reduce non-parametric electro-thermal (ET) coupled problems with many inputs. The method leads to block-wise sparse reduced-order models (ROMs) which are accurate and computationally cheaper compared to the existing MOR methods. In this work, we extend the modified BDSM-ET method to parametrized ET coupled problems with many inputs.

Index-aware Model Order Reduction for higher index DAEs

There exists many Model Order Reduction (MOR) methods for ODEs but little had been done to reduce DAEs especially higher index DAEs. In principle, if the matrix pencil of a DAE is regular, it is possible to use conventional MOR techniques to obtain reduced order models, which are generally ODEs. However, as far as their numerical treatment is concerned, the reduced models may be close to higher index models, that is, to DAEs. Thus the numerical solution of the reduced models might be computationally expensive, or even not feasible. In the worst cases, the reduced models may be unsolvable, i.e. their matrix pencil is singular. This problem is very pronounced for systems with index higher than 1, but it may occur even if the index of the problem does not exceed 1. Thus MOR methods for ODEs cannot generally be used for DAEs. This motivated us to introduce a new MOR method for DAEs which we call the index-aware MOR (IMOR) which can reduce DAEs while preserving the index of the system. This method involves first splitting the DAEs into differential and algebraic parts. Then, we use the existing MOR methods to reduce the differential part. We observed that the reduction of the differential part induces a reduction in the algebraic part. This enabled us to construct a method which reduces both the differential and the algebraic part. As a result a DAE is reduced. This method can also be used as a new method to solve DAEs. In this paper, we generalize the IMOR method to higher index DAEs and we shall call this method the GIMOR method. We use index-3 systems for testing and validating the accuracy of the GIMOR method.