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 Future Reservoir Simulation Systems and Technology Research
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Software Research
 Solvers Research
 Advanced Process Research

We develop, distribute, and maintain peer-reviewed software with three purposes:
  1. Disseminate our research on solvers and advanced processes in a reproducible manner.
  2. Enable our industry partners to freely evaluate, utilize, reproduce, extend, and distribute, commercially or otherwise, our innovations.
  3. Further our research into the science of how simulation software is developed, maintained, and distributed.
Our Software Research Mission

A quintessential target area for innovation today is to bridge the gap between mathematical semantics, physical notions, and computer programming languages. Owing to the physical complexity inherent to reservoir engineering problems, simulator developers have long recognized the pains and needs in this area. The goal of this research direction is to rethink and reengineer the way that we develop, deliver, and maintain simulation software in order to realize a future where:
  1. Customization and ubiquitous interoperability are instantaneous and cost-free.
  2. Domain-expert users are able to make rapid modifications to the Physics directly.
We aim to accomplish our mission as the culmination of three major directions:

Discrete Problem
Programming Toolkit
DPPT
 Generic Solvers
GenSOL
 Automated Simulator
Generator System
ASGS


Discrete Problem Programming Toolkit (DPPT)

A Discrete Problem is a software abstraction that implements the fully discretized equations that are solved by a simulator in order to obtain discrete approximations to the state variables in space and time.

Sketch of a DIscrete Problem
 Interchange Discrete Problem objects easily

As illustrated in the figures above, a Discrete Problem must offer a two-way interface that is well-engineered to admit a wide and growing plethora of numerical solution methods while simultaneously preventing the exposure of its internal particulars. A standardized interface will ensure effortless interchangeability of Discrete Problem implementations, thereby supporting both the Tailor- and General-Purpose paradigms.

At a minimum, a conforming Discrete Problem interface should be able to produce a discrete residual system and Jacobian matrix that are evaluated at given input states. Generic designs allow the parameterization of the Physics to any conforming numerical datastructures. The interface must also accommodate requests to adapt the internal specifics of the discrete numerical approximation.

Our research in this area focuses on developing a universal interface, and more importantly, on providing a software toolkit that cuts the development cost of any Discrete Problem to a minimum. This is to be accomplished by the automation of the activities entailed in developing a Discrete Problem.

The Discrete Problem Programming Toolkit (DPPT) is a multilayered library of highly configurable generic datastructures and algorithms. Modules within different layers can be used to develop a generic Discrete Problem using different semantics and levels of abstraction. Below is a depiction of the DPPT modules that are arranged in three layers.

Schematic of the Discrete Problem Programming Toolkit

1. Base Layer
The DPPT base layer offers several modules that implement efficient numerical datastructures and algorithms. The semantics are closely tied to standard library concepts when efficiency is not sacrificed. For example, while standard library memory allocators cannot maintain state, our alternatives bypass these concept requirements in order to admit multithreaded pools. A beta point of departure for these modules is available in the faSTL library.
  • Numerical datastructures
    • Dense collections including numeric arrays and vectors.
    • Indirection devices (iterators) that separate the storage pattern of variables in memory from their logical ordering.
    • Sparse collections including block sparse matrices and vectors.
    • Algebraic expression encodings using multiple implementations including expression templates.
  • Memory managements
    • Heap allocators offering configurable pools and multithreading.
    • Casting and construction utilities.
  • Thread Management
    • Interchangeable Policies for threading using multiple protocols including OpenMP, POSIX, and standard library protocols.
  • Numerical algorithms
    • Polyalgorithmic sparse and dense linear combination kernels including recent algorithmic developments and expression templates.
    • Forced vectorization using inline SIMD instructions including SSE and intrinsics (platform dependent).
    • Miscellaneous: bit hacks, unrolling, and tiling .
2. Middle Layer
The middle layer offers modules that generically implement all aspects of discretizing and linearizing vector calculus operators. The semantics are mathematical. Configuration choices for all orthogonal aspects can be made by changing single tags within user code. For example, the following listing calculates the discrete nonlinear Laplacian and its analytical Jacobian matrix using single point upwinding and the MPFA O-method on a Cartesian topology that is ordered according to a Hilbert space-filling curve:

Variableset< memoryLayout, ADvector > U;
DiscreteContinuum mesh( UniformCartesianBuilder< PeanoHilbert > build( "datafile.txt" ) );
Laplacian< Omethod > ( mesh, U[TRANS].begin(), U[POTENTIAL].begin(), F.begin() );

  • Discrete Operators: Implementations of finite element and finite volume approximations to nonlinear differential operators. These are independent of the mesh topology and variable layout in memory, and they are parameterized by the desired numerical scheme.
  • Discrete Continuum: A generic representation of discrete spatial domains that may intersect. Alternate implementations are available in certain topologies for low-memory requirements in cases of massive meshes. These instances are built using input mesh data that are generated externally.
  • Automatic Variables: Building on the initial success of the Automatically Differentiable Expression Templates Library (ADETL), we are continuing to develop a module that efficiently automates the analytical computation of derivatives of all expressions that occur in the callstack of a discrete Reservoir Simulation problem. The ADETL was designed to be extendable but it provides a limited scope of datastructures and algorithms to act as a proof of concept. Our work is to integrate and extend emerging AD algorithms and implementations to accommodate the wide range of expressions that are encountered in reservoir simulation.
    • Detailed profiling analysis and benchmarks for various stages in the computation of linearized equations.
    • Improved automatic activation of variables for variable switching and reordering.
    • Tailor approaches to univariate, multivariate dense, and multivariate sparse derivatives.
    • Facilities to convert types and to operate on arguments with heterogeneous expressions.
    • Polyalgorithmic forward and reverse mode AD with recommendations for appropriate use in different calculations.
    • Improved performance by anhialating expression construction costs.
    • Compressed AD using seed matrices to dramatically improve runtime costs in cases with predictable sparsity coutcomes.

3. Top Layer
The top layer module will offer abstractions for general partial differential equations such as the nonlinear transient advection-reaction-diffusion equations, Helmholtz and Poisson forms, and the time-dependent second-order wave equation.


GenSOL

We are designing and developing datastructure-neutral implementations of timestepping, nonlinear, and linear solution algorithms. The prime purpose for GenSOL is to provide a convenient platform with which to reproduce, analyze, compare, and even use all of our contributions in the solvers area.


Automated Simulator Generator System

Efforts such as our proposed DPPT promise to cut down on the costs of computer programming for the development of the physics portion of a simulator. Such efforts are exclusively tied to the underlying programming language. Moreover, they are typically only used by expert developers, barring the domain expert from direct participation. Problem Solving Environments such as "multiphysics packages" (e.g. COMSOL and the MRST) provide the means to develop physical models and simulation tools without the need for advanced programming language semantics. The efficiency and scalability of these tools however, remain far from ideal relative to compiled software. The purpose of the ASGS direction is simply to bridge this gap. We propose to develop a system that can translate domain-specific and high-level mathematical markup into C++ using the DPPT constructs. The schematic below illustrates this process.

Schematic of the Automated Simulator Generator System

The ASGS will ultimately enable cost-free customization of the physics within simulators. Domain experts can use a graphical equation editor to write, share, and disseminate "new models", while vendors will be able to provide software that implements these models without incurring additional costs. The responsibility of devising well-posed physical models will be in the hands of the domain expert.

Schematic of a new simulator delivery market that is enabled by ASGS technology


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