Geothermal energyGeothermal energy is thermal energy in the Earth's crust. It combines energy from the formation of the planet and from radioactive decay. Geothermal energy has been exploited as a source of heat and/or electric power for millennia. Geothermal heating, using water from hot springs, for example, has been used for bathing since Paleolithic times and for space heating since Roman times. Geothermal power, (generation of electricity from geothermal energy), has been used since the 20th century.
Geothermal heatingGeothermal heating is the direct use of geothermal energy for some heating applications. Humans have taken advantage of geothermal heat this way since the Paleolithic era. Approximately seventy countries made direct use of a total of 270 PJ of geothermal heating in 2004. As of 2007, 28 GW of geothermal heating capacity is installed around the world, satisfying 0.07% of global primary energy consumption. Thermal efficiency is high since no energy conversion is needed, but capacity factors tend to be low (around 20%) since the heat is mostly needed in the winter.
Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
Numerical integrationIn analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.
Thermal energy storageThermal energy storage (TES) is achieved with widely different technologies. Depending on the specific technology, it allows excess thermal energy to be stored and used hours, days, months later, at scales ranging from the individual process, building, multiuser-building, district, town, or region. Usage examples are the balancing of energy demand between daytime and nighttime, storing summer heat for winter heating, or winter cold for summer air conditioning (Seasonal thermal energy storage).
Numerical methods for partial differential equationsNumerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.
Numerical stabilityIn the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.
Probabilistic numericsProbabilistic numerics is an active field of study at the intersection of applied mathematics, statistics, and machine learning centering on the concept of uncertainty in computation. In probabilistic numerics, tasks in numerical analysis such as finding numerical solutions for integration, linear algebra, optimization and simulation and differential equations are seen as problems of statistical, probabilistic, or Bayesian inference.
Solar thermal energySolar thermal energy (STE) is a form of energy and a technology for harnessing solar energy to generate thermal energy for use in industry, and in the residential and commercial sectors. Solar thermal collectors are classified by the United States Energy Information Administration as low-, medium-, or high-temperature collectors. Low-temperature collectors are generally unglazed and used to heat swimming pools or to heat ventilation air. Medium-temperature collectors are also usually flat plates but are used for heating water or air for residential and commercial use.
Numerical linear algebraNumerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which efficiently and accurately provide approximate answers to questions in continuous mathematics. It is a subfield of numerical analysis, and a type of linear algebra. Computers use floating-point arithmetic and cannot exactly represent irrational data, so when a computer algorithm is applied to a matrix of data, it can sometimes increase the difference between a number stored in the computer and the true number that it is an approximation of.
Ocean thermal energy conversionOcean Thermal Energy Conversion (OTEC) uses the ocean thermal gradient between cooler deep and warmer shallow or surface seawaters to run a heat engine and produce useful work, usually in the form of electricity. OTEC can operate with a very high capacity factor and so can operate in base load mode. The denser cold water masses, formed by ocean surface water interaction with cold atmosphere in quite specific areas of the North Atlantic and the Southern Ocean, sink into the deep sea basins and spread in entire deep ocean by the thermohaline circulation.
Grid energy storageGrid energy storage (also called large-scale energy storage) is a collection of methods used for energy storage on a large scale within an electrical power grid. Electrical energy is stored during times when electricity is plentiful and inexpensive (especially from intermittent power sources such as renewable electricity from wind power, tidal power and solar power) or when demand is low, and later returned to the grid when demand is high, and electricity prices tend to be higher.
Energy developmentEnergy development is the field of activities focused on obtaining sources of energy from natural resources. These activities include the production of renewable, nuclear, and fossil fuel derived sources of energy, and for the recovery and reuse of energy that would otherwise be wasted. Energy conservation and efficiency measures reduce the demand for energy development, and can have benefits to society with improvements to environmental issues.
Energy storageEnergy storage is the capture of energy produced at one time for use at a later time to reduce imbalances between energy demand and energy production. A device that stores energy is generally called an accumulator or battery. Energy comes in multiple forms including radiation, chemical, gravitational potential, electrical potential, electricity, elevated temperature, latent heat and kinetic. Energy storage involves converting energy from forms that are difficult to store to more conveniently or economically storable forms.
Numerical weather predictionNumerical weather prediction (NWP) uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in the 1950s that numerical weather predictions produced realistic results. A number of global and regional forecast models are run in different countries worldwide, using current weather observations relayed from radiosondes, weather satellites and other observing systems as inputs.
Compressed-air energy storageCompressed-air energy storage (CAES) is a way to store energy for later use using compressed air. At a utility scale, energy generated during periods of low demand can be released during peak load periods. The first utility-scale CAES project has been built in Huntorf, Germany, and is still operational. The Huntorf plant was initially developed as a load balancer for fossil fuel-generated electricity, the global shift towards renewable energy renewed interest in CAES systems, to help highly intermittent energy sources like photovoltaics and wind satisfy fluctuating electricity demands.
World energy supply and consumptionWorld energy supply and consumption refers to the global production and consumption of primary energy. Energy can be consumed in various different forms, as processed fuels or electricity, or for various different purposes, like for transportation or electricity generation. Energy production and consumption are an important part of the economy. This topic includes heat, but not energy from food. This article provides a brief overview of energy supply and consumption, using statistics summarized in tables, of the countries and regions that produce and consume the most energy.
Numerical methods for linear least squaresNumerical methods for linear least squares entails the numerical analysis of linear least squares problems. A general approach to the least squares problem can be described as follows. Suppose that we can find an n by m matrix S such that XS is an orthogonal projection onto the image of X. Then a solution to our minimization problem is given by simply because is exactly a sought for orthogonal projection of onto an image of X (see the picture below and note that as explained in the next section the image of X is just a subspace generated by column vectors of X).
Geothermal powerGeothermal power is electrical power generated from geothermal energy. Technologies in use include dry steam power stations, flash steam power stations and binary cycle power stations. Geothermal electricity generation is currently used in 26 countries, while geothermal heating is in use in 70 countries. As of 2019, worldwide geothermal power capacity amounts to 15.4 gigawatts (GW), of which 23.9 percent or 3.68 GW are installed in the United States.
Energy securityEnergy security is the association between national security and the availability of natural resources for energy consumption (as opposed to household energy insecurity). Access to cheaper energy has become essential to the functioning of modern economies. However, the uneven distribution of energy supplies among countries has led to significant vulnerabilities. International energy relations have contributed to the globalization of the world leading to energy security and energy vulnerability at the same time.
